id
string | setting_key
string | difficulty
string | level
int64 | messages
list | ground_truth
string | dataset
string | omega_split
string | __index_level_0__
int64 |
|---|---|---|---|---|---|---|---|---|
math_algebra_func_area_level_2_2_100
|
algebra_func_area2
|
medium (level 2,3)
| 2 |
[
{
"content": "Calculate the area enclosed between the functions f(x) = (3(4(2|x + 2| + 3)^2 + 5(2|x + 2| + 3) - 3) + 1)/(-2(4(2|x + 2| + 3)^2 + 5(2|x + 2| + 3) - 3)) and g(x) = -2sin(2π(2x^2 - 5) - 2) - 3 from x = -2.8 to x = -2.6999999999999997. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
0.2
|
math
|
train
| 160,165 |
math_algebra_func_area_level_2_2_101
|
algebra_func_area2
|
medium (level 2,3)
| 2 |
[
{
"content": "Find the area of the region bounded by the curves f(x) = 2(1(-2e^(2x)) + 2)^2 + 4(1(-2e^(2x)) + 2) - 5, g(x) = 2cos(2π(-2x^2 - 4x + 3) - 2) - 2, x = -0.2, and x = 0.4. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
2.1
|
math
|
train
| 160,166 |
math_algebra_func_area_level_2_2_102
|
algebra_func_area2
|
medium (level 2,3)
| 2 |
[
{
"content": "Find the area of the region bounded by the curves f(x) = 4(-1sin(1π((1x - 2)/(-3x - 2)) + 1)) + 4, g(x) = 4(-3e^(-1x)) + 2, x = 2.6, and x = 3.3. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
0.0
|
math
|
train
| 160,167 |
math_algebra_func_area_level_2_2_103
|
algebra_func_area2
|
medium (level 2,3)
| 2 |
[
{
"content": "Find the area of the region bounded by the curves f(x) = -1(-2cos(3π((3x + 1)/(3x + 3)) + 2) + 1)^2 - 3(-2cos(3π((3x + 1)/(3x + 3)) + 2) + 1) + 5, g(x) = -2|(4x^2 + 4x - 4)|, x = -1.2, and x = -1.0999999999999999. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
0.8
|
math
|
train
| 160,168 |
math_algebra_func_area_level_2_2_104
|
algebra_func_area2
|
medium (level 2,3)
| 2 |
[
{
"content": "Determine the area of the region enclosed by the graphs of f(x) = 1|(-3(3sin(1πx + 1) - 3) + 2) - 1| - 3 and g(x) = (3(2sin(1πx + 1) + 1) - 3)/(3(2sin(1πx + 1) + 1) + 2) between the vertical lines x = 1.3 and x = 1.9. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
16.7
|
math
|
train
| 160,169 |
math_algebra_func_area_level_2_2_105
|
algebra_func_area2
|
medium (level 2,3)
| 2 |
[
{
"content": "Find the area of the region bounded by the curves f(x) = 2e^(-2((1((-1x - 3)/(-2x + 1)) + 3)/(1((-1x - 3)/(-2x + 1)) + 1))) - 2, g(x) = (1(-4x^2 - 3x + 2))/(-3(-4x^2 - 3x + 2) - 3), x = 0.0, and x = 0.6. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
1.3
|
math
|
train
| 160,170 |
math_algebra_func_area_level_2_2_106
|
algebra_func_area2
|
medium (level 2,3)
| 2 |
[
{
"content": "Find the area of the region bounded by the curves f(x) = (-2(-1sin(1π((1x - 2)/(2x - 3)) + 2) - 3) - 3)/(-1(-1sin(1π((1x - 2)/(2x - 3)) + 2) - 3) + 3), g(x) = -3|((2x)/(-1x + 2)) - 2| + 2, x = 0.8, and x = 1.1. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
0.3
|
math
|
train
| 160,171 |
math_algebra_func_area_level_2_2_107
|
algebra_func_area2
|
medium (level 2,3)
| 2 |
[
{
"content": "Find the area of the region bounded by the curves f(x) = (-1((3(-3x^2 - 3x + 2) - 3)/(-2(-3x^2 - 3x + 2))) + 3)/(2((3(-3x^2 - 3x + 2) - 3)/(-2(-3x^2 - 3x + 2))) + 1), g(x) = 3|(-1|x + 1| + 1) - 1| - 3, x = -1.6, and x = 0.3. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
22.5
|
math
|
train
| 160,172 |
math_algebra_func_area_level_2_2_108
|
algebra_func_area2
|
medium (level 2,3)
| 2 |
[
{
"content": "Calculate the area enclosed between the functions f(x) = -3|(-2sin(1π(5x^2 - 1x - 4)) - 3) + 3| and g(x) = 4(1sin(1πx - 3) - 1)^2 - 3(1sin(1πx - 3) - 1) - 4 from x = 3.7 to x = 3.8000000000000003. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
0.2
|
math
|
train
| 160,173 |
math_algebra_func_area_level_2_2_109
|
algebra_func_area2
|
medium (level 2,3)
| 2 |
[
{
"content": "Determine the area of the region enclosed by the graphs of f(x) = 1|(5(2|x + 1|)^2 - 3(2|x + 1|) - 3) - 3| - 2 and g(x) = 1|(3sin(2πx + 3)) - 1| between the vertical lines x = -1.5 and x = -0.7. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
1.8
|
math
|
train
| 160,174 |
math_algebra_func_area_level_2_2_110
|
algebra_func_area2
|
medium (level 2,3)
| 2 |
[
{
"content": "Determine the area of the region enclosed by the graphs of f(x) = 5((-1(-2sin(2πx + 1)) - 2)/(2(-2sin(2πx + 1)) + 2)) + 1 and g(x) = (2(-1x^2 - 4x + 1) - 2)/(1(-1x^2 - 4x + 1) + 3) between the vertical lines x = 4.0 and x = 4.2. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
0.2
|
math
|
train
| 160,175 |
math_algebra_func_area_level_2_2_111
|
algebra_func_area2
|
medium (level 2,3)
| 2 |
[
{
"content": "Find the area of the region bounded by the curves f(x) = (-2((2(3x^2 + 5x - 2) + 2)/(-1(3x^2 + 5x - 2) - 1)) + 2)/(2((2(3x^2 + 5x - 2) + 2)/(-1(3x^2 + 5x - 2) - 1)) - 3), g(x) = -5(2cos(2πx - 2) - 1)^2 + 5(2cos(2πx - 2) - 1) - 2, x = -3.6, and x = -2.8. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
