id
string | setting_key
string | difficulty
string | level
int32 | messages
dict | ground_truth
string | dataset
string | omega_split
string |
|---|---|---|---|---|---|---|---|
math_algebra_func_area_level_3_3_200
|
algebra_func_area3
|
medium (level 2,3)
| 3 |
{
"role": [
"user"
],
"content": [
"Determine the area of the region enclosed by the graphs of f(x) = 1(2((1((-3x + 2)/(-1x - 1)) - 1)/(1((-3x + 2)/(-1x - 1)) - 3))^2 - 3((1((-3x + 2)/(-1x - 1)) - 1)/(1((-3x + 2)/(-1x - 1)) - 3)) - 4)^2 - 3(2((1((-3x + 2)/(-1x - 1)) - 1)/(1((-3x + 2)/(-1x - 1)) - 3))^2 - 3((1((-3x + 2)/(-1x - 1)) - 1)/(1((-3x + 2)/(-1x - 1)) - 3)) - 4) - 3 and g(x) = 1|(-1|(3x - 4) + 1| + 1) - 3| + 2 between the vertical lines x = -2.9 and x = 2.6. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
110.8
|
math
|
train
|
math_algebra_func_area_level_3_3_201
|
algebra_func_area3
|
medium (level 2,3)
| 3 |
{
"role": [
"user"
],
"content": [
"Determine the area of the region enclosed by the graphs of f(x) = 2(3(1((1x - 1)/(-3x + 1)) - 5)^2 + 3) - 1 and g(x) = (-2((1((2x - 3)/(1x - 3)) + 3)/(-3((2x - 3)/(1x - 3)) + 1)) + 3)/(1((1((2x - 3)/(1x - 3)) + 3)/(-3((2x - 3)/(1x - 3)) + 1)) + 3) 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}"
]
}
|
5.1
|
math
|
train
|
math_algebra_func_area_level_3_3_202
|
algebra_func_area3
|
medium (level 2,3)
| 3 |
{
"role": [
"user"
],
"content": [
"Find the area of the region bounded by the curves f(x) = 1((-2((1(1|x - 1| + 2) - 3)/(-2(1|x - 1| + 2) + 3)) - 3)/(1((1(1|x - 1| + 2) - 3)/(-2(1|x - 1| + 2) + 3)) + 2)) - 2, g(x) = 1(-5(1sin(3πx - 3)) - 5) + 1, x = -0.7, and x = -0.4. 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_3_3_203
|
algebra_func_area3
|
medium (level 2,3)
| 3 |
{
"role": [
"user"
],
"content": [
"Find the area of the region bounded by the curves f(x) = -2|(2|(-4(1|x + 2| + 2) + 5) - 3|) + 1| + 2, g(x) = -2|((1(3|x + 2| - 2) - 3)/(-2(3|x + 2| - 2) + 1)) + 2| + 2, x = -2.8, and x = -1.2. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
48.3
|
math
|
train
|
math_algebra_func_area_level_3_3_204
|
algebra_func_area3
|
medium (level 2,3)
| 3 |
{
"role": [
"user"
],
"content": [
"Find the area of the region bounded by the curves f(x) = -3(3sin(3π(-3|(-5x^2 - 3x + 1) - 1|) + 2) + 1) - 3, g(x) = 1(-3sin(1π(-4x + 1))) + 3, x = 1.2, and x = 1.3. 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_3_3_205
|
algebra_func_area3
|
medium (level 2,3)
| 3 |
{
"role": [
"user"
],
"content": [
"Determine the area of the region enclosed by the graphs of f(x) = 4(-2sin(2π(3|(5x - 5) - 3| - 2) - 1) - 3)^2 + 2(-2sin(2π(3|(5x - 5) - 3| - 2) - 1) - 3) + 2 and g(x) = 2(-1(-1|x| + 1) + 3)^2 - 4(-1(-1|x| + 1) + 3) - 1 between the vertical lines x = 2.4 and x = 2.5. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
