id
string | family
string | difficulty_level
int64 | messages
list | ground_truth
string | dataset
string |
|---|---|---|---|---|---|
algebra_func_area_level_1_0000
|
algebra_func_area
| 1 |
[
{
"role": "user",
"content": "Find the area of the region bounded by the curves f(x) = -3|(-2sin(1πx - 2) + 2) - 2| + 2, g(x) = 4x^2 + 1x - 5, x = -1.4, and x = -1.3. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
0.1
|
MATH_PROB_FAMILIES
|
algebra_func_area_level_1_0001
|
algebra_func_area
| 1 |
[
{
"role": "user",
"content": "Find the area of the region bounded by the curves f(x) = 2sin(3π(3x - 2) + 2) + 1, g(x) = -2x^2 + 2x + 4, x = -0.6, and x = -0.5. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
0.2
|
MATH_PROB_FAMILIES
|
algebra_func_area_level_1_0002
|
algebra_func_area
| 1 |
[
{
"role": "user",
"content": "Determine the area of the region enclosed by the graphs of f(x) = (3(-1e^(-1x) - 2) - 1)/(-3(-1e^(-1x) - 2) - 3) and g(x) = -3|x + 1| + 3 between the vertical lines x = -2.4 and x = 0.6. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
6.5
|
MATH_PROB_FAMILIES
|
algebra_func_area_level_1_0003
|
algebra_func_area
| 1 |
[
{
"role": "user",
"content": "Calculate the area enclosed between the functions f(x) = -2(-4x^2 - 5x + 5) - 1 and g(x) = -2x - 4 from x = -2.0 to x = 0.4. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
18.4
|
MATH_PROB_FAMILIES
|
algebra_func_area_level_1_0004
|
algebra_func_area
| 1 |
[
{
"role": "user",
"content": "Find the area of the region bounded by the curves f(x) = -1(-1cos(1πx - 2) + 1) + 5, g(x) = 2|x + 2| - 1, x = -4.1, and x = 0.9. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
12.7
|
MATH_PROB_FAMILIES
|
algebra_func_area_level_1_0005
|
algebra_func_area
| 1 |
[
{
"role": "user",
"content": "Determine the area of the region enclosed by the graphs of f(x) = -2(4x^2 + 1x) - 3 and g(x) = -4x^2 - 5x - 4 between the vertical lines x = -0.2 and x = 1.0. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
1.3
|
MATH_PROB_FAMILIES
|
algebra_func_area_level_1_0006
|
algebra_func_area
| 1 |
[
{
"role": "user",
"content": "Determine the area of the region enclosed by the graphs of f(x) = (3(3sin(1πx + 3) + 1) - 2)/(-2(3sin(1πx + 3) + 1) + 3) and g(x) = 1|x + 2| - 1 between the vertical lines x = 3.1 and x = 4.0. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
10.6
|
MATH_PROB_FAMILIES
|
algebra_func_area_level_1_0007
|
algebra_func_area
| 1 |
[
{
"role": "user",
"content": "Find the area of the region bounded by the curves f(x) = 4(-2cos(3πx - 2) + 2) + 4, g(x) = -2x + 2, x = -3.0, and x = -2.6. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
3.4
|
MATH_PROB_FAMILIES
|
algebra_func_area_level_1_0008
|
algebra_func_area
| 1 |
[
{
"role": "user",
"content": "Determine the area of the region enclosed by the graphs of f(x) = -2sin(2π(-2|x - 1|) - 2) - 1 and g(x) = (-2x + 3)/(-3x) between the vertical lines x = 4.4 and x = 4.5. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
0.0
|
MATH_PROB_FAMILIES
|
algebra_func_area_level_1_0009
|
algebra_func_area
| 1 |
[
{
"role": "user",
"content": "Find the area of the region bounded by the curves f(x) = -2sin(1π(-3|x - 3| + 3)), g(x) = (-2x + 3)/(-2x - 2), x = 2.4, and x = 2.6. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
0.3
|
MATH_PROB_FAMILIES
|
algebra_func_area_level_1_0010
|
algebra_func_area
| 1 |
[
{
"role": "user",
"content": "Calculate the area enclosed between the functions f(x) = 3sin(1π(1|x + 3| + 2)) - 3 and g(x) = 4x^2 + 4x - 5 from x = -1.2 to x = 0.2. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
4.9
|
MATH_PROB_FAMILIES
|
algebra_func_area_level_1_0011
|
algebra_func_area
| 1 |
[
{
"role": "user",
"content": "Calculate the area enclosed between the functions f(x) = -2|((-2x + 2)/(2x - 1)) + 1| and g(x) = 2|x - 2| - 1 from x = 1.9 to x = 2.2. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
0.1
|
MATH_PROB_FAMILIES
|
algebra_func_area_level_1_0012
|
algebra_func_area
