id
string | setting_key
string | difficulty
string | level
int32 | messages
dict | ground_truth
string | dataset
string | omega_split
string |
|---|---|---|---|---|---|---|---|
math_algebra_func_area_level_2_2_200
|
algebra_func_area2
|
medium (level 2,3)
| 2 |
{
"role": [
"user"
],
"content": [
"Find the area of the region bounded by the curves f(x) = 1cos(3π(-4(5x + 2)^2 - 5)), g(x) = -3e^(-1((-2x - 3)/(1x + 3))) + 2, x = -1.7, and x = -1.5999999999999999. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
0.1
|
math
|
train
|
math_algebra_func_area_level_2_2_201
|
algebra_func_area2
|
medium (level 2,3)
| 2 |
{
"role": [
"user"
],
"content": [
"Determine the area of the region enclosed by the graphs of f(x) = -3sin(1π(-2((1x - 2)/(-2x)) + 5) + 2) + 1 and g(x) = -1(-3x - 1) + 3 between the vertical lines x = -0.1 and x = 0.0. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
0.3
|
math
|
train
|
math_algebra_func_area_level_2_2_202
|
algebra_func_area2
|
medium (level 2,3)
| 2 |
{
"role": [
"user"
],
"content": [
"Find the area of the region bounded by the curves f(x) = 1|(-1(1x - 4) + 4) + 2| + 1, g(x) = 3(1cos(2πx - 1)) + 4, x = 4.1, and x = 4.2. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
0.0
|
math
|
train
|
math_algebra_func_area_level_2_2_203
|
algebra_func_area2
|
medium (level 2,3)
| 2 |
{
"role": [
"user"
],
"content": [
"Find the area of the region bounded by the curves f(x) = 3cos(3π((-2(1x^2 + 4x - 3) + 3)/(1(1x^2 + 4x - 3) + 3)) - 1) + 1, g(x) = 1(2|x + 3| + 2) + 1, x = -3.1, and x = -2.8. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
0.9
|
math
|
train
|
math_algebra_func_area_level_2_2_204
|
algebra_func_area2
|
medium (level 2,3)
| 2 |
{
"role": [
"user"
],
"content": [
"Find the area of the region bounded by the curves f(x) = -2cos(2π((-3(5x + 5) + 2)/(2(5x + 5) + 2)) + 1), g(x) = 3cos(1π(1|x - 1| + 2) - 3) - 3, x = 3.9, and x = 4.0. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
0.0
|
math
|
train
|
math_algebra_func_area_level_2_2_205
|
algebra_func_area2
|
medium (level 2,3)
| 2 |
{
"role": [
"user"
],
"content": [
"Determine the area of the region enclosed by the graphs of f(x) = -1((-2(1|x + 2|) + 3)/(1(1|x + 2|) + 2))^2 + 3((-2(1|x + 2|) + 3)/(1(1|x + 2|) + 2)) + 3 and g(x) = 2|(2|x| + 3) - 3| - 3 between the vertical lines x = -2.1 and x = 1.0. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
8.2
|
math
|
train
|
math_algebra_func_area_level_2_2_206
|
algebra_func_area2
|
medium (level 2,3)
| 2 |
{
"role": [
"user"
],
"content": [
"Find the area of the region bounded by the curves f(x) = -1cos(1π(3(-2x^2 + 2x - 3) - 4) - 2) - 3, g(x) = (1(3sin(2πx) + 2) - 3)/(3(3sin(2πx) + 2) + 2), x = -2.4, and x = -2.2. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
4.3
|
math
|
train
|
math_algebra_func_area_level_2_2_207
|
algebra_func_area2
|
medium (level 2,3)
| 2 |
{
"role": [
"user"
],
"content": [
"Find the area of the region bounded by the curves f(x) = (-2(-1(-4x^2 - 1x - 4) + 4))/(-2(-1(-4x^2 - 1x - 4) + 4) - 3), g(x) = 3cos(1π(5x + 4) - 3) - 2, x = 1.8, and x = 2.2. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
1.2
|
math
|
train
|
math_algebra_func_area_level_2_2_208
|
algebra_func_area2
|
medium (level 2,3)
| 2 |
{
"role": [
"user"
],
"content": [
"Calculate the area enclosed between the functions f(x) = 5(5(2|x + 2| - 3)^2 - 5)^2 - 5 and g(x) = 1(-2|x - 1|) + 4 from x = -3.0 to x = -2.9. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
0.7
|
math
|
train
|
math_algebra_func_area_level_2_2_209
|
algebra_func_area2
|
medium (level 2,3)
| 2 |
{
"role": [
"user"
],
"content": [
"Determine the area of the region enclosed by the graphs of f(x) = (-2(5(-4x + 2)^2 + 3(-4x + 2) - 2) - 2)/(-2(5(-4x + 2)^2 + 3(-4x + 2) - 2) + 3) and g(x) = (1(2sin(1πx - 2) - 1) - 2)/(2(2sin(1πx - 2) - 1) - 1) between the vertical lines x = 2.6 and x = 3.6. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
9.5
|
math
|
train
|
math_algebra_func_area_level_2_2_210
|
algebra_func_area2
|
medium (level 2,3)
| 2 |
{
"role": [
"user"
],
"content": [
"Determine the area of the region enclosed by the graphs of f(x) = -3(2(-1x - 1) + 5) + 4 and g(x) = -2(-1cos(1πx - 2) - 2)^2 + 5(-1cos(1πx - 2) - 2) - 5 between the vertical lines x = -2.8 and x = -2.0. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
4.0
|
math
|
train
|
math_algebra_func_area_level_2_2_211
|
algebra_func_area2
|
medium (level 2,3)
| 2 |
{
"role": [
"user"
],
"content": [
"Find the area of the region bounded by the curves f(x) = 3sin(3π(-3(1|x - 2| + 1)^2 + 5(1|x - 2| + 1) + 1) + 3) + 2, g(x) = (-1(-1cos(3πx + 2)) - 3)/(-3(-1cos(3πx + 2)) - 3), x = -4.4, and x = -4.300000000000001. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
0.2
|
math
|
train
|
math_algebra_func_area_level_2_2_212
|
algebra_func_area2
|
medium (level 2,3)
| 2 |
{
"role": [
"user"
],
"content": [