3.2
|
math
|
train
|
math_algebra_func_area_level_3_3_206
|
algebra_func_area3
|
medium (level 2,3)
| 3 |
{
"role": [
"user"
],
"content": [
"Find the area of the region bounded by the curves f(x) = 5(5(3|((-1x + 3)/(3x)) - 1|) - 4)^2 + 3, g(x) = -4(-2((-2x + 1)/(-2x - 3))^2 + 2((-2x + 1)/(-2x - 3)) - 4) + 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}"
]
}
|
1.1
|
math
|
train
|
math_algebra_func_area_level_3_3_207
|
algebra_func_area3
|
medium (level 2,3)
| 3 |
{
"role": [
"user"
],
"content": [
"Calculate the area enclosed between the functions f(x) = -3(1(3(3x - 4) - 3)^2 + 3(3(3x - 4) - 3) - 2)^2 + 5(1(3(3x - 4) - 3)^2 + 3(3(3x - 4) - 3) - 2) - 2 and g(x) = 3(4(1sin(3πx + 3) - 2) + 3) - 5 from x = 1.7 to x = 1.8. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
0.9
|
math
|
train
|
math_algebra_func_area_level_3_3_208
|
algebra_func_area3
|
medium (level 2,3)
| 3 |
{
"role": [
"user"
],
"content": [
"Calculate the area enclosed between the functions f(x) = (1(2((-3(3sin(2πx + 2) + 2) - 1)/(2(3sin(2πx + 2) + 2) + 3)) + 2) + 3)/(1(2((-3(3sin(2πx + 2) + 2) - 1)/(2(3sin(2πx + 2) + 2) + 3)) + 2) - 3) and g(x) = 2|((-2(5x - 5) + 1)/(-2(5x - 5) - 3)) + 1| - 3 from x = 0.5 to x = 0.8. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
37.3
|
math
|
train
|
math_algebra_func_area_level_3_3_209
|
algebra_func_area3
|
medium (level 2,3)
| 3 |
{
"role": [
"user"
],
"content": [
"Find the area of the region bounded by the curves f(x) = -1|(-1|(-1|(2cos(3πx) + 2) - 2| + 3) - 3| + 3)| - 1, g(x) = (3((2(3x^2 - 4) - 2)/(-1(3x^2 - 4) + 3)) + 2)/(-2((2(3x^2 - 4) - 2)/(-1(3x^2 - 4) + 3)) + 3), x = -1.4, and x = 1.4. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
10.1
|
math
|
train
|
math_algebra_func_area_level_3_3_210
|
algebra_func_area3
|
medium (level 2,3)
| 3 |
{
"role": [
"user"
],
"content": [
"Determine the area of the region enclosed by the graphs of f(x) = 1|(-5(-1|(-1x + 2) - 1| + 3) + 2)| and g(x) = 2|((-2(-5x + 3) - 1)/(-1(-5x + 3) - 3)) + 1| - 3 between the vertical lines x = 1.1 and x = 1.5. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
91.7
|
math
|
train
|
math_algebra_func_area_level_3_3_211
|
algebra_func_area3
|
medium (level 2,3)
| 3 |
{
"role": [
"user"
],
"content": [
"Calculate the area enclosed between the functions f(x) = (-2(-3(3e^(-1(-2x^2 - 2x + 4)) + 3)^2 - 5(3e^(-1(-2x^2 - 2x + 4)) + 3) + 5) - 1)/(-3(-3(3e^(-1(-2x^2 - 2x + 4)) + 3)^2 - 5(3e^(-1(-2x^2 - 2x + 4)) + 3) + 5) - 3) and g(x) = -1|(-1((3x)/(2x - 1))^2 - 4((3x)/(2x - 1)) - 1) + 2| + 2 from x = 0.0 to x = 0.4. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
0.8
|
math
|
train
|
math_algebra_func_area_level_3_3_212
|
algebra_func_area3
|
medium (level 2,3)
| 3 |
{
"role": [
"user"
],
"content": [