| 1 |
[
{
"role": "user",
"content": "Determine the area of the region enclosed by the graphs of f(x) = (-1(-4x^2 + 3x - 3) - 1)/(1(-4x^2 + 3x - 3) - 2) and g(x) = -2|x - 2| + 2 between the vertical lines x = 0.8 and x = 3.5. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
3.8
|
MATH_PROB_FAMILIES
|
algebra_func_area_level_1_0013
|
algebra_func_area
| 1 |
[
{
"role": "user",
"content": "Find the area of the region bounded by the curves f(x) = 3cos(3π(-3x^2 + 1) + 3) + 2, g(x) = -1x - 3, x = -2.2, and x = -2.1. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
0.3
|
MATH_PROB_FAMILIES
|
algebra_func_area_level_1_0014
|
algebra_func_area
| 1 |
[
{
"role": "user",
"content": "Determine the area of the region enclosed by the graphs of f(x) = 3sin(1π((2x - 2)/(1x)) + 3) - 1 and g(x) = 5x + 3 between the vertical lines x = -0.4 and x = -0.30000000000000004. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
0.2
|
MATH_PROB_FAMILIES
|
algebra_func_area_level_1_0015
|
algebra_func_area
| 1 |
[
{
"role": "user",
"content": "Calculate the area enclosed between the functions f(x) = -3cos(3π(-1x^2 - 5x + 1) + 3) + 1 and g(x) = 1x - 4 from x = 4.5 to x = 4.6. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
0.2
|
MATH_PROB_FAMILIES
|
algebra_func_area_level_1_0016
|
algebra_func_area
| 1 |
[
{
"role": "user",
"content": "Find the area of the region bounded by the curves f(x) = 5(-1x^2 + 3x - 1)^2 + 1(-1x^2 + 3x - 1), g(x) = -1x + 3, x = 0.0, and x = 0.7. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
1.2
|
MATH_PROB_FAMILIES
|
algebra_func_area_level_1_0017
|
algebra_func_area
| 1 |
[
{
"role": "user",
"content": "Calculate the area enclosed between the functions f(x) = (1(5x^2 - 3x + 4) - 1)/(-2(5x^2 - 3x + 4) - 1) and g(x) = -2x^2 + 1x + 4 from x = -1.3 to x = 1.8. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
9.0
|
MATH_PROB_FAMILIES
|
algebra_func_area_level_1_0018
|
algebra_func_area
| 1 |
[
{
"role": "user",
"content": "Find the area of the region bounded by the curves f(x) = (3((2x - 2)/(1x)) + 3)/(2((2x - 2)/(1x)) - 1), g(x) = (-1x + 1)/(2x + 2), x = -0.6, and x = 0.6. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
0.9
|
MATH_PROB_FAMILIES
|
algebra_func_area_level_1_0019
|
algebra_func_area
| 1 |
[
{
"role": "user",
"content": "Determine the area of the region enclosed by the graphs of f(x) = -3|((-1x - 2)/(2x + 2)) - 3| + 3 and g(x) = 1x - 2 between the vertical lines x = -1.4 and x = -1.1. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
0.6
|
MATH_PROB_FAMILIES
|
algebra_func_area_level_1_0020
|
algebra_func_area
| 1 |
[
{
"role": "user",
"content": "Find the area of the region bounded by the curves f(x) = (1(1|x - 3| + 2))/(3(1|x - 3| + 2) + 1), g(x) = -3x^2 + 2x + 2, x = -0.5, and x = 1.2. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
2.2
|
MATH_PROB_FAMILIES
|
algebra_func_area_level_1_0021
|
algebra_func_area
| 1 |
[
{
"role": "user",
"content": "Calculate the area enclosed between the functions f(x) = 1((1x + 2)/(2x + 3)) - 3 and g(x) = -3x^2 + 4x + 3 from x = -1.5 to x = -0.8. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
8.3
|
MATH_PROB_FAMILIES
|
algebra_func_area_level_1_0022
|
algebra_func_area
| 1 |
[
{
"role": "user",
"content": "Calculate the area enclosed between the functions f(x) = -1(-2sin(2πx - 2) - 3)^2 + 1(-2sin(2πx - 2) - 3) and g(x) = 2x from x = -3.7 to x = -3.1. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
8.3
|
MATH_PROB_FAMILIES
|
algebra_func_area_level_1_0023
|
algebra_func_area
| 1 |
[
{
"role": "user",
"content": "Find the area of the region bounded by the curves f(x) = -5(-1x^2 - 4x + 2)^2 + 3(-1x^2 - 4x + 2) - 5, g(x) = -2|x - 2| - 3, x = 0.2, and x = 0.5. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
0.3
|
MATH_PROB_FAMILIES
|
algebra_func_area_level_1_0024
|
algebra_func_area
| 1 |
[
{
"role": "user",