"Find the area of the region bounded by the curves f(x) = 4(2((-3x + 1)/(1x + 1))^2 - 1((-3x + 1)/(1x + 1)) - 4) - 3, g(x) = -1(2|x - 2|) + 4, x = -0.2, and x = 1.6. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
20.1
|
math
|
train
|
math_algebra_func_area_level_2_2_213
|
algebra_func_area2
|
medium (level 2,3)
| 2 |
{
"role": [
"user"
],
"content": [
"Determine the area of the region enclosed by the graphs of f(x) = (1(2sin(1π(-2|x - 3| + 1) - 3) + 1) - 3)/(-3(2sin(1π(-2|x - 3| + 1) - 3) + 1) - 2) and g(x) = 3e^(-2((-3x + 1)/(-1x + 3))) - 3 between the vertical lines x = 0.3 and x = 0.6. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
0.2
|
math
|
train
|
math_algebra_func_area_level_2_2_214
|
algebra_func_area2
|
medium (level 2,3)
| 2 |
{
"role": [
"user"
],
"content": [
"Calculate the area enclosed between the functions f(x) = -2e^(2((-1((-2x - 3)/(-2x - 2)) + 3)/(3((-2x - 3)/(-2x - 2)) - 2))) + 1 and g(x) = 1|(-1e^(-1x) + 2)| - 3 from x = -1.8 to x = -0.4. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
2.1
|
math
|
train
|
math_algebra_func_area_level_2_2_215
|
algebra_func_area2
|
medium (level 2,3)
| 2 |
{
"role": [
"user"
],
"content": [
"Calculate the area enclosed between the functions f(x) = (1(1(-1|x + 1| + 3)^2 + 1(-1|x + 1| + 3) - 5) - 2)/(-3(1(-1|x + 1| + 3)^2 + 1(-1|x + 1| + 3) - 5) - 1) and g(x) = -2e^(-1(5x + 3)) - 1 from x = 0.6 to x = 4.4. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
1.6
|
math
|
train
|
math_algebra_func_area_level_2_2_216
|
algebra_func_area2
|
medium (level 2,3)
| 2 |
{
"role": [
"user"
],
"content": [
"Calculate the area enclosed between the functions f(x) = (2(-2sin(1π(-4x^2 + 1x - 2) - 2) + 1) - 1)/(1(-2sin(1π(-4x^2 + 1x - 2) - 2) + 1) + 3) and g(x) = (2(3x) + 1)/(3(3x) - 1) from x = 3.4 to x = 3.5. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
0.1
|
math
|
train
|
math_algebra_func_area_level_2_2_217
|
algebra_func_area2
|
medium (level 2,3)
| 2 |
{
"role": [
"user"
],
"content": [
"Calculate the area enclosed between the functions f(x) = -2sin(2π(1(3|x| - 2)^2 + 2(3|x| - 2) + 4) - 3) + 2 and g(x) = 2e^(-1(-3x^2 + 1x + 4)) + 2 from x = 1.1 to x = 1.2. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
0.1
|
math
|
train
|
math_algebra_func_area_level_2_2_218
|
algebra_func_area2
|
medium (level 2,3)
| 2 |
{
"role": [
"user"
],
"content": [
"Find the area of the region bounded by the curves f(x) = (-1((1(2e^(1x) - 2) + 3)/(1(2e^(1x) - 2))) - 1)/(2((1(2e^(1x) - 2) + 3)/(1(2e^(1x) - 2))) + 3), g(x) = 2|(3cos(2πx + 3) - 3) + 3| - 3, x = -1.1, and x = -1.0. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
0.1
|
math
|
train
|
math_algebra_func_area_level_2_2_219
|
algebra_func_area2
|
medium (level 2,3)
| 2 |
{
"role": [
"user"
],
"content": [
"Find the area of the region bounded by the curves f(x) = 3|(-5(5x + 3)^2 + 2(5x + 3) + 4)| - 3, g(x) = 1(4x + 2), x = -0.8, and x = -0.7. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
0.2
|
math
|
train
|
math_algebra_func_area_level_2_2_220
|
algebra_func_area2
|
medium (level 2,3)
| 2 |
{
"role": [
"user"
],
"content": [
"Calculate the area enclosed between the functions f(x) = -4((-3(1x) - 3)/(2(1x) - 1))^2 + 3((-3(1x) - 3)/(2(1x) - 1)) + 3 and g(x) = 2cos(2π(-2|x + 2| + 3) - 2) from x = -1.8 to x = -1.6. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
0.2
|
math
|
train
|
math_algebra_func_area_level_2_2_221
|
algebra_func_area2
|
medium (level 2,3)
| 2 |
{
"role": [
"user"
],
"content": [
"Find the area of the region bounded by the curves f(x) = (-2(-5(1x^2 + 1x)^2 - 3(1x^2 + 1x) + 5))/(2(-5(1x^2 + 1x)^2 - 3(1x^2 + 1x) + 5) - 1), g(x) = -3(1cos(2πx + 3) + 2)^2 + 1, x = -1.5, and x = 0.5. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
23.6
|
math
|
train
|
math_algebra_func_area_level_2_2_222
|
algebra_func_area2
|
medium (level 2,3)
| 2 |
{
"role": [
"user"
],
"content": [
"Calculate the area enclosed between the functions f(x) = -2sin(1π(3(-3x)^2 - 5(-3x) + 5) + 2) + 3 and g(x) = 2((1x + 2)/(-3x)) - 1 from x = -0.4 to x = -0.2. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
0.3
|
math
|
train
|
math_algebra_func_area_level_2_2_223
|
algebra_func_area2
|
medium (level 2,3)
| 2 |
{
"role": [
"user"
],
"content": [
"Find the area of the region bounded by the curves f(x) = 3cos(1π(-2(2|x - 1| - 2) - 1) + 3) - 1, g(x) = -4(-2e^(1x) + 2) + 3, x = -0.8, and x = -0.6. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
0.4
|
math
|
train
|
math_algebra_func_area_level_2_2_224
|
algebra_func_area2
|
medium (level 2,3)
| 2 |
{
"role": [
"user"
],
"content": [
"Determine the area of the region enclosed by the graphs of f(x) = (1(-2|((-2x + 1)/(-2x - 3)) - 2| + 2) - 3)/(-3(-2|((-2x + 1)/(-2x - 3)) - 2| + 2) + 1) and g(x) = 1(-3sin(1πx + 1) + 1)^2 + 2(-3sin(1πx + 1) + 1) - 2 between the vertical lines x = 2.6 and x = 3.8. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
14.4