"Calculate the area enclosed between the functions f(x) = 4((-3(-2((2x + 1)/(-1x + 2))) + 3)/(2(-2((2x + 1)/(-1x + 2))) - 1)) and g(x) = 3|(-3cos(3π(3x^2 - 3x + 2) - 3) + 1) + 3| + 3 from x = -1.0 to x = -0.9. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
1.1
|
math
|
train
|
math_algebra_func_area_level_3_3_213
|
algebra_func_area3
|
medium (level 2,3)
| 3 |
{
"role": [
"user"
],
"content": [
"Calculate the area enclosed between the functions f(x) = -1cos(1π((1(1|((2x + 2)/(-1x + 2)) - 1| + 2) + 1)/(-1(1|((2x + 2)/(-1x + 2)) - 1| + 2) - 1))) + 3 and g(x) = 3((-3(2cos(2πx - 3)))/(-3(2cos(2πx - 3)) - 1)) + 2 from x = 1.3 to x = 1.7. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
0.2
|
math
|
train
|
math_algebra_func_area_level_3_3_214
|
algebra_func_area3
|
medium (level 2,3)
| 3 |
{
"role": [
"user"
],
"content": [
"Find the area of the region bounded by the curves f(x) = (2((2(-4((1x + 3)/(-3x - 2))^2 - 1((1x + 3)/(-3x - 2)) + 4) + 1)/(1(-4((1x + 3)/(-3x - 2))^2 - 1((1x + 3)/(-3x - 2)) + 4) - 2)) - 1)/(2((2(-4((1x + 3)/(-3x - 2))^2 - 1((1x + 3)/(-3x - 2)) + 4) + 1)/(1(-4((1x + 3)/(-3x - 2))^2 - 1((1x + 3)/(-3x - 2)) + 4) - 2)) - 3), g(x) = -1|((3(-2sin(2πx + 1) - 3) + 3)/(2(-2sin(2πx + 1) - 3) + 3)) - 1| - 1, x = -1.2, and x = -0.0. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
25.6
|
math
|
train
|
math_algebra_func_area_level_3_3_215
|
algebra_func_area3
|
medium (level 2,3)
| 3 |
{
"role": [
"user"
],
"content": [
"Determine the area of the region enclosed by the graphs of f(x) = -2|(1cos(1π(-2((-3x + 2)/(-2x))^2 + 4((-3x + 2)/(-2x)) + 5) - 3)) - 2| - 3 and g(x) = (-3((-1(5x^2 - 3) - 1)/(3(5x^2 - 3))) - 2)/(-2((-1(5x^2 - 3) - 1)/(3(5x^2 - 3))) + 1) between the vertical lines x = -0.7 and x = 0.7. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
7.9
|
math
|
train
|
math_algebra_func_area_level_3_3_216
|
algebra_func_area3
|
medium (level 2,3)
| 3 |
{
"role": [
"user"
],
"content": [
"Find the area of the region bounded by the curves f(x) = 3|(1((2(-2x + 5) - 1)/(-2(-2x + 5)))^2 + 1((2(-2x + 5) - 1)/(-2(-2x + 5))) - 1) + 2| + 3, g(x) = 2|((3((2x + 2)/(-2x + 3)))/(-2((2x + 2)/(-2x + 3)) + 3)) + 2| - 3, x = 0.2, and x = 0.7. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
80.6
|
math
|
train
|
math_algebra_func_area_level_3_3_217
|
algebra_func_area3
|
medium (level 2,3)
| 3 |
{
"role": [
"user"
],
"content": [
"Determine the area of the region enclosed by the graphs of f(x) = 5(1cos(1π((-3(2x^2 - 2x + 5))/(-1(2x^2 - 2x + 5) - 1)) - 2) - 2) - 2 and g(x) = -1|(-2|((-3x + 3)/(-2x + 3)) - 1| + 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}"
]
}
|
67.6
|
math
|
train
|
math_algebra_func_area_level_3_3_218
|
algebra_func_area3
|
medium (level 2,3)
| 3 |
{
"role": [
"user"
],
"content": [