21.0
|
math
|
train
| 160,176 |
math_algebra_func_area_level_2_2_112
|
algebra_func_area2
|
medium (level 2,3)
| 2 |
[
{
"content": "Determine the area of the region enclosed by the graphs of f(x) = -2(-3|((-2x + 3)/(-1x + 2))| + 3)^2 - 5(-3|((-2x + 3)/(-1x + 2))| + 3) - 5 and g(x) = -2(-1|x - 3| - 3)^2 - 3(-1|x - 3| - 3) + 2 between the vertical lines x = 1.4 and x = 1.6. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
1.0
|
math
|
train
| 160,177 |
math_algebra_func_area_level_2_2_113
|
algebra_func_area2
|
medium (level 2,3)
| 2 |
[
{
"content": "Calculate the area enclosed between the functions f(x) = (-3(2|((-3x - 1)/(2x - 1)) - 1| + 3) - 2)/(-1(2|((-3x - 1)/(2x - 1)) - 1| + 3) - 1) and g(x) = 1(2|x + 2| - 3) from x = -4.9 to x = 1.0. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
17.3
|
math
|
train
| 160,178 |
math_algebra_func_area_level_2_2_114
|
algebra_func_area2
|
medium (level 2,3)
| 2 |
[
{
"content": "Find the area of the region bounded by the curves f(x) = (-3((-1(4x - 1))/(2(4x - 1) - 1)) - 3)/(1((-1(4x - 1))/(2(4x - 1) - 1)) + 2), g(x) = -2sin(1π(-3x - 5)) - 2, x = -4.0, and x = -3.6. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
0.8
|
math
|
train
| 160,179 |
math_algebra_func_area_level_2_2_115
|
algebra_func_area2
|
medium (level 2,3)
| 2 |
[
{
"content": "Determine the area of the region enclosed by the graphs of f(x) = 3sin(2π(-1(-1x^2 - 3x - 1)^2 - 2(-1x^2 - 3x - 1) - 1) - 3) + 1 and g(x) = 3|(-4x)| - 2 between the vertical lines x = 0.2 and x = 0.3. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
0.2
|
math
|
train
| 160,180 |
math_algebra_func_area_level_2_2_116
|
algebra_func_area2
|
medium (level 2,3)
| 2 |
[
{
"content": "Find the area of the region bounded by the curves f(x) = (-1(3(-3e^(-1x) - 1)^2 + 4(-3e^(-1x) - 1) - 3) + 1)/(2(3(-3e^(-1x) - 1)^2 + 4(-3e^(-1x) - 1) - 3) - 1), g(x) = (3(-2sin(1πx) - 1))/(-2(-2sin(1πx) - 1) - 2), x = -0.3, and x = 1.1. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
14.6
|
math
|
train
| 160,181 |
math_algebra_func_area_level_2_2_117
|
algebra_func_area2
|
medium (level 2,3)
| 2 |
[
{
"content": "Find the area of the region bounded by the curves f(x) = -3((-3(3x^2 + 1x - 1))/(1(3x^2 + 1x - 1)))^2 - 3((-3(3x^2 + 1x - 1))/(1(3x^2 + 1x - 1))) + 2, g(x) = (1(2cos(3πx - 2) + 1) + 2)/(1(2cos(3πx - 2) + 1) - 2), x = -2.6, and x = -2.3. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
11.8
|
math
|
train
| 160,182 |
math_algebra_func_area_level_2_2_118
|
algebra_func_area2
|
medium (level 2,3)
| 2 |
[
{
"content": "Find the area of the region bounded by the curves f(x) = 5(1(-3x - 5))^2 - 1(1(-3x - 5)) - 2, g(x) = 3|(2|x + 1|) + 3| + 1, x = -2.4, and x = -1.2. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
13.2
|
math
|
train
| 160,183 |
math_algebra_func_area_level_2_2_119
|
algebra_func_area2
|
medium (level 2,3)
| 2 |
[
{
"content": "Determine the area of the region enclosed by the graphs of f(x) = -1(-2cos(3π((-3x + 2)/(-1x)) - 2)) + 4 and g(x) = 5(1|x + 2| - 2)^2 - 3(1|x + 2| - 2) + 4 between the vertical lines x = 0.4 and x = 0.5. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
0.1
|
math
|
train
| 160,184 |
math_algebra_func_area_level_2_2_120
|
algebra_func_area2
|
medium (level 2,3)
| 2 |
[
{
"content": "Determine the area of the region enclosed by the graphs of f(x) = -4(2sin(3π(1x - 3) - 2) - 1)^2 + 3(2sin(3π(1x - 3) - 2) - 1) + 3 and g(x) = (3(3sin(1πx + 2) - 3) - 1)/(2(3sin(1πx + 2) - 3) - 1) between the vertical lines x = -0.1 and x = 0.2. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
0.5
|
math
|
train
| 160,185 |
math_algebra_func_area_level_2_2_121
|
algebra_func_area2
|
medium (level 2,3)
| 2 |
[
{
"content": "Find the area of the region bounded by the curves f(x) = 2(-2|(5x) - 3|)^2 + 2(-2|(5x) - 3|) - 3, g(x) = -1sin(2π((-3x)/(3x - 2)) - 2) + 2, x = 0.4, and x = 0.8. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
1.7
|
math
|
train
| 160,186 |
math_algebra_func_area_level_2_2_122
|
algebra_func_area2
|
medium (level 2,3)
| 2 |
[
{
"content": "Find the area of the region bounded by the curves f(x) = -5(-2|(2sin(2πx + 3))|) + 4, g(x) = 2|(-2|x - 1| - 3) - 3| - 3, x = 4.2, and x = 4.3. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
0.1
|
math
|
train
| 160,187 |
math_algebra_func_area_level_2_2_123
|
algebra_func_area2
|
medium (level 2,3)
| 2 |
[
{
"content": "Calculate the area enclosed between the functions f(x) = -1sin(3π(1(3|x - 2| - 3) - 1) + 3) and g(x) = (-3(-3|x + 2| - 2) + 1)/(3(-3|x + 2| - 2) - 1) from x = -4.8 to x = -4.6. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