"content": "Calculate the area enclosed between the functions f(x) = -2sin(1π(-5x + 4) - 2) and g(x) = 1|x + 2| from x = -2.1 to x = -1.9. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
0.2
|
MATH_PROB_FAMILIES
|
algebra_func_area_level_1_0025
|
algebra_func_area
| 1 |
[
{
"role": "user",
"content": "Determine the area of the region enclosed by the graphs of f(x) = -1(-1cos(1πx) + 3) + 2 and g(x) = 1x between the vertical lines x = -0.2 and x = 0.0. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
0.0
|
MATH_PROB_FAMILIES
|
algebra_func_area_level_1_0026
|
algebra_func_area
| 1 |
[
{
"role": "user",
"content": "Calculate the area enclosed between the functions f(x) = -2(3x^2 - 2x - 4)^2 + 1(3x^2 - 2x - 4) + 2 and g(x) = (2x)/(2x + 2) from x = 1.4 to x = 1.7. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
0.3
|
MATH_PROB_FAMILIES
|
algebra_func_area_level_1_0027
|
algebra_func_area
| 1 |
[
{
"role": "user",
"content": "Calculate the area enclosed between the functions f(x) = -1(-2sin(2πx + 2) - 2) + 5 and g(x) = 2x^2 + 3x + 3 from x = -2.3 to x = 1.1. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
11.3
|
MATH_PROB_FAMILIES
|
algebra_func_area_level_1_0028
|
algebra_func_area
| 1 |
[
{
"role": "user",
"content": "Find the area of the region bounded by the curves f(x) = -2cos(2π(-1x^2 - 5x + 3) - 3) - 3, g(x) = -3x^2 + 5x + 2, x = -0.8, and x = -0.6. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
0.2
|
MATH_PROB_FAMILIES
|
algebra_func_area_level_1_0029
|
algebra_func_area
| 1 |
[
{
"role": "user",
"content": "Calculate the area enclosed between the functions f(x) = -5(2|x + 1| - 2) - 1 and g(x) = -4x - 4 from x = -1.6 to x = 0.5. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
9.6
|
MATH_PROB_FAMILIES
|
algebra_func_area_level_1_0030
|
algebra_func_area
| 1 |
[
{
"role": "user",
"content": "Determine the area of the region enclosed by the graphs of f(x) = 3e^(2(-3x - 3)) - 1 and g(x) = (-2x - 3)/(1x + 3) between the vertical lines x = -0.6 and x = -0.0. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
0.0
|
MATH_PROB_FAMILIES
|
algebra_func_area_level_1_0031
|
algebra_func_area
| 1 |
[
{
"role": "user",
"content": "Calculate the area enclosed between the functions f(x) = 2cos(1π(3x - 2) - 1) + 3 and g(x) = -4x - 5 from x = -2.0 to x = -1.6. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
0.6
|
MATH_PROB_FAMILIES
|
algebra_func_area_level_1_0032
|
algebra_func_area
| 1 |
[
{
"role": "user",
"content": "Calculate the area enclosed between the functions f(x) = 1(-4x^2 + 2x - 1) - 1 and g(x) = 2x - 4 from x = -0.7 to x = 0.7. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
1.9
|
MATH_PROB_FAMILIES
|
algebra_func_area_level_1_0033
|
algebra_func_area
| 1 |
[
{
"role": "user",
"content": "Calculate the area enclosed between the functions f(x) = -3(1sin(3πx) - 1)^2 + 4(1sin(3πx) - 1) + 1 and g(x) = -4x^2 + 2x from x = 0.2 to x = 0.7. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
5.0
|
MATH_PROB_FAMILIES
|
algebra_func_area_level_1_0034
|
algebra_func_area
| 1 |
[
{
"role": "user",
"content": "Calculate the area enclosed between the functions f(x) = 2|(-3x^2 + 1)| - 1 and g(x) = 3x^2 - 5x + 2 from x = -2.4 to x = 0.7. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
11.4
|
MATH_PROB_FAMILIES
|
algebra_func_area_level_1_0035
|
algebra_func_area
| 1 |
[
{
"role": "user",
"content": "Calculate the area enclosed between the functions f(x) = 2(1cos(3πx - 1)) + 2 and g(x) = 2x + 3 from x = -0.8 to x = -0.4. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
0.5
|
MATH_PROB_FAMILIES
|
algebra_func_area_level_1_0036
|
algebra_func_area
| 1 |
[
{
"role": "user",
"content": "Calculate the area enclosed between the functions f(x) = -1e^(-1(-2x^2 + 5x + 5)) + 2 and g(x) = -2|x - 3| + 2 from x = -1.0 to x = 3.0. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
15.1
|
MATH_PROB_FAMILIES
|
algebra_func_area_level_1_0037
|
algebra_func_area
| 1 |
[
{
"role": "user",