"Determine the area of the region enclosed by the graphs of f(x) = (-3(2|(-5(1x^2 + 3x + 3)^2 + 4(1x^2 + 3x + 3) - 3) + 1| - 1) - 2)/(-3(2|(-5(1x^2 + 3x + 3)^2 + 4(1x^2 + 3x + 3) - 3) + 1| - 1) + 2) and g(x) = -4(3sin(2π(4x - 5) + 3) + 1)^2 - 2(3sin(2π(4x - 5) + 3) + 1) + 5 between the vertical lines x = -4.5 and x = -4.4. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
0.4
|
math
|
train
|
math_algebra_func_area_level_3_3_219
|
algebra_func_area3
|
medium (level 2,3)
| 3 |
{
"role": [
"user"
],
"content": [
"Determine the area of the region enclosed by the graphs of f(x) = 2|(-2cos(3π(3|(2|x - 2| + 1) + 2|) - 1) - 2)| and g(x) = -2|((-1((1x - 1)/(-1x + 2)) + 2)/(1((1x - 1)/(-1x + 2)) - 2)) + 2| + 2 between the vertical lines x = -2.2 and x = -2.1. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
0.4
|
math
|
train
|
math_algebra_func_area_level_3_3_220
|
algebra_func_area3
|
medium (level 2,3)
| 3 |
{
"role": [
"user"
],
"content": [
"Determine the area of the region enclosed by the graphs of f(x) = (3(-4((-2(-2sin(1πx + 3) + 2) + 2)/(-1(-2sin(1πx + 3) + 2) - 1))^2 + 4))/(-3(-4((-2(-2sin(1πx + 3) + 2) + 2)/(-1(-2sin(1πx + 3) + 2) - 1))^2 + 4) + 1) and g(x) = (-1((-1(-1x^2 - 2x + 3) + 1)/(-3(-1x^2 - 2x + 3))) - 2)/(-3((-1(-1x^2 - 2x + 3) + 1)/(-3(-1x^2 - 2x + 3))) + 2) between the vertical lines x = -0.6 and x = -0.3. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
0.2
|
math
|
train
|
math_algebra_func_area_level_3_3_221
|
algebra_func_area3
|
medium (level 2,3)
| 3 |
{
"role": [
"user"
],
"content": [
"Calculate the area enclosed between the functions f(x) = 1|(-1|(-2|(-1x^2 - 2x + 4) + 3| + 2)|) - 3| + 3 and g(x) = 3|(1(2x^2 - 3x - 3)^2 + 1(2x^2 - 3x - 3) - 5) + 2| + 3 from x = 1.6 to x = 1.8. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
0.4
|
math
|
train
|
math_algebra_func_area_level_3_3_222
|
algebra_func_area3
|
medium (level 2,3)
| 3 |
{
"role": [
"user"
],
"content": [
"Find the area of the region bounded by the curves f(x) = 1(-2cos(1π(-3(3|x - 3| + 2)^2 - 3(3|x - 3| + 2) + 4) - 3) - 3)^2 + 2(-2cos(1π(-3(3|x - 3| + 2)^2 - 3(3|x - 3| + 2) + 4) - 3) - 3) - 3, g(x) = 3|(-2|(-5x^2 + 2x + 1) + 1| + 3) - 1| - 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}"
]
}
|
0.5
|
math
|
train
|
math_algebra_func_area_level_3_3_223
|
algebra_func_area3
|
medium (level 2,3)
| 3 |
{
"role": [
"user"
],
"content": [
"Determine the area of the region enclosed by the graphs of f(x) = 1(-4(5(3|x + 2|)^2 - 5(3|x + 2|)) - 4) + 4 and g(x) = (-3(-2(3x + 2)^2 + 1(3x + 2) + 2) - 1)/(2(-2(3x + 2)^2 + 1(3x + 2) + 2) - 1) between the vertical lines x = -1.6 and x = -0.9. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
43.8
|
math
|
train
|
math_algebra_func_area_level_3_3_224
|
algebra_func_area3
|
medium (level 2,3)
| 3 |
{
"role": [
"user"
],
"content": [