0.2
|
math
|
train
| 160,188 |
math_algebra_func_area_level_2_2_124
|
algebra_func_area2
|
medium (level 2,3)
| 2 |
[
{
"content": "Find the area of the region bounded by the curves f(x) = 3sin(1π(-5(-3|x - 2| - 1) - 3) + 2) + 1, g(x) = -4(-4x - 5) + 1, x = -1.4, and x = -1.3. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
0.2
|
math
|
train
| 160,189 |
math_algebra_func_area_level_2_2_125
|
algebra_func_area2
|
medium (level 2,3)
| 2 |
[
{
"content": "Calculate the area enclosed between the functions f(x) = (-2(2(3x^2 + 5x + 2)^2 - 3(3x^2 + 5x + 2) + 4) + 2)/(-1(2(3x^2 + 5x + 2)^2 - 3(3x^2 + 5x + 2) + 4) - 2) and g(x) = -2sin(3π(-2|x - 2| + 3)) from x = -4.6 to x = -4.5. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
0.1
|
math
|
train
| 160,190 |
math_algebra_func_area_level_2_2_126
|
algebra_func_area2
|
medium (level 2,3)
| 2 |
[
{
"content": "Determine the area of the region enclosed by the graphs of f(x) = -1sin(3π(-2|((3x - 1)/(2x)) - 2| - 2)) + 3 and g(x) = -1(1x^2 - 5x + 3)^2 + 4(1x^2 - 5x + 3) + 5 between the vertical lines x = -0.2 and x = 0.8. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
4.3
|
math
|
train
| 160,191 |
math_algebra_func_area_level_2_2_127
|
algebra_func_area2
|
medium (level 2,3)
| 2 |
[
{
"content": "Determine the area of the region enclosed by the graphs of f(x) = -2sin(1π(3|(3x - 5)| + 1) - 1) and g(x) = (3(-3x - 4) + 1)/(2(-3x - 4) - 1) between the vertical lines x = -1.0 and x = -0.9. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
0.2
|
math
|
train
| 160,192 |
math_algebra_func_area_level_2_2_128
|
algebra_func_area2
|
medium (level 2,3)
| 2 |
[
{
"content": "Find the area of the region bounded by the curves f(x) = -4(-3cos(3π(-5x - 1) + 3) + 1)^2 + 2, g(x) = 5(-3sin(3πx + 3) - 1) - 2, x = -0.2, and x = -0.1. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
1.8
|
math
|
train
| 160,193 |
math_algebra_func_area_level_2_2_129
|
algebra_func_area2
|
medium (level 2,3)
| 2 |
[
{
"content": "Determine the area of the region enclosed by the graphs of f(x) = -2sin(1π(2(4x^2 + 3) - 5)) + 2 and g(x) = -3(-3sin(1πx))^2 + 4(-3sin(1πx)) + 4 between the vertical lines x = 3.0 and x = 3.2. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
0.5
|
math
|
train
| 160,194 |
math_algebra_func_area_level_2_2_130
|
algebra_func_area2
|
medium (level 2,3)
| 2 |
[
{
"content": "Calculate the area enclosed between the functions f(x) = 2|(-2|(-1|x + 1| + 3) - 2| + 3) - 3| + 1 and g(x) = -2cos(2π((-3x + 3)/(3x + 2)) - 1) + 2 from x = -0.4 to x = -0.30000000000000004. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
0.1
|
math
|
train
| 160,195 |
math_algebra_func_area_level_2_2_131
|
algebra_func_area2
|
medium (level 2,3)
| 2 |
[
{
"content": "Find the area of the region bounded by the curves f(x) = 2sin(1π(5(-1|x| - 2)^2) - 3), g(x) = 1|(-1cos(2πx + 3) - 1) - 1| - 2, x = 1.3, and x = 1.4000000000000001. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
0.1
|
math
|
train
| 160,196 |
math_algebra_func_area_level_2_2_132
|
algebra_func_area2
|
medium (level 2,3)
| 2 |
[
{
"content": "Find the area of the region bounded by the curves f(x) = -2cos(1π(-1|((3x)/(1x + 3)) - 1| + 2) + 2) + 2, g(x) = 2(-3e^(2x) + 1), x = -2.8, and x = -2.6999999999999997. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
0.1
|
math
|
train
| 160,197 |
math_algebra_func_area_level_2_2_133
|
algebra_func_area2
|
medium (level 2,3)
| 2 |
[
{
"content": "Find the area of the region bounded by the curves f(x) = 2|(-2|(2sin(2πx - 2) - 3) - 2| + 3) - 3| + 2, g(x) = 3(2x^2 + 3x + 1)^2 + 2(2x^2 + 3x + 1) + 1, x = -2.0, and x = 0.3. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
37.8
|
math
|
train
| 160,198 |
math_algebra_func_area_level_2_2_134
|
algebra_func_area2
|
medium (level 2,3)
| 2 |
[
{
"content": "Find the area of the region bounded by the curves f(x) = 3(2cos(3π(4x^2 + 2x - 2) - 1)) + 4, g(x) = -1(-5x^2 + 4x + 2)^2 + 4(-5x^2 + 4x + 2) + 2, x = 1.1, and x = 1.2000000000000002. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
0.4
|
math
|
train
| 160,199 |
math_algebra_func_area_level_2_2_135
|
algebra_func_area2
|
medium (level 2,3)
| 2 |
[
{
"content": "Calculate the area enclosed between the functions f(x) = 2|((-3(-2e^(2x) + 1) - 2)/(-2(-2e^(2x) + 1) + 3)) - 1| + 3 and g(x) = 1|(-1x^2 + 2x + 2)| + 1 from x = 1.4 to x = 3.4. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
2.7
|
math
|
train
| 160,200 |
math_algebra_func_area_level_2_2_136
|
algebra_func_area2
|
medium (level 2,3)
| 2 |
[
{
"content": "Determine the area of the region enclosed by the graphs of f(x) = 4(3cos(2π((-2x + 1)/(-3x + 4)) - 1) - 2) - 1 and g(x) = -2|((-3x + 2)/(-3x + 1)) - 1| + 2 between the vertical lines x = 1.2 and x = 1.3. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