"content": "Find the area of the region bounded by the curves f(x) = 1|(-1sin(3πx - 1) + 2)| + 3, g(x) = -2x + 1, x = -1.9, and x = -1.6. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
0.1
|
MATH_PROB_FAMILIES
|
algebra_func_area_level_1_0038
|
algebra_func_area
| 1 |
[
{
"role": "user",
"content": "Find the area of the region bounded by the curves f(x) = 1cos(3π(-1x^2 + 3x - 4) + 2) + 2, g(x) = (1x)/(3x + 2), x = -0.9, and x = -0.8. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
0.1
|
MATH_PROB_FAMILIES
|
algebra_func_area_level_1_0039
|
algebra_func_area
| 1 |
[
{
"role": "user",
"content": "Find the area of the region bounded by the curves f(x) = -1cos(3π(4x + 3) - 2) + 2, g(x) = 5x^2 + 2x - 1, x = 0.5, and x = 0.6. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
0.1
|
MATH_PROB_FAMILIES
|
algebra_func_area_level_1_0040
|
algebra_func_area
| 1 |
[
{
"role": "user",
"content": "Determine the area of the region enclosed by the graphs of f(x) = -3sin(1π(-1x + 2) - 2) + 1 and g(x) = (2x - 1)/(2x + 2) between the vertical lines x = 2.4 and x = 3.3. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
1.5
|
MATH_PROB_FAMILIES
|
algebra_func_area_level_1_0041
|
algebra_func_area
| 1 |
[
{
"role": "user",
"content": "Find the area of the region bounded by the curves f(x) = 2cos(3π(2|x + 2| + 2) - 3) - 3, g(x) = -2x - 3, x = 0.6, and x = 0.7. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
0.0
|
MATH_PROB_FAMILIES
|
algebra_func_area_level_1_0042
|
algebra_func_area
| 1 |
[
{
"role": "user",
"content": "Calculate the area enclosed between the functions f(x) = 1((-2x - 1)/(-3x - 2)) + 3 and g(x) = 2|x + 3| from x = -1.0 to x = -0.8. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
0.0
|
MATH_PROB_FAMILIES
|
algebra_func_area_level_1_0043
|
algebra_func_area
| 1 |
[
{
"role": "user",
"content": "Calculate the area enclosed between the functions f(x) = 1cos(2π(4x^2 - 5x + 5)) + 2 and g(x) = -5x + 2 from x = 0.1 to x = 0.2. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
0.1
|
MATH_PROB_FAMILIES
|
algebra_func_area_level_1_0044
|
algebra_func_area
| 1 |
[
{
"role": "user",
"content": "Calculate the area enclosed between the functions f(x) = -2|(-3cos(1πx - 1) + 1) + 3| - 2 and g(x) = 4x + 5 from x = -4.3 to x = -3.3. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
3.8
|
MATH_PROB_FAMILIES
|
algebra_func_area_level_1_0045
|
algebra_func_area
| 1 |
[
{
"role": "user",
"content": "Find the area of the region bounded by the curves f(x) = 2|(3cos(2πx)) + 3| - 1, g(x) = 1x^2 - 3, x = 2.3, and x = 2.7. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
1.1
|
MATH_PROB_FAMILIES
|
algebra_func_area_level_1_0046
|
algebra_func_area
| 1 |
[
{
"role": "user",
"content": "Determine the area of the region enclosed by the graphs of f(x) = 2sin(3π(1x - 4) - 1) + 3 and g(x) = (1x - 3)/(1x + 1) between the vertical lines x = -3.2 and x = -2.9. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
0.4
|
MATH_PROB_FAMILIES
|
algebra_func_area_level_1_0047
|
algebra_func_area
| 1 |
[
{
"role": "user",
"content": "Find the area of the region bounded by the curves f(x) = (3(3cos(3πx + 3)) + 2)/(-3(3cos(3πx + 3)) - 1), g(x) = -1|x + 3| + 1, x = 0.8, and x = 1.2. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
1.1
|
MATH_PROB_FAMILIES
|
algebra_func_area_level_1_0048
|
algebra_func_area
| 1 |
[
{
"role": "user",
"content": "Find the area of the region bounded by the curves f(x) = -1((1x + 2)/(3x + 2))^2 - 5((1x + 2)/(3x + 2)) - 3, g(x) = -1x, x = -1.0, and x = -0.8. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
0.3
|
MATH_PROB_FAMILIES
|
algebra_func_area_level_1_0049
|
algebra_func_area
| 1 |
[
{
"role": "user",
"content": "Calculate the area enclosed between the functions f(x) = -5(-3sin(1πx + 2) + 2) - 4 and g(x) = (2x)/(-1x - 2) from x = 1.7 to x = 2.0. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
0.4
|
MATH_PROB_FAMILIES
|
algebra_func_area_level_1_0050
|
algebra_func_area
| 1 |
[
{
"role": "user",