"Calculate the area enclosed between the functions f(x) = 4(-1(-1|(1|x + 2| + 1) + 1| + 2))^2 + 2(-1(-1|(1|x + 2| + 1) + 1| + 2)) - 4 and g(x) = (1(-2(-2cos(1πx - 1) + 2)^2 + 5) + 1)/(-1(-2(-2cos(1πx - 1) + 2)^2 + 5) + 2) from x = -0.1 to x = 0.7. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
20.5
|
math
|
train
|
math_algebra_func_area_level_3_3_225
|
algebra_func_area3
|
medium (level 2,3)
| 3 |
{
"role": [
"user"
],
"content": [
"Determine the area of the region enclosed by the graphs of f(x) = (-3(-1(4(-1x - 3) - 3) - 4) + 3)/(-1(-1(4(-1x - 3) - 3) - 4) + 2) and g(x) = 1|(1|((-1x + 3)/(2x)) + 3| + 2)| - 2 between the vertical lines x = -0.3 and x = 2.2. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
71.9
|
math
|
train
|
math_algebra_func_area_level_3_3_226
|
algebra_func_area3
|
medium (level 2,3)
| 3 |
{
"role": [
"user"
],
"content": [
"Calculate the area enclosed between the functions f(x) = 3(2(4(2cos(2πx)) - 3) + 2) + 4 and g(x) = (-3(-3|(-4x + 4) + 3| + 3) + 1)/(-3(-3|(-4x + 4) + 3| + 3) + 4) from x = -4.8 to x = -4.2. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
20.2
|
math
|
train
|
math_algebra_func_area_level_3_3_227
|
algebra_func_area3
|
medium (level 2,3)
| 3 |
{
"role": [
"user"
],
"content": [
"Find the area of the region bounded by the curves f(x) = 2(-1|(-3(-3|x - 1| - 1)) - 2|) + 3, g(x) = (3(2sin(3π(1|x + 1| + 1) - 2) + 3) + 1)/(-2(2sin(3π(1|x + 1| + 1) - 2) + 3) + 3), x = 4.1, and x = 4.6. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
31.1
|
math
|
train
|
math_algebra_func_area_level_3_3_228
|
algebra_func_area3
|
medium (level 2,3)
| 3 |
{
"role": [
"user"
],
"content": [
"Find the area of the region bounded by the curves f(x) = -2(-1|(5(2e^(-2x) - 2) + 5) - 3| + 2) - 5, g(x) = 1cos(3π(-1(-1x^2 - 2x + 1) - 2) - 3) + 3, x = -0.2, and x = 0.8. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
5.2
|
math
|
train
|
math_algebra_func_area_level_3_3_229
|
algebra_func_area3
|
medium (level 2,3)
| 3 |
{
"role": [
"user"
],
"content": [
"Find the area of the region bounded by the curves f(x) = (-2(-3sin(2π((-3((-2x + 3)/(3x + 2)) - 3)/(-1((-2x + 3)/(3x + 2)))) - 1) + 2) + 2)/(1(-3sin(2π((-3((-2x + 3)/(3x + 2)) - 3)/(-1((-2x + 3)/(3x + 2)))) - 1) + 2)), g(x) = (2(4(-2x^2 - 1x + 1)^2 + 4(-2x^2 - 1x + 1) + 2) + 1)/(1(4(-2x^2 - 1x + 1)^2 + 4(-2x^2 - 1x + 1) + 2) - 3), x = 2.2, and x = 2.3000000000000003. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
0.7
|
math
|
train
|
math_algebra_func_area_level_3_3_230
|
algebra_func_area3
|
medium (level 2,3)
| 3 |
{
"role": [
"user"
],
"content": [
"Find the area of the region bounded by the curves f(x) = (-3(-2(1(-2cos(3πx) - 3)^2 + 3(-2cos(3πx) - 3) + 2)^2 + 4(1(-2cos(3πx) - 3)^2 + 3(-2cos(3πx) - 3) + 2) + 1) - 3)/(2(-2(1(-2cos(3πx) - 3)^2 + 3(-2cos(3πx) - 3) + 2)^2 + 4(1(-2cos(3πx) - 3)^2 + 3(-2cos(3πx) - 3) + 2) + 1) - 1), g(x) = 3|(1e^(2(3x - 3))) - 1| + 2, x = 0.5, and x = 0.8. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