|
math
|
train
|
math_algebra_func_area_level_2_2_225
|
algebra_func_area2
|
medium (level 2,3)
| 2 |
{
"role": [
"user"
],
"content": [
"Determine the area of the region enclosed by the graphs of f(x) = -1sin(2π(3((1x + 3)/(3x + 3))) + 2) + 2 and g(x) = 3cos(1π(2|x - 1| + 1) - 2) + 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}"
]
}
|
0.1
|
math
|
train
|
math_algebra_func_area_level_2_2_226
|
algebra_func_area2
|
medium (level 2,3)
| 2 |
{
"role": [
"user"
],
"content": [
"Determine the area of the region enclosed by the graphs of f(x) = 3cos(3π(5(-2x^2 + 1x + 2) + 3) - 3) - 2 and g(x) = (1(3x + 1) - 2)/(-2(3x + 1) - 3) between the vertical lines x = -3.4 and x = -3.3. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
0.2
|
math
|
train
|
math_algebra_func_area_level_2_2_227
|
algebra_func_area2
|
medium (level 2,3)
| 2 |
{
"role": [
"user"
],
"content": [
"Determine the area of the region enclosed by the graphs of f(x) = -2cos(3π(2|(3|x - 3| - 3) + 2| + 3) - 3) - 3 and g(x) = (1(-1|x + 3| + 2) - 1)/(2(-1|x + 3| + 2) - 1) between the vertical lines x = -1.6 and x = -1.5. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
5.3
|
math
|
train
|
math_algebra_func_area_level_2_2_228
|
algebra_func_area2
|
medium (level 2,3)
| 2 |
{
"role": [
"user"
],
"content": [
"Determine the area of the region enclosed by the graphs of f(x) = -1|(-1(5x - 5)^2 - 1(5x - 5) - 3) + 3| + 1 and g(x) = -1|(2e^(-1x) + 3) + 1| - 1 between the vertical lines x = 0.4 and x = 1.4. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
4.9
|
math
|
train
|
math_algebra_func_area_level_2_2_229
|
algebra_func_area2
|
medium (level 2,3)
| 2 |
{
"role": [
"user"
],
"content": [
"Determine the area of the region enclosed by the graphs of f(x) = (-2(5(-3|x - 3| - 3) - 5) - 2)/(3(5(-3|x - 3| - 3) - 5) - 2) and g(x) = (3(5x^2 + 4x - 5) - 3)/(3(5x^2 + 4x - 5) - 2) between the vertical lines x = -1.6 and x = 0.8. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
4.9
|
math
|
train
|
math_algebra_func_area_level_2_2_230
|
algebra_func_area2
|
medium (level 2,3)
| 2 |
{
"role": [
"user"
],
"content": [
"Find the area of the region bounded by the curves f(x) = -1(-1|(1|x + 2| + 2) - 2| + 2)^2 + 4(-1|(1|x + 2| + 2) - 2| + 2) - 1, g(x) = (-1(-1|x| + 2) - 1)/(3(-1|x| + 2) + 2), x = -3.8, and x = -2.7. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
1.4
|
math
|
train
|
math_algebra_func_area_level_2_2_231
|
algebra_func_area2
|
medium (level 2,3)
| 2 |
{
"role": [
"user"
],
"content": [
"Calculate the area enclosed between the functions f(x) = 3e^(-2(2(-3x + 1) + 2)) - 3 and g(x) = -3(-2|x + 3| - 1)^2 - 3(-2|x + 3| - 1) + 1 from x = -3.4 to x = -2.6. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
1.7
|
math
|
train
|
math_algebra_func_area_level_2_2_232
|
algebra_func_area2
|
medium (level 2,3)
| 2 |
{
"role": [
"user"
],
"content": [
"Calculate the area enclosed between the functions f(x) = -1cos(1π(-2((1x + 1)/(3x + 2))^2 - 4((1x + 1)/(3x + 2)) - 2) - 2) + 3 and g(x) = (-1(-2cos(1πx - 3) - 1) + 3)/(3(-2cos(1πx - 3) - 1) + 3) from x = -2.5 to x = -1.6. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
1.4
|
math
|
train
|
math_algebra_func_area_level_2_2_233
|
algebra_func_area2
|
medium (level 2,3)
| 2 |
{
"role": [
"user"
],
"content": [
"Calculate the area enclosed between the functions f(x) = 4(-3cos(1π((-3x - 2)/(-1x - 2)) - 3) - 3)^2 + 1(-3cos(1π((-3x - 2)/(-1x - 2)) - 3) - 3) - 3 and g(x) = -1cos(2π(2|x - 1| + 2)) + 2 from x = -1.9 to x = -1.7999999999999998. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
4.9
|
math
|
train
|
math_algebra_func_area_level_2_2_234
|
algebra_func_area2
|
medium (level 2,3)
| 2 |
{
"role": [
"user"
],
"content": [
"Find the area of the region bounded by the curves f(x) = -2cos(1π(-3((-3x + 2)/(-3x + 1)) + 3)) + 3, g(x) = 1|(3x - 1) - 1| - 1, x = -0.1, and x = 2.1. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
6.1
|
math
|
train
|
math_algebra_func_area_level_2_2_235
|
algebra_func_area2
|
medium (level 2,3)
| 2 |
{
"role": [
"user"
],
"content": [
"Calculate the area enclosed between the functions f(x) = -4((2(-3|x - 3| - 1))/(-2(-3|x - 3| - 1) - 1)) - 4 and g(x) = (1(-3cos(1πx - 1) - 2) - 3)/(-3(-3cos(1πx - 1) - 2) - 2) from x = 3.0 to x = 3.5. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
0.5
|
math
|
train
|
math_algebra_func_area_level_2_2_236
|
algebra_func_area2
|
medium (level 2,3)
| 2 |
{
"role": [
"user"
],
"content": [
"Find the area of the region bounded by the curves f(x) = 1(5(1x^2 - 3) - 4) + 3, g(x) = -2e^(-1(-5x^2 + 4x + 1)) - 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}"
]
}
|
17.2
|
math
|
train
|
math_algebra_func_area_level_2_2_237
|
algebra_func_area2
|
medium (level 2,3)
| 2 |
{
"role": [
"user"
],
"content": [
"Find the area of the region bounded by the curves f(x) = 1e^(2(-3(3|x - 2| + 2) - 3)) + 2, g(x) = -1(-3x)^2 + 4, x = -0.5, and x = 0.5. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