"content": "Find the area of the region bounded by the curves f(x) = -3(-5x^2 + 2x + 1)^2 - 3(-5x^2 + 2x + 1) + 1, g(x) = (1x + 1)/(3x + 2), x = -0.3, and x = 0.6. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
4.1
|
MATH_PROB_FAMILIES
|
algebra_func_area_level_1_0051
|
algebra_func_area
| 1 |
[
{
"role": "user",
"content": "Calculate the area enclosed between the functions f(x) = -4(1x^2 - 5x + 2)^2 + 4 and g(x) = 1|x| + 2 from x = 0.3 to x = 0.6. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
0.3
|
MATH_PROB_FAMILIES
|
algebra_func_area_level_1_0052
|
algebra_func_area
| 1 |
[
{
"role": "user",
"content": "Determine the area of the region enclosed by the graphs of f(x) = -1(1x - 1) and g(x) = -4x^2 + 3x + 5 between the vertical lines x = -0.6 and x = 1.6. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
7.5
|
MATH_PROB_FAMILIES
|
algebra_func_area_level_1_0053
|
algebra_func_area
| 1 |
[
{
"role": "user",
"content": "Find the area of the region bounded by the curves f(x) = (-2(2cos(3πx + 3) - 2) - 3)/(-2(2cos(3πx + 3) - 2) - 1), g(x) = (-2x + 1)/(-2x + 3), x = 1.1, and x = 1.6. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
44.5
|
MATH_PROB_FAMILIES
|
algebra_func_area_level_1_0054
|
algebra_func_area
| 1 |
[
{
"role": "user",
"content": "Determine the area of the region enclosed by the graphs of f(x) = (1(-3sin(2πx + 2) - 3) + 2)/(-2(-3sin(2πx + 2) - 3) - 3) and g(x) = 2|x| between the vertical lines x = 3.3 and x = 3.6. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
2.8
|
MATH_PROB_FAMILIES
|
algebra_func_area_level_1_0055
|
algebra_func_area
| 1 |
[
{
"role": "user",
"content": "Determine the area of the region enclosed by the graphs of f(x) = 3((1x + 2)/(-3x - 1))^2 + 1((1x + 2)/(-3x - 1)) + 5 and g(x) = 3|x + 2| + 2 between the vertical lines x = -3.0 and x = 0.2. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
-2.1
|
MATH_PROB_FAMILIES
|
algebra_func_area_level_1_0056
|
algebra_func_area
| 1 |
[
{
"role": "user",
"content": "Calculate the area enclosed between the functions f(x) = (3(2x^2 + 4x - 1) + 2)/(3(2x^2 + 4x - 1)) and g(x) = 3x - 2 from x = 0.2 to x = 1.0. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
7.5
|
MATH_PROB_FAMILIES
|
algebra_func_area_level_1_0057
|
algebra_func_area
| 1 |
[
{
"role": "user",
"content": "Calculate the area enclosed between the functions f(x) = (-1(1cos(2πx + 1) + 1) + 3)/(-2(1cos(2πx + 1) + 1) + 3) and g(x) = -1x - 5 from x = 4.0 to x = 4.7. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
12.7
|
MATH_PROB_FAMILIES
|
algebra_func_area_level_1_0058
|
algebra_func_area
| 1 |
[
{
"role": "user",
"content": "Calculate the area enclosed between the functions f(x) = -2e^(1(-1|x + 3| + 3)) + 1 and g(x) = 3|x| - 3 from x = -0.4 to x = 1.1. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
1.6
|
MATH_PROB_FAMILIES
|
algebra_func_area_level_1_0059
|
algebra_func_area
| 1 |
[
{
"role": "user",
"content": "Find the area of the region bounded by the curves f(x) = (1(1x^2 - 5x + 1) - 1)/(-2(1x^2 - 5x + 1)), g(x) = -1|x + 2| - 3, x = 0.2, and x = 4.8. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
32.3
|
MATH_PROB_FAMILIES
|
algebra_func_area_level_1_0060
|
algebra_func_area
| 1 |
[
{
"role": "user",
"content": "Find the area of the region bounded by the curves f(x) = 1cos(2π(-3x^2 + 3x + 4) - 3) + 3, g(x) = -2x - 1, x = -2.4, and x = -2.3. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
0.1
|
MATH_PROB_FAMILIES
|
algebra_func_area_level_1_0061
|
algebra_func_area
| 1 |
[
{
"role": "user",
"content": "Determine the area of the region enclosed by the graphs of f(x) = (1(-3cos(1πx + 3)) + 1)/(-3(-3cos(1πx + 3)) + 2) and g(x) = -3x^2 - 1x + 1 between the vertical lines x = -3.5 and x = -2.4. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
24.8
|
MATH_PROB_FAMILIES
|
algebra_func_area_level_1_0062
|
algebra_func_area
| 1 |
[
{
"role": "user",