1.0
|
math
|
train
| 160,201 |
math_algebra_func_area_level_2_2_137
|
algebra_func_area2
|
medium (level 2,3)
| 2 |
[
{
"content": "Calculate the area enclosed between the functions f(x) = -3|((-1(2x^2 + 1x + 5) + 1)/(2(2x^2 + 1x + 5) - 3)) - 1| + 2 and g(x) = 1(4x^2 + 5x - 1) - 1 from x = -1.1 to x = -0.2. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
0.5
|
math
|
train
| 160,202 |
math_algebra_func_area_level_2_2_138
|
algebra_func_area2
|
medium (level 2,3)
| 2 |
[
{
"content": "Calculate the area enclosed between the functions f(x) = -3((1(5x^2 + 4x - 2) - 1)/(2(5x^2 + 4x - 2) + 2))^2 + 3 and g(x) = -2e^(2(-4x - 5)) - 3 from x = -0.0 to x = 0.3. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
-2.1
|
math
|
train
| 160,203 |
math_algebra_func_area_level_2_2_139
|
algebra_func_area2
|
medium (level 2,3)
| 2 |
[
{
"content": "Find the area of the region bounded by the curves f(x) = -4(-3|(-1x - 2) + 3| + 1) - 5, g(x) = -2e^(1(-4x^2 - 4x + 4)) + 2, x = 0.5, and x = 1.9. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
8.4
|
math
|
train
| 160,204 |
math_algebra_func_area_level_2_2_140
|
algebra_func_area2
|
medium (level 2,3)
| 2 |
[
{
"content": "Calculate the area enclosed between the functions f(x) = (3(4(-3cos(1πx - 3) - 3) - 1))/(-3(4(-3cos(1πx - 3) - 3) - 1)) and g(x) = -1e^(-1(-5x^2 + 5x + 1)) + 2 from x = -0.3 to x = 1.3. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
4.0
|
math
|
train
| 160,205 |
math_algebra_func_area_level_2_2_141
|
algebra_func_area2
|
medium (level 2,3)
| 2 |
[
{
"content": "Find the area of the region bounded by the curves f(x) = (3(-3|(-2|x - 2| + 2) + 1| + 1) - 1)/(-3(-3|(-2|x - 2| + 2) + 1| + 1) + 4), g(x) = 3(5x^2 - 2x - 3)^2 - 5(5x^2 - 2x - 3) + 1, x = 1.1, and x = 1.2000000000000002. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
0.1
|
math
|
train
| 160,206 |
math_algebra_func_area_level_2_2_142
|
algebra_func_area2
|
medium (level 2,3)
| 2 |
[
{
"content": "Find the area of the region bounded by the curves f(x) = (3(-1(-5x - 5)) + 2)/(-3(-1(-5x - 5))), g(x) = 4(2sin(3πx - 2) + 2) - 2, x = 4.7, and x = 4.8. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
0.1
|
math
|
train
| 160,207 |
math_algebra_func_area_level_2_2_143
|
algebra_func_area2
|
medium (level 2,3)
| 2 |
[
{
"content": "Find the area of the region bounded by the curves f(x) = -3(-1sin(1π(-1x - 4) + 3))^2 + 3, g(x) = -3cos(3π(4x^2 - 5x - 3) + 1), x = 3.6, and x = 3.7. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
0.2
|
math
|
train
| 160,208 |
math_algebra_func_area_level_2_2_144
|
algebra_func_area2
|
medium (level 2,3)
| 2 |
[
{
"content": "Find the area of the region bounded by the curves f(x) = 1cos(2π(-3|(-5x - 3) - 2| + 2)) + 2, g(x) = -1(-2x^2 - 3x + 5)^2 + 3(-2x^2 - 3x + 5) + 2, x = -2.0, and x = -1.9. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
0.1
|
math
|
train
| 160,209 |
math_algebra_func_area_level_2_2_145
|
algebra_func_area2
|
medium (level 2,3)
| 2 |
[
{
"content": "Calculate the area enclosed between the functions f(x) = -2|(-5(-3|x + 3| + 2) + 3) + 2| + 3 and g(x) = 2cos(2π(-4x - 2) + 1) + 1 from x = -3.3 to x = -2.7. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
2.3
|
math
|
train
| 160,210 |
math_algebra_func_area_level_2_2_146
|
algebra_func_area2
|
medium (level 2,3)
| 2 |
[
{
"content": "Calculate the area enclosed between the functions f(x) = -2|(-3(-2x^2 - 1x + 4)^2 + 5(-2x^2 - 1x + 4) + 4) - 1| + 1 and g(x) = -2(3sin(3πx) + 3) + 4 from x = -1.1 to x = 0.7. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
61.4
|
math
|
train
| 160,211 |
math_algebra_func_area_level_2_2_147
|
algebra_func_area2
|
medium (level 2,3)
| 2 |
[
{
"content": "Determine the area of the region enclosed by the graphs of f(x) = (1(1(-2x^2 - 2x)^2 + 4(-2x^2 - 2x) - 2) - 2)/(1(1(-2x^2 - 2x)^2 + 4(-2x^2 - 2x) - 2) - 3) and g(x) = (-3(-5x^2 + 2x + 3))/(1(-5x^2 + 2x + 3)) between the vertical lines x = -2.2 and x = 1.2. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
13.8
|
math
|
train
| 160,212 |
math_algebra_func_area_level_2_2_148
|
algebra_func_area2
|
medium (level 2,3)
| 2 |
[
{
"content": "Calculate the area enclosed between the functions f(x) = -3(-3(2x + 2) + 1) and g(x) = (2((3x + 2)/(-3x)) - 1)/(1((3x + 2)/(-3x)) - 3) from x = -0.8 to x = -0.2. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
3.8
|
math
|
train
| 160,213 |
math_algebra_func_area_level_2_2_149
|
algebra_func_area2
|
medium (level 2,3)
| 2 |
[
{
"content": "Determine the area of the region enclosed by the graphs of f(x) = 1|((1(5x - 4) - 1)/(2(5x - 4) - 3)) - 2| - 1 and g(x) = (-1(-1sin(2πx + 1) - 3) - 1)/(-2(-1sin(2πx + 1) - 3) + 3) between the vertical lines x = 1.1 and x = 1.3. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