1.9
|
math
|
train
|
math_algebra_func_area_level_3_3_231
|
algebra_func_area3
|
medium (level 2,3)
| 3 |
{
"role": [
"user"
],
"content": [
"Calculate the area enclosed between the functions f(x) = -3((3(-2(5x^2 + 4x + 2) + 2) + 2)/(-3(-2(5x^2 + 4x + 2) + 2) - 3)) - 3 and g(x) = (2(2e^(1(2|x + 1| + 3)) - 3) + 1)/(2(2e^(1(2|x + 1| + 3)) - 3) - 1) from x = -0.8 to x = -0.0. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
6.3
|
math
|
train
|
math_algebra_func_area_level_3_3_232
|
algebra_func_area3
|
medium (level 2,3)
| 3 |
{
"role": [
"user"
],
"content": [
"Determine the area of the region enclosed by the graphs of f(x) = (-1(-1(-4(3x^2 + 1x - 4) - 4) + 5))/(-1(-1(-4(3x^2 + 1x - 4) - 4) + 5) - 2) and g(x) = -1sin(3π(2((1x - 2)/(2x - 1))^2 + 5((1x - 2)/(2x - 1)) + 3) - 1) between the vertical lines x = -1.7 and x = -1.5999999999999999. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
0.0
|
math
|
train
|
math_algebra_func_area_level_3_3_233
|
algebra_func_area3
|
medium (level 2,3)
| 3 |
{
"role": [
"user"
],
"content": [
"Find the area of the region bounded by the curves f(x) = 2|(3(1|(-3|x + 2|) - 2| + 2)^2 - 4(1|(-3|x + 2|) - 2| + 2) - 3) + 2| + 3, g(x) = (-1(2sin(2π(1|x + 2| - 2) + 3) + 2) - 2)/(3(2sin(2π(1|x + 2| - 2) + 3) + 2) - 1), x = -2.4, and x = -2.2. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
22.9
|
math
|
train
|
math_algebra_func_area_level_3_3_234
|
algebra_func_area3
|
medium (level 2,3)
| 3 |
{
"role": [
"user"
],
"content": [
"Find the area of the region bounded by the curves f(x) = 1cos(3π(-1(-5(1x^2 + 3x + 1)^2 - 4(1x^2 + 3x + 1) - 2) + 2) + 1), g(x) = 2cos(2π(1|(5x + 2) + 3|) - 3) - 2, x = -3.5, and x = -3.4. 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_3_3_235
|
algebra_func_area3
|
medium (level 2,3)
| 3 |
{
"role": [
"user"
],
"content": [
"Calculate the area enclosed between the functions f(x) = (2(-2e^(-2(5(1|x| - 3) + 4))) + 3)/(-3(-2e^(-2(5(1|x| - 3) + 4)))) and g(x) = -4(2(-5x^2 + 2x + 1) + 1) + 1 from x = -0.4 to x = 0.8. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
8.8
|
math
|
train
|
math_algebra_func_area_level_3_3_236
|
algebra_func_area3
|
medium (level 2,3)
| 3 |
{
"role": [
"user"
],
"content": [
"Calculate the area enclosed between the functions f(x) = 3|(1(-1|(2x - 3) + 2| + 3) - 1) + 2| - 2 and g(x) = 4((3(1|x + 3| - 2) - 3)/(1(1|x + 3| - 2) - 3)) + 5 from x = -3.7 to x = -0.2. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
23.6
|
math
|
train
|
math_algebra_func_area_level_3_3_237
|
algebra_func_area3
|
medium (level 2,3)
| 3 |
{
"role": [
"user"
],
"content": [