"content": "Determine the area of the region enclosed by the graphs of f(x) = (-1(-3cos(3πx) - 1) + 2)/(-3(-3cos(3πx) - 1) - 1) and g(x) = -1x^2 + 5x + 5 between the vertical lines x = -2.5 and x = -2.2. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
4.1
|
MATH_PROB_FAMILIES
|
algebra_func_area_level_1_0063
|
algebra_func_area
| 1 |
[
{
"role": "user",
"content": "Calculate the area enclosed between the functions f(x) = (3(-1x - 5) + 2)/(-2(-1x - 5) - 1) and g(x) = 3|x - 3| - 3 from x = 2.5 to x = 3.5. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
0.8
|
MATH_PROB_FAMILIES
|
algebra_func_area_level_1_0064
|
algebra_func_area
| 1 |
[
{
"role": "user",
"content": "Calculate the area enclosed between the functions f(x) = (2(2cos(2πx - 1) - 2) - 1)/(3(2cos(2πx - 1) - 2) + 1) and g(x) = -4x + 1 from x = -3.9 to x = -3.7. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
3.8
|
MATH_PROB_FAMILIES
|
algebra_func_area_level_1_0065
|
algebra_func_area
| 1 |
[
{
"role": "user",
"content": "Calculate the area enclosed between the functions f(x) = 1|((-3x + 2)/(3x - 1))| - 1 and g(x) = -3|x - 2| + 2 from x = 1.2 to x = 2.7. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
1.6
|
MATH_PROB_FAMILIES
|
algebra_func_area_level_1_0066
|
algebra_func_area
| 1 |
[
{
"role": "user",
"content": "Find the area of the region bounded by the curves f(x) = -2sin(1π((3x + 1)/(2x + 3)) - 3) - 2, g(x) = (-1x)/(1x - 3), x = -1.3, and x = -1.2. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
0.2
|
MATH_PROB_FAMILIES
|
algebra_func_area_level_1_0067
|
algebra_func_area
| 1 |
[
{
"role": "user",
"content": "Find the area of the region bounded by the curves f(x) = (-1(-4x^2 + 3x + 3) - 1)/(3(-4x^2 + 3x + 3) - 2), g(x) = 3|x + 1| + 1, x = -0.5, and x = 1.2. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
13.5
|
MATH_PROB_FAMILIES
|
algebra_func_area_level_1_0068
|
algebra_func_area
| 1 |
[
{
"role": "user",
"content": "Calculate the area enclosed between the functions f(x) = 1sin(3π(2x^2 - 5x) - 1) and g(x) = 4x^2 - 4x - 4 from x = -0.6 to x = -0.5. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
0.1
|
MATH_PROB_FAMILIES
|
algebra_func_area_level_1_0069
|
algebra_func_area
| 1 |
[
{
"role": "user",
"content": "Find the area of the region bounded by the curves f(x) = (-1(1|x - 2| - 1) + 3)/(3(1|x - 2| - 1) + 2), g(x) = -1|x| - 3, x = 1.9, and x = 2.1. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
0.1
|
MATH_PROB_FAMILIES
|
algebra_func_area_level_1_0070
|
algebra_func_area
| 1 |
[
{
"role": "user",
"content": "Calculate the area enclosed between the functions f(x) = -2(2x + 2) and g(x) = (-1x + 3)/(2x - 1) from x = -0.6 to x = 0.2. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
0.5
|
MATH_PROB_FAMILIES
|
algebra_func_area_level_1_0071
|
algebra_func_area
| 1 |
[
{
"role": "user",
"content": "Determine the area of the region enclosed by the graphs of f(x) = -1cos(1π(-1x^2 + 1)) - 3 and g(x) = 1x - 4 between the vertical lines x = 2.0 and x = 2.1. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
0.0
|
MATH_PROB_FAMILIES
|
algebra_func_area_level_1_0072
|
algebra_func_area
| 1 |
[
{
"role": "user",
"content": "Determine the area of the region enclosed by the graphs of f(x) = 1|(1cos(2πx + 1) + 3) - 1| and g(x) = 2x^2 - 5x between the vertical lines x = -0.4 and x = 3.0. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
11.2
|
MATH_PROB_FAMILIES
|
algebra_func_area_level_1_0073
|
algebra_func_area
| 1 |
[
{
"role": "user",
"content": "Find the area of the region bounded by the curves f(x) = (2(3cos(3πx + 3) + 2) - 3)/(1(3cos(3πx + 3) + 2)), g(x) = (2x + 3)/(3x + 1), x = 2.2, and x = 2.5. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
0.1
|
MATH_PROB_FAMILIES
|
algebra_func_area_level_1_0074
|
algebra_func_area
| 1 |
[
{
"role": "user",
"content": "Determine the area of the region enclosed by the graphs of f(x) = -2(-1sin(2πx - 2)) + 1 and g(x) = -5x^2 - 3x + 3 between the vertical lines x = -1.1 and x = 0.4. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
2.9
|
MATH_PROB_FAMILIES
|