1.1
|
math
|
train
| 160,214 |
math_algebra_func_area_level_2_2_150
|
algebra_func_area2
|
medium (level 2,3)
| 2 |
[
{
"content": "Calculate the area enclosed between the functions f(x) = -2|(5((1x)/(1x)) - 4)| - 3 and g(x) = -3cos(1π(-1x - 4) - 1) - 3 from x = -2.6 to x = -2.0. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
0.4
|
math
|
train
| 160,215 |
math_algebra_func_area_level_2_2_151
|
algebra_func_area2
|
medium (level 2,3)
| 2 |
[
{
"content": "Find the area of the region bounded by the curves f(x) = (2(1(5x + 5) + 4) + 2)/(1(1(5x + 5) + 4) + 3), g(x) = -1|((-1x + 1)/(-2x + 3)) + 2| + 3, x = 1.3, and x = 1.4. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
0.0
|
math
|
train
| 160,216 |
math_algebra_func_area_level_2_2_152
|
algebra_func_area2
|
medium (level 2,3)
| 2 |
[
{
"content": "Calculate the area enclosed between the functions f(x) = (-3((2(2x^2 - 5x - 3) + 1)/(-3(2x^2 - 5x - 3) - 1)))/(1((2(2x^2 - 5x - 3) + 1)/(-3(2x^2 - 5x - 3) - 1)) + 3) and g(x) = (2(-3cos(2πx - 3) + 1) - 2)/(1(-3cos(2πx - 3) + 1) + 1) from x = -1.2 to x = -0.9. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
0.1
|
math
|
train
| 160,217 |
math_algebra_func_area_level_2_2_153
|
algebra_func_area2
|
medium (level 2,3)
| 2 |
[
{
"content": "Find the area of the region bounded by the curves f(x) = 2|(-2|(3|x - 1| - 3) - 2|)| + 3, g(x) = 1(-3x + 1)^2 - 3(-3x + 1) + 4, x = -0.6, and x = 1.2. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
14.7
|
math
|
train
| 160,218 |
math_algebra_func_area_level_2_2_154
|
algebra_func_area2
|
medium (level 2,3)
| 2 |
[
{
"content": "Find the area of the region bounded by the curves f(x) = 4(3cos(2π(-5x - 4)) - 3), g(x) = (-2((3x - 1)/(2x + 2)) - 1)/(1((3x - 1)/(2x + 2)) + 2), x = 2.8, and x = 3.0. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
2.2
|
math
|
train
| 160,219 |
math_algebra_func_area_level_2_2_155
|
algebra_func_area2
|
medium (level 2,3)
| 2 |
[
{
"content": "Find the area of the region bounded by the curves f(x) = (-1(-3((-2x - 1)/(-1x - 1))^2 - 5((-2x - 1)/(-1x - 1)) - 1))/(2(-3((-2x - 1)/(-1x - 1))^2 - 5((-2x - 1)/(-1x - 1)) - 1) - 1), g(x) = -2(1cos(3πx - 3) + 1) + 5, x = -0.7, and x = -0.6. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
0.9
|
math
|
train
| 160,220 |
math_algebra_func_area_level_2_2_156
|
algebra_func_area2
|
medium (level 2,3)
| 2 |
[
{
"content": "Find the area of the region bounded by the curves f(x) = (1((2(3e^(1x) + 2) + 2)/(-1(3e^(1x) + 2) - 3)) + 1)/(-1((2(3e^(1x) + 2) + 2)/(-1(3e^(1x) + 2) - 3)) + 3), g(x) = 3sin(2π(3x^2 - 1x)) - 1, x = -3.4, and x = -3.3. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
0.2
|
math
|
train
| 160,221 |
math_algebra_func_area_level_2_2_157
|
algebra_func_area2
|
medium (level 2,3)
| 2 |
[
{
"content": "Find the area of the region bounded by the curves f(x) = 3(1sin(3π((3x - 2)/(3x + 1)) + 3) + 1)^2 + 3(1sin(3π((3x - 2)/(3x + 1)) + 3) + 1) - 4, g(x) = (-3(-4x^2 - 4x - 3))/(-1(-4x^2 - 4x - 3) - 1), x = -0.2, and x = -0.1. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
0.6
|
math
|
train
| 160,222 |
math_algebra_func_area_level_2_2_158
|
algebra_func_area2
|
medium (level 2,3)
| 2 |
[
{
"content": "Find the area of the region bounded by the curves f(x) = 3sin(3π(-4((3x)/(-3x - 2)) - 5) + 1) + 1, g(x) = -3cos(2π(-1x - 5) + 2) - 3, x = -1.2, and x = -1.0999999999999999. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
0.2
|
math
|
train
| 160,223 |
math_algebra_func_area_level_2_2_159
|
algebra_func_area2
|
medium (level 2,3)
| 2 |
[
{
"content": "Calculate the area enclosed between the functions f(x) = 3(2sin(1π(3x - 2) - 1) - 2)^2 - 5(2sin(1π(3x - 2) - 1) - 2) - 4 and g(x) = (-2(-1e^(2x) - 2) - 2)/(3(-1e^(2x) - 2) - 1) from x = -1.0 to x = -0.5. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
16.6
|
math
|
train
| 160,224 |
math_algebra_func_area_level_2_2_160
|
algebra_func_area2
|
medium (level 2,3)
| 2 |
[
{
"content": "Find the area of the region bounded by the curves f(x) = 4((-1((3x)/(2x)) + 3)/(2((3x)/(2x)) + 3))^2 + 4((-1((3x)/(2x)) + 3)/(2((3x)/(2x)) + 3)) - 1, g(x) = 1|(2x + 5)|, x = -2.6, and x = -2.4. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
0.0
|
math
|
train
| 160,225 |
math_algebra_func_area_level_2_2_161
|
algebra_func_area2
|
medium (level 2,3)
| 2 |
[
{
"content": "Find the area of the region bounded by the curves f(x) = -1|((2(3sin(2πx - 2) - 1))/(1(3sin(2πx - 2) - 1) + 1)) - 3| + 3, g(x) = 3|(-3sin(2πx) - 1)|, x = 2.6, and x = 2.9. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
3.5
|
math
|
train
| 160,226 |
math_algebra_func_area_level_2_2_162
|
algebra_func_area2
|
medium (level 2,3)
| 2 |
[
{