1.3
|
math
|
train
|
math_algebra_func_area_level_2_2_238
|
algebra_func_area2
|
medium (level 2,3)
| 2 |
{
"role": [
"user"
],
"content": [
"Calculate the area enclosed between the functions f(x) = (-2((-3(4x + 4) - 2)/(1(4x + 4) + 2)) + 3)/(-3((-3(4x + 4) - 2)/(1(4x + 4) + 2)) - 2) and g(x) = 2(2x - 4) from x = -1.1 to x = 2.3. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
27.6
|
math
|
train
|
math_algebra_func_area_level_2_2_239
|
algebra_func_area2
|
medium (level 2,3)
| 2 |
{
"role": [
"user"
],
"content": [
"Find the area of the region bounded by the curves f(x) = 5(3(-1cos(1πx + 2))^2 + 2(-1cos(1πx + 2)) - 1) - 5, g(x) = -2e^(-2(3x - 5)) - 1, x = 4.0, and x = 4.7. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
6.6
|
math
|
train
|
math_algebra_func_area_level_2_2_240
|
algebra_func_area2
|
medium (level 2,3)
| 2 |
{
"role": [
"user"
],
"content": [
"Calculate the area enclosed between the functions f(x) = 2|(1|(-1x^2)| - 2) - 2| and g(x) = -3(-3cos(3πx - 2)) + 5 from x = -1.3 to x = -1.0. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
1.7
|
math
|
train
|
math_algebra_func_area_level_2_2_241
|
algebra_func_area2
|
medium (level 2,3)
| 2 |
{
"role": [
"user"
],
"content": [
"Find the area of the region bounded by the curves f(x) = 1|(4(2|x| - 1)^2 + 1(2|x| - 1) - 5) - 3| + 1, g(x) = 2sin(3π(-1|x - 2| + 3) + 3) + 2, x = -1.2, and x = -1.0. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
0.3
|
math
|
train
|
math_algebra_func_area_level_2_2_242
|
algebra_func_area2
|
medium (level 2,3)
| 2 |
{
"role": [
"user"
],
"content": [
"Determine the area of the region enclosed by the graphs of f(x) = (-1(1((3x + 2)/(2x + 2)) + 5) + 2)/(1(1((3x + 2)/(2x + 2)) + 5) + 3) and g(x) = 1sin(2π(-4x^2 + 5x - 5) - 3) between the vertical lines x = 4.8 and x = 4.8999999999999995. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
0.1
|
math
|
train
|
math_algebra_func_area_level_2_2_243
|
algebra_func_area2
|
medium (level 2,3)
| 2 |
{
"role": [
"user"
],
"content": [
"Determine the area of the region enclosed by the graphs of f(x) = 1(1((3x - 3)/(3x + 1))^2 - 3((3x - 3)/(3x + 1)) + 5)^2 - 3(1((3x - 3)/(3x + 1))^2 - 3((3x - 3)/(3x + 1)) + 5) + 1 and g(x) = -3|(1x - 2) - 2| + 3 between the vertical lines x = 3.8 and x = 4.2. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
0.1
|
math
|
train
|
math_algebra_func_area_level_2_2_244
|
algebra_func_area2
|
medium (level 2,3)
| 2 |
{
"role": [
"user"
],
"content": [
"Determine the area of the region enclosed by the graphs of f(x) = (-2((-2(3e^(-1x) - 1) - 3)/(-3(3e^(-1x) - 1) - 3)) + 2)/(3((-2(3e^(-1x) - 1) - 3)/(-3(3e^(-1x) - 1) - 3)) + 1) and g(x) = 2sin(3π(1|x| - 3) - 2) between the vertical lines x = 1.9 and x = 2.2. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
0.5
|
math
|
train
|
math_algebra_func_area_level_2_2_245
|
algebra_func_area2
|
medium (level 2,3)
| 2 |
{
"role": [
"user"
],
"content": [
"Calculate the area enclosed between the functions f(x) = -2((-1(5x - 2) - 2)/(1(5x - 2) + 3))^2 + 1((-1(5x - 2) - 2)/(1(5x - 2) + 3)) - 1 and g(x) = 2cos(3π(-3x^2 + 5x - 5) + 3) - 3 from x = -4.4 to x = -4.300000000000001. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
0.2
|
math
|
train
|
math_algebra_func_area_level_2_2_246
|
algebra_func_area2
|
medium (level 2,3)
| 2 |
{
"role": [
"user"
],
"content": [
"Calculate the area enclosed between the functions f(x) = -2sin(2π((-3(-1x - 3) - 3)/(1(-1x - 3) + 3)) - 3) and g(x) = -3cos(1π(2x + 5) + 2) from x = -0.1 to x = 0.0. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
0.1
|
math
|
train
|
math_algebra_func_area_level_2_2_247
|
algebra_func_area2
|
medium (level 2,3)
| 2 |
{
"role": [
"user"
],
"content": [
"Calculate the area enclosed between the functions f(x) = 5((-2(2cos(2πx + 1)) - 1)/(-2(2cos(2πx + 1)) - 2))^2 - 1((-2(2cos(2πx + 1)) - 1)/(-2(2cos(2πx + 1)) - 2)) + 1 and g(x) = 2(-2e^(-1x) + 2) + 1 from x = 2.2 to x = 2.5. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
4.6
|
math
|
train
|
math_algebra_func_area_level_2_2_248
|
algebra_func_area2
|
medium (level 2,3)
| 2 |
{
"role": [
"user"
],
"content": [
"Find the area of the region bounded by the curves f(x) = 3|(1((1x)/(-1x + 2)) + 5) + 3|, g(x) = 5(1sin(2πx - 1) + 1)^2 + 3(1sin(2πx - 1) + 1), x = 2.2, and x = 2.6. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
5.9
|
math
|
train
|
math_algebra_func_area_level_2_2_249
|
algebra_func_area2
|
medium (level 2,3)
| 2 |
{
"role": [
"user"
],
"content": [
"Calculate the area enclosed between the functions f(x) = (-1(-3|(3sin(1πx - 1) - 2) + 2| + 2) - 1)/(-2(-3|(3sin(1πx - 1) - 2) + 2| + 2) + 3) and g(x) = -1(-5x^2 - 5) + 2 from x = 2.3 to x = 3.3. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
47.3
|
math
|
train
|
math_algebra_func_area_level_2_2_250
|
algebra_func_area2
|