algebra_func_area_level_1_0075
|
algebra_func_area
| 1 |
[
{
"role": "user",
"content": "Determine the area of the region enclosed by the graphs of f(x) = -3(3x^2 + 1x) + 2 and g(x) = 3x between the vertical lines x = -0.9 and x = 0.2. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
2.3
|
MATH_PROB_FAMILIES
|
algebra_func_area_level_1_0076
|
algebra_func_area
| 1 |
[
{
"role": "user",
"content": "Calculate the area enclosed between the functions f(x) = -1(-2x^2 - 1x + 3) - 2 and g(x) = -1x^2 - 2x + 2 from x = -2.1 to x = 1.1. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
16.6
|
MATH_PROB_FAMILIES
|
algebra_func_area_level_1_0077
|
algebra_func_area
| 1 |
[
{
"role": "user",
"content": "Calculate the area enclosed between the functions f(x) = 1cos(3π(-1x^2 - 4x)) - 2 and g(x) = (3x + 1)/(-1x + 2) from x = -3.2 to x = -3.1. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
0.0
|
MATH_PROB_FAMILIES
|
algebra_func_area_level_1_0078
|
algebra_func_area
| 1 |
[
{
"role": "user",
"content": "Find the area of the region bounded by the curves f(x) = (-3(-1cos(3πx - 3) + 3) + 2)/(1(-1cos(3πx - 3) + 3) - 2), g(x) = -3x + 1, x = 2.5, and x = 2.8. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
0.5
|
MATH_PROB_FAMILIES
|
algebra_func_area_level_1_0079
|
algebra_func_area
| 1 |
[
{
"role": "user",
"content": "Find the area of the region bounded by the curves f(x) = (-1(-2|x - 2| + 3) - 3)/(-3(-2|x - 2| + 3) - 1), g(x) = 1x + 2, x = 0.5, and x = 3.6. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
9.1
|
MATH_PROB_FAMILIES
|
algebra_func_area_level_1_0080
|
algebra_func_area
| 1 |
[
{
"role": "user",
"content": "Calculate the area enclosed between the functions f(x) = -1((-2x - 2)/(-2x)) - 5 and g(x) = 1x - 2 from x = -3.7 to x = -0.3. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
4.3
|
MATH_PROB_FAMILIES
|
algebra_func_area_level_1_0081
|
algebra_func_area
| 1 |
[
{
"role": "user",
"content": "Find the area of the region bounded by the curves f(x) = (2(-2cos(2πx + 2) + 1) + 3)/(-1(-2cos(2πx + 2) + 1) + 2), g(x) = 5x^2 - 1x, x = -1.6, and x = -1.0. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
5.1
|
MATH_PROB_FAMILIES
|
algebra_func_area_level_1_0082
|
algebra_func_area
| 1 |
[
{
"role": "user",
"content": "Determine the area of the region enclosed by the graphs of f(x) = -1cos(2π(2x + 4) + 2) + 1 and g(x) = 3x^2 + 5x - 2 between the vertical lines x = -2.1 and x = 0.3. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
8.8
|
MATH_PROB_FAMILIES
|
algebra_func_area_level_1_0083
|
algebra_func_area
| 1 |
[
{
"role": "user",
"content": "Calculate the area enclosed between the functions f(x) = 4(-3cos(3πx - 2) + 2) + 2 and g(x) = 3x + 2 from x = -1.1 to x = -0.5. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
7.1
|
MATH_PROB_FAMILIES
|
algebra_func_area_level_1_0084
|
algebra_func_area
| 1 |
[
{
"role": "user",
"content": "Determine the area of the region enclosed by the graphs of f(x) = (2(-2e^(2x)) + 3)/(-1(-2e^(2x)) + 2) and g(x) = (1x + 3)/(-3x + 2) between the vertical lines x = -0.6 and x = 1.5. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
22.5
|
MATH_PROB_FAMILIES
|
algebra_func_area_level_1_0085
|
algebra_func_area
| 1 |
[
{
"role": "user",
"content": "Find the area of the region bounded by the curves f(x) = -5(-1sin(3πx - 3) + 1)^2 - 4(-1sin(3πx - 3) + 1) + 2, g(x) = -1x + 1, x = 0.6, and x = 1.1. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
6.7
|
MATH_PROB_FAMILIES
|
algebra_func_area_level_1_0086
|
algebra_func_area
| 1 |
[
{
"role": "user",
"content": "Determine the area of the region enclosed by the graphs of f(x) = (-2(-2|x| - 1) - 1)/(-2(-2|x| - 1) + 3) and g(x) = -3|x - 3| + 2 between the vertical lines x = 2.6 and x = 3.4. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
0.5
|
MATH_PROB_FAMILIES
|
algebra_func_area_level_1_0087
|
algebra_func_area
| 1 |
[
{
"role": "user",