"content": "Calculate the area enclosed between the functions f(x) = 2((-2(2sin(1πx)) - 1)/(2(2sin(1πx)))) - 4 and g(x) = (3(2x + 3) - 2)/(1(2x + 3) - 3) from x = 1.0 to x = 2.0. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
15.1
|
math
|
train
| 160,227 |
math_algebra_func_area_level_2_2_163
|
algebra_func_area2
|
medium (level 2,3)
| 2 |
[
{
"content": "Determine the area of the region enclosed by the graphs of f(x) = (-1(1|(2|x - 3|) - 1|) - 3)/(2(1|(2|x - 3|) - 1|)) and g(x) = -3|(1cos(2πx - 1) + 1) - 3| between the vertical lines x = 2.2 and x = 2.6. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
33.7
|
math
|
train
| 160,228 |
math_algebra_func_area_level_2_2_164
|
algebra_func_area2
|
medium (level 2,3)
| 2 |
[
{
"content": "Determine the area of the region enclosed by the graphs of f(x) = (2((-1(4x^2 + 3x + 2) - 1)/(3(4x^2 + 3x + 2) - 2)) + 3)/(-1((-1(4x^2 + 3x + 2) - 1)/(3(4x^2 + 3x + 2) - 2)) + 2) and g(x) = -2(2|x - 1| - 1)^2 + 1(2|x - 1| - 1) + 1 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}",
"role": "user"
}
] |
1.1
|
math
|
train
| 160,229 |
math_algebra_func_area_level_2_2_165
|
algebra_func_area2
|
medium (level 2,3)
| 2 |
[
{
"content": "Determine the area of the region enclosed by the graphs of f(x) = 2(-3(-5x^2 + 5x + 3) + 4) - 2 and g(x) = 4(5x + 3)^2 + 1(5x + 3) + 4 between the vertical lines x = -1.8 and x = -0.4. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
27.4
|
math
|
train
| 160,230 |
math_algebra_func_area_level_2_2_166
|
algebra_func_area2
|
medium (level 2,3)
| 2 |
[
{
"content": "Determine the area of the region enclosed by the graphs of f(x) = 1(2cos(2π(-2|x + 2| + 2) + 3)) and g(x) = 3e^(-1(1x - 1)) - 1 between the vertical lines x = 3.6 and x = 3.9. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
0.5
|
math
|
train
| 160,231 |
math_algebra_func_area_level_2_2_167
|
algebra_func_area2
|
medium (level 2,3)
| 2 |
[
{
"content": "Determine the area of the region enclosed by the graphs of f(x) = 2|(2cos(3π(-2x^2 - 4x + 4) - 3) + 1) - 3| + 1 and g(x) = 4(-4x - 2)^2 - 4(-4x - 2) between the vertical lines x = -1.0 and x = -0.3. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
3.3
|
math
|
train
| 160,232 |
math_algebra_func_area_level_2_2_168
|
algebra_func_area2
|
medium (level 2,3)
| 2 |
[
{
"content": "Calculate the area enclosed between the functions f(x) = -3(3cos(1π((1x - 1)/(-3x + 4)) - 1) - 2)^2 + 2(3cos(1π((1x - 1)/(-3x + 4)) - 1) - 2) + 5 and g(x) = -4(3|x + 3| - 1)^2 + 2(3|x + 3| - 1) + 2 from x = -4.4 to x = -1.6. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
68.8
|
math
|
train
| 160,233 |
math_algebra_func_area_level_2_2_169
|
algebra_func_area2
|
medium (level 2,3)
| 2 |
[
{
"content": "Determine the area of the region enclosed by the graphs of f(x) = 2|(-1|((2x - 1)/(1x - 3))| + 1) - 3| + 1 and g(x) = 2|(-5x^2 - 5x + 5) + 2| + 2 between the vertical lines x = 0.9 and x = 2.9. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
60.4
|
math
|
train
| 160,234 |
math_algebra_func_area_level_2_2_170
|
algebra_func_area2
|
medium (level 2,3)
| 2 |
[
{
"content": "Calculate the area enclosed between the functions f(x) = -2(1sin(1π(5x^2 - 1x) - 3) - 2)^2 + 3(1sin(1π(5x^2 - 1x) - 3) - 2) + 5 and g(x) = -3(3e^(1x))^2 - 1(3e^(1x)) - 3 from x = -3.0 to x = -2.9. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
0.6
|
math
|
train
| 160,235 |
math_algebra_func_area_level_2_2_171
|
algebra_func_area2
|
medium (level 2,3)
| 2 |
[
{
"content": "Determine the area of the region enclosed by the graphs of f(x) = -3|(-3(-2|x + 3| - 1) + 4) + 3| + 2 and g(x) = -2((3x + 2)/(-2x - 2))^2 - 2((3x + 2)/(-2x - 2)) - 1 between the vertical lines x = -1.1 and x = -0.9. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
46.6
|
math
|
train
| 160,236 |
math_algebra_func_area_level_2_2_172
|
algebra_func_area2
|
medium (level 2,3)
| 2 |
[
{
"content": "Find the area of the region bounded by the curves f(x) = -1|((-3((1x + 2)/(2x)) - 3)/(-1((1x + 2)/(2x)) + 3)) - 2|, g(x) = (1(2e^(1x) + 2) - 1)/(-3(2e^(1x) + 2) - 3), x = -0.1, and x = 0.0. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
0.0
|
math
|
train
| 160,237 |
math_algebra_func_area_level_2_2_173
|
algebra_func_area2
|
medium (level 2,3)
| 2 |
[
{
"content": "Calculate the area enclosed between the functions f(x) = (-3(-4(2|x|) + 2))/(-1(-4(2|x|) + 2) + 2) and g(x) = -4(2x^2 - 4x - 3)^2 - 4 from x = -0.0 to x = 0.1. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
18.5
|
math
|
train
| 160,238 |
math_algebra_func_area_level_2_2_174
|
algebra_func_area2
|
medium (level 2,3)
| 2 |
[
{
"content": "Determine the area of the region enclosed by the graphs of f(x) = 5(-3cos(1π(3|x + 1| - 2)) + 3) + 2 and g(x) = -5(4x + 5) between the vertical lines x = -2.7 and x = -2.6. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