"Find the area of the region bounded by the curves f(x) = -3((-3(1|(-3|x - 3| - 2) - 2| - 3) + 3)/(-3(1|(-3|x - 3| - 2) - 2| - 3) - 1))^2 + 3((-3(1|(-3|x - 3| - 2) - 2| - 3) + 3)/(-3(1|(-3|x - 3| - 2) - 2| - 3) - 1)) - 4, g(x) = -2(3(2|x + 2| - 2) - 3) - 5, x = -3.4, and x = -0.6. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
23.4
|
math
|
train
|
math_algebra_func_area_level_3_3_238
|
algebra_func_area3
|
medium (level 2,3)
| 3 |
{
"role": [
"user"
],
"content": [
"Determine the area of the region enclosed by the graphs of f(x) = 1(4((-1(-4x + 4) + 3)/(-1(-4x + 4) - 3)) + 1) + 1 and g(x) = (2(-2|(1x^2 - 2x - 5)| + 3) + 3)/(-2(-2|(1x^2 - 2x - 5)| + 3)) 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}"
]
}
|
5.9
|
math
|
train
|
math_algebra_func_area_level_3_3_239
|
algebra_func_area3
|
medium (level 2,3)
| 3 |
{
"role": [
"user"
],
"content": [
"Find the area of the region bounded by the curves f(x) = 2(2((-1(-3|x + 2|))/(2(-3|x + 2|) + 2))^2 - 2) - 3, g(x) = 1(-1|(-3x^2 + 5x - 4) + 1| - 3) + 1, x = -0.1, and x = 1.8. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
3.6
|
math
|
train
|
math_algebra_func_area_level_3_3_240
|
algebra_func_area3
|
medium (level 2,3)
| 3 |
{
"role": [
"user"
],
"content": [
"Determine the area of the region enclosed by the graphs of f(x) = -3sin(3π(2(2(3|x + 3| - 2)^2 - 3(3|x + 3| - 2) + 5) - 4)) + 3 and g(x) = 1((1(2x - 1) + 1)/(1(2x - 1) + 3)) + 3 between the vertical lines x = -2.9 and x = -2.8. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
0.2
|
math
|
train
|
math_algebra_func_area_level_3_3_241
|
algebra_func_area3
|
medium (level 2,3)
| 3 |
{
"role": [
"user"
],
"content": [
"Determine the area of the region enclosed by the graphs of f(x) = -5((-1(-1(1x + 2)^2 + 3))/(2(-1(1x + 2)^2 + 3)))^2 + 4((-1(-1(1x + 2)^2 + 3))/(2(-1(1x + 2)^2 + 3))) - 1 and g(x) = -2|(-2(3x^2 - 2x - 2) + 2) + 3| + 2 between the vertical lines x = 1.4 and x = 1.8. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
1.3
|
math
|
train
|
math_algebra_func_area_level_3_3_242
|
algebra_func_area3
|
medium (level 2,3)
| 3 |
{
"role": [
"user"
],
"content": [
"Calculate the area enclosed between the functions f(x) = (1(-2(-1|(1x + 4) + 1| - 3) - 3))/(2(-2(-1|(1x + 4) + 1| - 3) - 3) - 3) and g(x) = -2(1((2x - 2)/(2x - 3))^2 - 4((2x - 2)/(2x - 3)) - 1) + 2 from x = 1.1 to x = 1.6. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
-8.1
|
math
|
train
|
math_algebra_func_area_level_3_3_243
|
algebra_func_area3
|
medium (level 2,3)
| 3 |
{
"role": [
"user"
],
"content": [
"Determine the area of the region enclosed by the graphs of f(x) = -1|(-5((-1(2sin(3πx + 3) + 2) + 2)/(1(2sin(3πx + 3) + 2) - 3))^2 - 3((-1(2sin(3πx + 3) + 2) + 2)/(1(2sin(3πx + 3) + 2) - 3)) - 1) + 3| - 3 and g(x) = (-1(2sin(1π(-2x - 3) - 1) + 1) + 1)/(3(2sin(1π(-2x - 3) - 1) + 1) + 1) between the vertical lines x = -3.5 and x = -3.3. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