medium (level 2,3)
| 2 |
{
"role": [
"user"
],
"content": [
"Calculate the area enclosed between the functions f(x) = -3|(3(1x - 5) + 3) + 1| + 2 and g(x) = -1|(-3sin(2πx + 2) - 1) + 1| + 3 from x = 3.4 to x = 3.6. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
0.0
|
math
|
train
|
math_algebra_func_area_level_2_2_251
|
algebra_func_area2
|
medium (level 2,3)
| 2 |
{
"role": [
"user"
],
"content": [
"Determine the area of the region enclosed by the graphs of f(x) = 2(-1(1e^(-2x)) + 2)^2 + 5(-1(1e^(-2x)) + 2) - 4 and g(x) = -5((-3x - 2)/(-3x + 4))^2 - 3((-3x - 2)/(-3x + 4)) - 4 between the vertical lines x = -0.8 and x = -0.3. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
1.0
|
math
|
train
|
math_algebra_func_area_level_2_2_252
|
algebra_func_area2
|
medium (level 2,3)
| 2 |
{
"role": [
"user"
],
"content": [
"Find the area of the region bounded by the curves f(x) = -1((-2(-1x^2 + 2) - 3)/(-1(-1x^2 + 2) + 3)) - 4, g(x) = 2|(5x^2 + 5x - 2) + 3| - 3, x = -1.0, and x = 0.3. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
4.1
|
math
|
train
|
math_algebra_func_area_level_2_2_253
|
algebra_func_area2
|
medium (level 2,3)
| 2 |
{
"role": [
"user"
],
"content": [
"Determine the area of the region enclosed by the graphs of f(x) = -2(-1((-3x - 2)/(2x + 3)) + 2)^2 - 3(-1((-3x - 2)/(2x + 3)) + 2) - 2 and g(x) = -4(4x^2 - 1x - 5) - 3 between the vertical lines x = -1.0 and x = 1.9. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
84.6
|
math
|
train
|
math_algebra_func_area_level_2_2_254
|
algebra_func_area2
|
medium (level 2,3)
| 2 |
{
"role": [
"user"
],
"content": [
"Determine the area of the region enclosed by the graphs of f(x) = 4(-3(1cos(1πx - 2) + 2)^2 + 5) and g(x) = 2|(-1|x - 3| + 3) + 1| between the vertical lines x = -4.2 and x = -2.6. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
78.2
|
math
|
train
|
math_algebra_func_area_level_2_2_255
|
algebra_func_area2
|
medium (level 2,3)
| 2 |
{
"role": [
"user"
],
"content": [
"Determine the area of the region enclosed by the graphs of f(x) = (-1(-3sin(2π(-2x^2 - 4x + 5) + 2)) + 3)/(-2(-3sin(2π(-2x^2 - 4x + 5) + 2)) + 3) and g(x) = -3sin(3π(1x^2 + 1x - 4) - 1) - 3 between the vertical lines x = -4.8 and x = -4.7. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
0.5
|
math
|
train
|
math_algebra_func_area_level_2_2_256
|
algebra_func_area2
|
medium (level 2,3)
| 2 |
{
"role": [
"user"
],
"content": [
"Determine the area of the region enclosed by the graphs of f(x) = (1(2cos(1π((-2x - 1)/(-3x + 2)) + 2) + 1) - 2)/(-2(2cos(1π((-2x - 1)/(-3x + 2)) + 2) + 1) - 1) and g(x) = (-2(2|x + 1| - 2) + 2)/(-2(2|x + 1| - 2)) between the vertical lines x = 0.8 and x = 0.9. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
1.4
|
math
|
train
|
math_algebra_func_area_level_2_2_257
|
algebra_func_area2
|
medium (level 2,3)
| 2 |
{
"role": [
"user"
],
"content": [
"Find the area of the region bounded by the curves f(x) = (2(-3((-1x + 1)/(1x + 3)) - 4) + 2)/(-2(-3((-1x + 1)/(1x + 3)) - 4) + 1), g(x) = -5(-3sin(1πx) - 2)^2 + 4(-3sin(1πx) - 2) + 3, x = -0.2, and x = 1.2. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
96.0
|
math
|
train
|
math_algebra_func_area_level_2_2_258
|
algebra_func_area2
|
medium (level 2,3)
| 2 |
{
"role": [
"user"
],
"content": [
"Calculate the area enclosed between the functions f(x) = -2(-5(-1sin(1πx - 1) + 3) - 3) + 3 and g(x) = 3|(-2x^2 + 2x - 4) - 1| + 1 from x = -1.1 to x = 2.4. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
67.7
|
math
|
train
|
math_algebra_func_area_level_2_2_259
|
algebra_func_area2
|
medium (level 2,3)
| 2 |
{
"role": [
"user"
],
"content": [
"Find the area of the region bounded by the curves f(x) = 1(2(2e^(-2x) + 1) - 5) + 1, g(x) = -4(1cos(1πx - 3))^2 + 4(1cos(1πx - 3)), x = 2.3, and x = 3.6. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
2.8
|
math
|
train
|
math_algebra_func_area_level_2_2_260
|
algebra_func_area2
|
medium (level 2,3)
| 2 |
{
"role": [
"user"
],
"content": [
"Calculate the area enclosed between the functions f(x) = 3(-3|((-2x - 2)/(-3x + 1)) + 2|)^2 + 4(-3|((-2x - 2)/(-3x + 1)) + 2|) - 5 and g(x) = -3e^(-1(3|x + 3| - 3)) from x = -0.1 to x = 0.1. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
1.1
|
math
|
train
|
math_algebra_func_area_level_2_2_261
|
algebra_func_area2
|
medium (level 2,3)
| 2 |
{
"role": [
"user"
],
"content": [
"Determine the area of the region enclosed by the graphs of f(x) = -1(-2cos(3π((-1x - 2)/(1x)) - 3) - 3)^2 + 3(-2cos(3π((-1x - 2)/(1x)) - 3) - 3) - 2 and g(x) = 1(-2x^2 + 2x - 1) + 5 between the vertical lines x = -3.7 and x = -2.3. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
18.9
|
math
|
train
|
math_algebra_func_area_level_2_2_262
|
algebra_func_area2
|
medium (level 2,3)
| 2 |
{
"role": [
"user"
],
"content": [