0.3
|
math
|
train
| 160,239 |
math_algebra_func_area_level_2_2_175
|
algebra_func_area2
|
medium (level 2,3)
| 2 |
[
{
"content": "Find the area of the region bounded by the curves f(x) = 2|(2(5x^2 + 5x - 3) + 3) - 2| + 1, g(x) = -3(-2cos(2πx - 1) - 2) + 5, x = -0.7, and x = -0.1. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
4.2
|
math
|
train
| 160,240 |
math_algebra_func_area_level_2_2_176
|
algebra_func_area2
|
medium (level 2,3)
| 2 |
[
{
"content": "Determine the area of the region enclosed by the graphs of f(x) = 1((1(3x^2 - 4x - 5) - 3)/(1(3x^2 - 4x - 5))) - 4 and g(x) = 3|((-1x - 1)/(1x - 3)) - 1| - 3 between the vertical lines x = -0.6 and x = 0.8. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
1.5
|
math
|
train
| 160,241 |
math_algebra_func_area_level_2_2_177
|
algebra_func_area2
|
medium (level 2,3)
| 2 |
[
{
"content": "Find the area of the region bounded by the curves f(x) = 3|(-1|(4x^2 - 2x - 2) - 1| + 3)| - 3, g(x) = 1(-4x + 5)^2 + 1(-4x + 5) + 2, x = 1.3, and x = 1.7. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
0.9
|
math
|
train
| 160,242 |
math_algebra_func_area_level_2_2_178
|
algebra_func_area2
|
medium (level 2,3)
| 2 |
[
{
"content": "Calculate the area enclosed between the functions f(x) = 3|(-4(-5x^2 + 2x + 2) - 4) - 1| + 1 and g(x) = 2e^(-2(1|x + 3| - 2)) + 3 from x = -0.7 to x = -0.6. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
0.2
|
math
|
train
| 160,243 |
math_algebra_func_area_level_2_2_179
|
algebra_func_area2
|
medium (level 2,3)
| 2 |
[
{
"content": "Calculate the area enclosed between the functions f(x) = -1|(-4(-2e^(1x) + 1)^2 - 5(-2e^(1x) + 1)) - 2| + 1 and g(x) = (1(-5x^2 + 5x - 4) + 1)/(2(-5x^2 + 5x - 4) - 3) from x = -0.4 to x = -0.1. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
0.0
|
math
|
train
| 160,244 |
math_algebra_func_area_level_2_2_180
|
algebra_func_area2
|
medium (level 2,3)
| 2 |
[
{
"content": "Calculate the area enclosed between the functions f(x) = -3(2e^(2(-1|x + 1| - 1)) + 2) + 1 and g(x) = 1(1sin(3πx - 2) + 3)^2 - 4(1sin(3πx - 2) + 3) - 3 from x = 2.5 to x = 2.9. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
0.6
|
math
|
train
| 160,245 |
math_algebra_func_area_level_2_2_181
|
algebra_func_area2
|
medium (level 2,3)
| 2 |
[
{
"content": "Determine the area of the region enclosed by the graphs of f(x) = -2|(-1e^(-2(-4x^2 + 4)) + 1) + 3| - 1 and g(x) = -5(-1|x + 1|) - 3 between the vertical lines x = -1.1 and x = -1.0. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
0.2
|
math
|
train
| 160,246 |
math_algebra_func_area_level_2_2_182
|
algebra_func_area2
|
medium (level 2,3)
| 2 |
[
{
"content": "Determine the area of the region enclosed by the graphs of f(x) = -4(3sin(2π(1|x - 1| - 2) + 1) - 3)^2 + 5(3sin(2π(1|x - 1| - 2) + 1) - 3) + 3 and g(x) = 4(3sin(1πx - 2) + 3) + 2 between the vertical lines x = 2.0 and x = 2.2. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
0.2
|
math
|
train
| 160,247 |
math_algebra_func_area_level_2_2_183
|
algebra_func_area2
|
medium (level 2,3)
| 2 |
[
{
"content": "Determine the area of the region enclosed by the graphs of f(x) = (1((-1(2x^2 - 5x))/(-3(2x^2 - 5x) + 4)) - 1)/(1((-1(2x^2 - 5x))/(-3(2x^2 - 5x) + 4)) - 3) and g(x) = -1sin(1π(-1x^2 - 3x - 3) - 2) - 1 between the vertical lines x = -0.3 and x = 2.8. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
4.4
|
math
|
train
| 160,248 |
math_algebra_func_area_level_2_2_184
|
algebra_func_area2
|
medium (level 2,3)
| 2 |
[
{
"content": "Calculate the area enclosed between the functions f(x) = -2|(-3sin(2π(2|x + 3| - 1)) + 1)| - 3 and g(x) = (1(-3|x + 1| + 1) + 2)/(-3(-3|x + 1| + 1) - 2) from x = -1.5 to x = -0.5. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
6.0
|
math
|
train
| 160,249 |
math_algebra_func_area_level_2_2_185
|
algebra_func_area2
|
medium (level 2,3)
| 2 |
[
{
"content": "Find the area of the region bounded by the curves f(x) = -1(-2|(3|x - 2| + 1) - 3| - 2) - 2, g(x) = 2(-5x - 5)^2 + 4(-5x - 5) - 1, x = -1.4, and x = -0.3. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
12.0
|
math
|
train
| 160,250 |
math_algebra_func_area_level_2_2_186
|
algebra_func_area2
|
medium (level 2,3)
| 2 |
[
{
"content": "Determine the area of the region enclosed by the graphs of f(x) = -1(1(-1e^(2x) + 1) + 5) + 2 and g(x) = (1((2x - 1)/(-1x - 2)) - 3)/(2((2x - 1)/(-1x - 2)) - 1) between the vertical lines x = -0.2 and x = 0.9. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
49.3
|
math
|
train
| 160,251 |
math_algebra_func_area_level_2_2_187
|
algebra_func_area2
|
medium (level 2,3)
| 2 |
[
{