"content": "Calculate the area enclosed between the functions f(x) = -3sin(2π(-4x^2 - 4x + 4) + 1) + 2 and g(x) = -2x - 5 from x = -3.1 to x = -3.0. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
0.2
|
MATH_PROB_FAMILIES
|
algebra_func_area_level_1_0088
|
algebra_func_area
| 1 |
[
{
"role": "user",
"content": "Find the area of the region bounded by the curves f(x) = -3e^(-1(3|x - 3| + 3)) + 1, g(x) = -2x^2 + 4x, x = 0.3, and x = 1.7. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
0.9
|
MATH_PROB_FAMILIES
|
algebra_func_area_level_1_0089
|
algebra_func_area
| 1 |
[
{
"role": "user",
"content": "Calculate the area enclosed between the functions f(x) = -2((3x + 1)/(-1x + 3)) - 1 and g(x) = 3|x| - 3 from x = -1.0 to x = 0.2. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
0.9
|
MATH_PROB_FAMILIES
|
algebra_func_area_level_1_0090
|
algebra_func_area
| 1 |
[
{
"role": "user",
"content": "Find the area of the region bounded by the curves f(x) = -1cos(3π(-1x - 2) - 3), g(x) = -4x + 3, x = 0.6, and x = 0.9. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
0.2
|
MATH_PROB_FAMILIES
|
algebra_func_area_level_1_0091
|
algebra_func_area
| 1 |
[
{
"role": "user",
"content": "Calculate the area enclosed between the functions f(x) = 3sin(2π(2|x + 3| + 2) - 2) + 2 and g(x) = 1x - 2 from x = 3.4 to x = 3.6. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
0.3
|
MATH_PROB_FAMILIES
|
algebra_func_area_level_1_0092
|
algebra_func_area
| 1 |
[
{
"role": "user",
"content": "Calculate the area enclosed between the functions f(x) = (-3((-2x - 1)/(-1x)) + 1)/(3((-2x - 1)/(-1x)) - 2) and g(x) = (-3x - 1)/(1x + 1) from x = -0.7 to x = -0.0. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
0.7
|
MATH_PROB_FAMILIES
|
algebra_func_area_level_1_0093
|
algebra_func_area
| 1 |
[
{
"role": "user",
"content": "Calculate the area enclosed between the functions f(x) = -2(-2sin(2πx + 1) + 3)^2 + 2(-2sin(2πx + 1) + 3) + 3 and g(x) = -1x^2 + 2x + 5 from x = 3.9 to x = 4.3. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
1.9
|
MATH_PROB_FAMILIES
|
algebra_func_area_level_1_0094
|
algebra_func_area
| 1 |
[
{
"role": "user",
"content": "Determine the area of the region enclosed by the graphs of f(x) = -3(2|x - 3| - 1)^2 - 3(2|x - 3| - 1) + 3 and g(x) = -3x + 3 between the vertical lines x = 2.0 and x = 4.3. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
17.0
|
MATH_PROB_FAMILIES
|
algebra_func_area_level_1_0095
|
algebra_func_area
| 1 |
[
{
"role": "user",
"content": "Calculate the area enclosed between the functions f(x) = 3sin(3π(-5x^2 + 1x - 3) - 2) - 3 and g(x) = -5x^2 - 2x + 3 from x = 0.9 to x = 1.0. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
0.2
|
MATH_PROB_FAMILIES
|
algebra_func_area_level_1_0096
|
algebra_func_area
| 1 |
[
{
"role": "user",
"content": "Determine the area of the region enclosed by the graphs of f(x) = -3|(2e^(1x) - 3) - 1| + 1 and g(x) = -5x^2 - 5x + 3 between the vertical lines x = 0.5 and x = 1.7. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
3.2
|
MATH_PROB_FAMILIES
|
algebra_func_area_level_1_0097
|
algebra_func_area
| 1 |
[
{
"role": "user",
"content": "Determine the area of the region enclosed by the graphs of f(x) = 1(3e^(1x) + 3) - 4 and g(x) = 1x + 2 between the vertical lines x = -2.8 and x = 0.0. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
1.7
|
MATH_PROB_FAMILIES
|
algebra_func_area_level_1_0098
|
algebra_func_area
| 1 |
[
{
"role": "user",
"content": "Find the area of the region bounded by the curves f(x) = 3cos(1π(2|x - 3| + 2) - 3), g(x) = 1x + 3, x = -1.3, and x = -0.6. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
2.2
|
MATH_PROB_FAMILIES
|
algebra_func_area_level_1_0099
|
algebra_func_area
| 1 |
[
{
"role": "user",
"content": "Calculate the area enclosed between the functions f(x) = 3((3x + 2)/(2x - 3))^2 - 5 and g(x) = (-1x + 3)/(-3x - 1) from x = -0.1 to x = 0.2. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
0.2
|
MATH_PROB_FAMILIES
|
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