"Find the area of the region bounded by the curves f(x) = (1(-5(3sin(2πx + 3) + 2) - 4))/(2(-5(3sin(2πx + 3) + 2) - 4) + 2), g(x) = 2(1|x + 2|)^2 - 2(1|x + 2|) - 3, x = 1.2, and x = 3.4. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
56.9
|
math
|
train
|
math_algebra_func_area_level_2_2_263
|
algebra_func_area2
|
medium (level 2,3)
| 2 |
{
"role": [
"user"
],
"content": [
"Find the area of the region bounded by the curves f(x) = (-1(-2(-3|x - 1| + 2)^2 - 5(-3|x - 1| + 2) - 1) - 3)/(2(-2(-3|x - 1| + 2)^2 - 5(-3|x - 1| + 2) - 1) + 3), g(x) = (-1(4x - 2) - 3)/(-3(4x - 2) + 1), x = 1.6, and x = 2.6. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
3.1
|
math
|
train
|
math_algebra_func_area_level_2_2_264
|
algebra_func_area2
|
medium (level 2,3)
| 2 |
{
"role": [
"user"
],
"content": [
"Calculate the area enclosed between the functions f(x) = 1sin(1π((3(1|x + 1| + 3) + 2)/(-2(1|x + 1| + 3) + 3)) - 3) - 1 and g(x) = -3|((1x)/(-1x + 2)) + 2| - 1 from x = 3.9 to x = 4.1. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
0.0
|
math
|
train
|
math_algebra_func_area_level_2_2_265
|
algebra_func_area2
|
medium (level 2,3)
| 2 |
{
"role": [
"user"
],
"content": [
"Calculate the area enclosed between the functions f(x) = -4(3cos(2π(4x - 1) - 1) - 1)^2 - 4(3cos(2π(4x - 1) - 1) - 1) + 1 and g(x) = 5(4x + 2) - 2 from x = -2.1 to x = -1.9. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
3.8
|
math
|
train
|
math_algebra_func_area_level_2_2_266
|
algebra_func_area2
|
medium (level 2,3)
| 2 |
{
"role": [
"user"
],
"content": [
"Calculate the area enclosed between the functions f(x) = 3sin(1π(-4(-1x^2 + 3x + 2) - 3) + 3) and g(x) = 1e^(2(-4x - 3)) from x = 4.3 to x = 4.3999999999999995. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
0.2
|
math
|
train
|
math_algebra_func_area_level_2_2_267
|
algebra_func_area2
|
medium (level 2,3)
| 2 |
{
"role": [
"user"
],
"content": [
"Determine the area of the region enclosed by the graphs of f(x) = 4(3cos(2π(-1x^2 - 4x) + 1) + 1)^2 - 4(3cos(2π(-1x^2 - 4x) + 1) + 1) - 5 and g(x) = (3(2e^(1x) + 2))/(-1(2e^(1x) + 2) + 3) between the vertical lines x = 3.4 and x = 3.5. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
1.9
|
math
|
train
|
math_algebra_func_area_level_2_2_268
|
algebra_func_area2
|
medium (level 2,3)
| 2 |
{
"role": [
"user"
],
"content": [
"Calculate the area enclosed between the functions f(x) = -2(-3|(3|x + 2| - 2) - 3| + 2) + 1 and g(x) = -3(-3|x + 1| - 1) - 4 from x = -0.6 to x = 0.6. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
4.7
|
math
|
train
|
math_algebra_func_area_level_2_2_269
|
algebra_func_area2
|
medium (level 2,3)
| 2 |
{
"role": [
"user"
],
"content": [
"Calculate the area enclosed between the functions f(x) = 2e^(2((-1(-5x^2 + 2x - 5) - 2)/(-1(-5x^2 + 2x - 5) + 2))) - 2 and g(x) = 2|(-4x^2 - 4x + 2) + 1| - 3 from x = -2.1 to x = -0.6. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
7.7
|
math
|
train
|
math_algebra_func_area_level_2_2_270
|
algebra_func_area2
|
medium (level 2,3)
| 2 |
{
"role": [
"user"
],
"content": [
"Determine the area of the region enclosed by the graphs of f(x) = -1cos(2π(-3(2|x + 3| - 1)^2 + 3(2|x + 3| - 1)) + 2) + 2 and g(x) = (2(-3e^(1x) - 3) + 3)/(1(-3e^(1x) - 3)) between the vertical lines x = 0.5 and x = 0.6. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
0.1
|
math
|
train
|
math_algebra_func_area_level_2_2_271
|
algebra_func_area2
|
medium (level 2,3)
| 2 |
{
"role": [
"user"
],
"content": [
"Determine the area of the region enclosed by the graphs of f(x) = 1|(-3e^(1(-5x + 1)) + 1) + 2| + 2 and g(x) = 5(2sin(2πx + 1)) + 4 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}"
]
}
|
3.8
|
math
|
train
|
math_algebra_func_area_level_2_2_272
|
algebra_func_area2
|
medium (level 2,3)
| 2 |
{
"role": [
"user"
],
"content": [
"Calculate the area enclosed between the functions f(x) = 5(2((-2x + 2)/(-2x - 2))) - 4 and g(x) = (1(-3x^2 + 2x + 2))/(2(-3x^2 + 2x + 2) - 1) from x = -0.4 to x = 1.1. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
17.2
|
math
|
train
|
math_algebra_func_area_level_2_2_273
|
algebra_func_area2
|
medium (level 2,3)
| 2 |
{
"role": [
"user"
],
"content": [
"Calculate the area enclosed between the functions f(x) = (-1(1|(1x - 5) - 3| - 1) + 2)/(-1(1|(1x - 5) - 3| - 1)) and g(x) = -1(2|x + 1| - 3) + 2 from x = -3.1 to x = 1.2. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
9.1
|
math
|
train
|
math_algebra_func_area_level_2_2_274
|
algebra_func_area2
|
medium (level 2,3)
| 2 |
{
"role": [
"user"
],
"content": [
"Determine the area of the region enclosed by the graphs of f(x) = -3|(-2|(-2cos(3πx - 2) + 1) - 3| + 2) - 1| + 1 and g(x) = -5(1|x - 1| - 3) + 1 between the vertical lines x = -4.3 and x = -4.0. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
2.3
|
math
|
train
|
math_algebra_func_area_level_2_2_275
|
algebra_func_area2
|
medium (level 2,3)
| 2 |
{
"role": [
"user"
],
"content": [