"content": "Find the area of the region bounded by the curves f(x) = (-1(-3|((3x + 3)/(3x + 2)) + 3|) - 2)/(-2(-3|((3x + 3)/(3x + 2)) + 3|) - 2), g(x) = 5(-2cos(1πx + 3) + 1) - 1, x = -1.3, and x = -0.8. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
2.5
|
math
|
train
| 160,252 |
math_algebra_func_area_level_2_2_188
|
algebra_func_area2
|
medium (level 2,3)
| 2 |
[
{
"content": "Find the area of the region bounded by the curves f(x) = 1|(-1|(-2x - 5)| + 1) + 3|, g(x) = 2cos(1π(1|x - 3| - 3) + 2), x = -1.5, and x = -1.0. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
0.1
|
math
|
train
| 160,253 |
math_algebra_func_area_level_2_2_189
|
algebra_func_area2
|
medium (level 2,3)
| 2 |
[
{
"content": "Calculate the area enclosed between the functions f(x) = 5((-3(-3sin(3πx + 2) - 3))/(-2(-3sin(3πx + 2) - 3) + 1))^2 - 1 and g(x) = -1(-2sin(2πx + 3) - 3)^2 - 4(-2sin(2πx + 3) - 3) + 4 from x = 1.4 to x = 1.7. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
0.7
|
math
|
train
| 160,254 |
math_algebra_func_area_level_2_2_190
|
algebra_func_area2
|
medium (level 2,3)
| 2 |
[
{
"content": "Determine the area of the region enclosed by the graphs of f(x) = 3sin(2π((1(-5x^2 - 3x - 1))/(1(-5x^2 - 3x - 1) + 2)) - 1) + 1 and g(x) = (-1(-1sin(3πx - 1) - 1) - 3)/(1(-1sin(3πx - 1) - 1) + 1) between the vertical lines x = 0.3 and x = 0.4. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
0.2
|
math
|
train
| 160,255 |
math_algebra_func_area_level_2_2_191
|
algebra_func_area2
|
medium (level 2,3)
| 2 |
[
{
"content": "Find the area of the region bounded by the curves f(x) = -1sin(1π(5(1|x + 2| - 2)^2 - 2(1|x + 2| - 2) - 4) + 2), g(x) = (-1(3|x - 1| + 1) + 1)/(-1(3|x - 1| + 1)), x = 2.8, and x = 2.9. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
0.1
|
math
|
train
| 160,256 |
math_algebra_func_area_level_2_2_192
|
algebra_func_area2
|
medium (level 2,3)
| 2 |
[
{
"content": "Find the area of the region bounded by the curves f(x) = -1cos(1π(-2(-2|x + 3| + 2) - 2)) + 2, g(x) = -3(-2x + 1)^2 - 5(-2x + 1), x = 0.9, and x = 1.1. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
0.1
|
math
|
train
| 160,257 |
math_algebra_func_area_level_2_2_193
|
algebra_func_area2
|
medium (level 2,3)
| 2 |
[
{
"content": "Determine the area of the region enclosed by the graphs of f(x) = 3|(-2|(-3x^2 - 1x + 2) - 2| + 1) + 1| - 3 and g(x) = -2sin(2π(-1x - 3) + 2) - 2 between the vertical lines x = 0.4 and x = 0.6. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
0.2
|
math
|
train
| 160,258 |
math_algebra_func_area_level_2_2_194
|
algebra_func_area2
|
medium (level 2,3)
| 2 |
[
{
"content": "Calculate the area enclosed between the functions f(x) = -3(3(3|x + 1| - 1) - 4) - 4 and g(x) = -5((1x - 1)/(-2x + 1))^2 + 2((1x - 1)/(-2x + 1)) + 3 from x = 0.3 to x = 0.6. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
-10.0
|
math
|
train
| 160,259 |
math_algebra_func_area_level_2_2_195
|
algebra_func_area2
|
medium (level 2,3)
| 2 |
[
{
"content": "Calculate the area enclosed between the functions f(x) = (1((2(-1x^2 - 2) - 2)/(2(-1x^2 - 2) + 3)) - 3)/(-1((2(-1x^2 - 2) - 2)/(2(-1x^2 - 2) + 3)) - 2) and g(x) = 3cos(2π(2x + 5) - 1) - 2 from x = 1.5 to x = 1.6. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
0.0
|
math
|
train
| 160,260 |
math_algebra_func_area_level_2_2_196
|
algebra_func_area2
|
medium (level 2,3)
| 2 |
[
{
"content": "Calculate the area enclosed between the functions f(x) = (2((1(-4x^2 + 4) - 3)/(-2(-4x^2 + 4) - 3)) + 1)/(-2((1(-4x^2 + 4) - 3)/(-2(-4x^2 + 4) - 3)) - 3) and g(x) = (1(-3x^2 - 2x - 4) - 2)/(-2(-3x^2 - 2x - 4) - 1) from x = -1.1 to x = 1.0. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
0.9
|
math
|
train
| 160,261 |
math_algebra_func_area_level_2_2_197
|
algebra_func_area2
|
medium (level 2,3)
| 2 |
[
{
"content": "Find the area of the region bounded by the curves f(x) = 1(-1cos(1π((-2x - 1)/(3x)) - 2) + 1)^2 + 2(-1cos(1π((-2x - 1)/(3x)) - 2) + 1) - 4, g(x) = 1((-2x + 3)/(-2x - 1)) + 5, x = 0.1, and x = 0.2. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
0.3
|
math
|
train
| 160,262 |
math_algebra_func_area_level_2_2_198
|
algebra_func_area2
|
medium (level 2,3)
| 2 |
[
{
"content": "Calculate the area enclosed between the functions f(x) = 5((-1(-2x - 3) + 2)/(1(-2x - 3))) - 4 and g(x) = -4(3cos(3πx - 3) - 1) - 4 from x = 2.3 to x = 2.4. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
0.1
|
math
|
train
| 160,263 |
math_algebra_func_area_level_2_2_199
|
algebra_func_area2
|
medium (level 2,3)
| 2 |
[
{
"content": "Calculate the area enclosed between the functions f(x) = 2|(5(2cos(1πx - 3) + 1) - 2)| - 2 and g(x) = (3(3|x + 2| - 2) - 3)/(1(3|x + 2| - 2) - 3) from x = -1.7 to x = -1.6. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
0.2
|
math
|
train
| 160,264 |
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