"Determine the area of the region enclosed by the graphs of f(x) = -2e^(-1(-1((3x)/(-3x - 2))^2 - 1((3x)/(-3x - 2)) - 5)) - 3 and g(x) = -1((3x + 3)/(2x - 1))^2 - 4((3x + 3)/(2x - 1)) - 4 between the vertical lines x = 0.4 and x = 0.7. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
-131.7
|
math
|
train
|
math_algebra_func_area_level_2_2_276
|
algebra_func_area2
|
medium (level 2,3)
| 2 |
{
"role": [
"user"
],
"content": [
"Find the area of the region bounded by the curves f(x) = 2((-3(2x^2 - 2x + 4))/(3(2x^2 - 2x + 4) - 2))^2 + 2, g(x) = 5(-1e^(-1x) + 3)^2 - 4(-1e^(-1x) + 3) - 4, x = -1.4, and x = -0.2. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
6.9
|
math
|
train
|
math_algebra_func_area_level_2_2_277
|
algebra_func_area2
|
medium (level 2,3)
| 2 |
{
"role": [
"user"
],
"content": [
"Determine the area of the region enclosed by the graphs of f(x) = 5(-4(1x^2 - 5x - 1)^2 + 1(1x^2 - 5x - 1) - 1) - 1 and g(x) = -3(4x + 5)^2 - 3(4x + 5) - 1 between the vertical lines x = -0.4 and x = 0.3. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
32.0
|
math
|
train
|
math_algebra_func_area_level_2_2_278
|
algebra_func_area2
|
medium (level 2,3)
| 2 |
{
"role": [
"user"
],
"content": [
"Find the area of the region bounded by the curves f(x) = -1((2((-3x + 1)/(-2x - 3)) - 2)/(-1((-3x + 1)/(-2x - 3)) - 2))^2 + 4((2((-3x + 1)/(-2x - 3)) - 2)/(-1((-3x + 1)/(-2x - 3)) - 2)) - 4, g(x) = 4(-1e^(2x) + 3)^2 + 4(-1e^(2x) + 3) - 1, 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
|
train
|
math_algebra_func_area_level_2_2_279
|
algebra_func_area2
|
medium (level 2,3)
| 2 |
{
"role": [
"user"
],
"content": [
"Determine the area of the region enclosed by the graphs of f(x) = -3e^(2(3(2x) - 2)) - 1 and g(x) = -5(-1|x + 1| + 1)^2 + 4(-1|x + 1| + 1) - 1 between the vertical lines x = -2.0 and x = -1.2. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
0.4
|
math
|
train
|
math_algebra_func_area_level_2_2_280
|
algebra_func_area2
|
medium (level 2,3)
| 2 |
{
"role": [
"user"
],
"content": [
"Find the area of the region bounded by the curves f(x) = 5(3(4x - 2)^2 + 1(4x - 2) - 3) - 5, g(x) = -2|((1x - 1)/(-3x - 1)) - 1|, x = 0.2, and x = 0.7. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
7.0
|
math
|
train
|
math_algebra_func_area_level_2_2_281
|
algebra_func_area2
|
medium (level 2,3)
| 2 |
{
"role": [
"user"
],
"content": [
"Calculate the area enclosed between the functions f(x) = (-2(1e^(-1(-1x - 5)) - 1) + 1)/(-1(1e^(-1(-1x - 5)) - 1)) and g(x) = 2|(-2sin(1πx - 1) - 1)| - 1 from x = -3.6 to x = -2.8. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
1.8
|
math
|
train
|
math_algebra_func_area_level_2_2_282
|
algebra_func_area2
|
medium (level 2,3)
| 2 |
{
"role": [
"user"
],
"content": [
"Find the area of the region bounded by the curves f(x) = -4((3(2|x - 1| + 1) + 2)/(3(2|x - 1| + 1) - 1)) + 3, g(x) = 1cos(3π(1|x + 3| - 3) + 2) - 2, x = 0.0, and x = 0.2. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
0.0
|
math
|
train
|
math_algebra_func_area_level_2_2_283
|
algebra_func_area2
|
medium (level 2,3)
| 2 |
{
"role": [
"user"
],
"content": [
"Find the area of the region bounded by the curves f(x) = -1(2|(-1|x - 1|) - 1| - 3) + 5, g(x) = 1(-3x^2 + 1x + 2) + 5, x = -1.2, and x = 0.8. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
4.2
|
math
|
train
|
math_algebra_func_area_level_2_2_284
|
algebra_func_area2
|
medium (level 2,3)
| 2 |
{
"role": [
"user"
],
"content": [
"Determine the area of the region enclosed by the graphs of f(x) = 1(3|(-1x^2 - 5x - 2) - 1| - 3) + 1 and g(x) = (-2((1x - 3)/(-2x + 1)) - 1)/(1((1x - 3)/(-2x + 1)) + 2) between the vertical lines x = -4.5 and x = -4.1. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
0.5
|
math
|
train
|
math_algebra_func_area_level_2_2_285
|
algebra_func_area2
|
medium (level 2,3)
| 2 |
{
"role": [
"user"
],
"content": [
"Find the area of the region bounded by the curves f(x) = (-1(-3(3sin(1πx - 3) - 1)^2 + 2))/(-3(-3(3sin(1πx - 3) - 1)^2 + 2) + 2), g(x) = -2sin(1π(-1x^2 - 1x - 4) + 3) - 2, x = 1.9, and x = 3.0. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
2.5
|
math
|
train
|
math_algebra_func_area_level_2_2_286
|
algebra_func_area2
|
medium (level 2,3)
| 2 |
{
"role": [
"user"
],
"content": [
"Find the area of the region bounded by the curves f(x) = 5(-3|(-3sin(2πx - 2) - 1)| + 1) + 1, g(x) = -4(3cos(2πx + 2) - 2)^2 + 1(3cos(2πx + 2) - 2) - 3, x = 0.4, and x = 0.8. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
13.9
|
math
|
train
|
math_algebra_func_area_level_2_2_287
|
algebra_func_area2
|
medium (level 2,3)
| 2 |
{
"role": [
"user"
],
"content": [
"Find the area of the region bounded by the curves f(x) = (1((-2(5x^2 + 1x + 4) - 1)/(-2(5x^2 + 1x + 4) - 2)) - 2)/(3((-2(5x^2 + 1x + 4) - 1)/(-2(5x^2 + 1x + 4) - 2)) - 2), g(x) = 3|(-1x^2 + 4x + 4)| - 3, x = 4.7, and x = 4.9. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
0.2
|
math
|
train
|
math_algebra_func_area_level_2_2_288
|
algebra_func_area2
|
medium (level 2,3)
| 2 |
{
"role": [
"user"
],
"content": [
"Find the area of the region bounded by the curves f(x) = 2cos(1π(-4(-2|x + 1|)^2 + 1)) - 2, g(x) = -1|(2|x + 3| - 1) + 2|, x = -2.6, and x = -2.5. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
0.1
|
math
|
train
|
math_algebra_func_area_level_2_2_289
|
algebra_func_area2
|
medium (level 2,3)
| 2 |
{
"role": [
"user"
],
"content": [
"Determine the area of the region enclosed by the graphs of f(x) = -1|(3(3|x - 3| - 3)^2 - 1(3|x - 3| - 3) - 3) + 1| and g(x) = -3|(-1cos(3πx - 3) + 1) + 1| + 2 between the vertical lines x = 1.4 and x = 2.3. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
1.9
|
math
|
train
|
math_algebra_func_area_level_2_2_290
|
algebra_func_area2
|
medium (level 2,3)
| 2 |
{
"role": [
"user"
],
"content": [
"Calculate the area enclosed between the functions f(x) = (2(-3(-4x^2 + 3x - 4)^2 - 3(-4x^2 + 3x - 4) + 5) - 1)/(-1(-3(-4x^2 + 3x - 4)^2 - 3(-4x^2 + 3x - 4) + 5)) and g(x) = -1|(-3e^(-2x) - 1) + 3| - 2 from x = 0.2 to x = 0.30000000000000004. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
0.0
|
math
|
train
|
math_algebra_func_area_level_2_2_291
|
algebra_func_area2
|
medium (level 2,3)
| 2 |
{
"role": [
"user"
],
"content": [
"Find the area of the region bounded by the curves f(x) = (3(-1(2cos(1πx - 2) + 2)^2 + 5(2cos(1πx - 2) + 2) - 4))/(-3(-1(2cos(1πx - 2) + 2)^2 + 5(2cos(1πx - 2) + 2) - 4) + 4), g(x) = 3(-1e^(2x) + 1) - 2, x = 0.4, and x = 0.9. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
7.7
|
math
|
train
|
math_algebra_func_area_level_2_2_292
|
algebra_func_area2
|
medium (level 2,3)
| 2 |
{
"role": [
"user"
],
"content": [
"Find the area of the region bounded by the curves f(x) = 2|((-1(-1x^2 + 1x + 4) - 1)/(3(-1x^2 + 1x + 4) - 1)) + 3| + 2, g(x) = 2(-2|x - 3|)^2 + 2(-2|x - 3|) - 1, x = 1.7, and x = 4.3. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
20.5
|
math
|
train
|
math_algebra_func_area_level_2_2_293
|
algebra_func_area2
|
medium (level 2,3)
| 2 |
{
"role": [
"user"
],
"content": [
"Find the area of the region bounded by the curves f(x) = -1(2e^(1(4x + 4)) - 3)^2 - 3(2e^(1(4x + 4)) - 3) + 4, g(x) = 1(-1x^2 + 4x + 5)^2 + 3(-1x^2 + 4x + 5) + 3, x = -1.5, and x = -0.9. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
2.1
|
math
|
train
|
math_algebra_func_area_level_2_2_294
|
algebra_func_area2
|
medium (level 2,3)
| 2 |
{
"role": [
"user"
],
"content": [
"Determine the area of the region enclosed by the graphs of f(x) = -3|(-1|(-3x^2 + 2x - 2) + 2| - 1) + 3| - 2 and g(x) = (-1(-2x^2 + 5x + 4) + 3)/(-2(-2x^2 + 5x + 4)) between the vertical lines x = -0.6 and x = 3.1. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
63.1
|
math
|
train
|
math_algebra_func_area_level_2_2_295
|
algebra_func_area2
|
medium (level 2,3)
| 2 |
{
"role": [
"user"
],
"content": [
"Determine the area of the region enclosed by the graphs of f(x) = (2(-1cos(2π(-1x^2 + 1x - 5) + 2) + 1) + 2)/(2(-1cos(2π(-1x^2 + 1x - 5) + 2) + 1) + 3) and g(x) = 3sin(3π(3|x + 1| + 3) + 3) + 3 between the vertical lines x = -3.4 and x = -3.3. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
0.2
|
math
|
train
|
math_algebra_func_area_level_2_2_296
|
algebra_func_area2
|
medium (level 2,3)
| 2 |
{
"role": [
"user"
],
"content": [
"Determine the area of the region enclosed by the graphs of f(x) = (-1(-2|(-2cos(1πx + 3)) + 1| - 3) + 2)/(2(-2|(-2cos(1πx + 3)) + 1| - 3) - 3) and g(x) = 1((3x - 2)/(3x - 1))^2 + 2((3x - 2)/(3x - 1)) between the vertical lines x = 0.5 and x = 0.6. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
0.0
|
math
|
train
|
math_algebra_func_area_level_2_2_297
|
algebra_func_area2
|
medium (level 2,3)
| 2 |
{
"role": [
"user"
],
"content": [
"Find the area of the region bounded by the curves f(x) = 4(-3(5x^2 - 1x - 3) - 3) - 1, g(x) = -2((2x - 2)/(-3x + 4)) + 4, x = 0.7, and x = 1.3. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
18.0
|
math
|
train
|
math_algebra_func_area_level_2_2_298
|
algebra_func_area2
|
medium (level 2,3)
| 2 |
{
"role": [
"user"
],
"content": [
"Determine the area of the region enclosed by the graphs of f(x) = -5(2cos(3π((-1x + 1)/(1x + 3)) + 3) - 3)^2 + 2(2cos(3π((-1x + 1)/(1x + 3)) + 3) - 3) + 4 and g(x) = 5(3sin(3πx - 2) + 2) - 2 between the vertical lines x = -3.3 and x = -3.1999999999999997. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
5.2
|
math
|
train
|
math_algebra_func_area_level_2_2_299
|
algebra_func_area2
|
medium (level 2,3)
| 2 |
{
"role": [
"user"
],
"content": [
"Find the area of the region bounded by the curves f(x) = (2(-1(1|x + 1| + 1) - 4) - 2)/(2(-1(1|x + 1| + 1) - 4) + 3), g(x) = 4(-3sin(1πx - 2) - 2)^2 + 4(-3sin(1πx - 2) - 2) + 2, x = 2.4, and x = 2.5. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
0.0
|
math
|
train
|
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