28.4
|
math
|
train
|
math_algebra_func_area_level_3_3_244
|
algebra_func_area3
|
medium (level 2,3)
| 3 |
{
"role": [
"user"
],
"content": [
"Calculate the area enclosed between the functions f(x) = -5(-2(4(1sin(2πx + 1) + 1) + 4) + 1) + 2 and g(x) = 4(-1(-5x - 1) + 1)^2 + 5(-1(-5x - 1) + 1) - 4 from x = -1.3 to x = 0.4. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
109.4
|
math
|
train
|
math_algebra_func_area_level_3_3_245
|
algebra_func_area3
|
medium (level 2,3)
| 3 |
{
"role": [
"user"
],
"content": [
"Find the area of the region bounded by the curves f(x) = (1(-2(1e^(-1(-1|x - 1| + 2)) + 3) + 1) + 2)/(-1(-2(1e^(-1(-1|x - 1| + 2)) + 3) + 1) - 2), g(x) = -3|(2(-3sin(2πx + 2) - 2) - 5) + 2| + 2, x = -0.6, and x = 0.4. 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_3_3_246
|
algebra_func_area3
|
medium (level 2,3)
| 3 |
{
"role": [
"user"
],
"content": [
"Find the area of the region bounded by the curves f(x) = -3(1((3(1x^2 + 1x - 4) + 1)/(3(1x^2 + 1x - 4) + 3)) - 2) - 2, g(x) = (-1((2(2|x + 2| + 3) + 3)/(2(2|x + 2| + 3))) + 2)/(-1((2(2|x + 2| + 3) + 3)/(2(2|x + 2| + 3))) - 2), x = -1.7, and x = 0.8. 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_3_3_247
|
algebra_func_area3
|
medium (level 2,3)
| 3 |
{
"role": [
"user"
],
"content": [
"Calculate the area enclosed between the functions f(x) = -3cos(1π(-2|(-3((3x - 1)/(-1x - 3)) + 4) - 1| + 3) - 3) - 1 and g(x) = 1|(3((3x + 2)/(1x + 1)) - 1) - 2| - 1 from x = -0.6 to x = -0.5. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
0.2
|
math
|
train
|
math_algebra_func_area_level_3_3_248
|
algebra_func_area3
|
medium (level 2,3)
| 3 |
{
"role": [
"user"
],
"content": [
"Determine the area of the region enclosed by the graphs of f(x) = -5(1cos(1π(-4(-1x^2 - 5x - 3) - 4) - 3))^2 + 2(1cos(1π(-4(-1x^2 - 5x - 3) - 4) - 3)) and g(x) = -1|(-2((-1x - 2)/(1x + 1)) - 4) + 2| - 2 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}"
]
}
|
0.2
|
math
|
train
|
math_algebra_func_area_level_3_3_249
|
algebra_func_area3
|
medium (level 2,3)
| 3 |
{
"role": [
"user"
],
"content": [
"Find the area of the region bounded by the curves f(x) = -2|(-1|(-3|(-1cos(1πx + 1) + 3) - 2|) - 2| + 1) + 3|, g(x) = (-2(1e^(-2(4x^2 - 3x + 5)) + 2) - 2)/(2(1e^(-2(4x^2 - 3x + 5)) + 2) - 3), x = -1.0, and x = 0.4. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
4.6
|
math
|
train
|
math_algebra_func_area_level_3_3_250
|
algebra_func_area3
|
medium (level 2,3)
| 3 |
{
"role": [
"user"
],
"content": [
"Determine the area of the region enclosed by the graphs of f(x) = -3e^(-2((-3(-4(-3x^2 - 2x - 1) + 4) + 2)/(-2(-4(-3x^2 - 2x - 1) + 4) + 3))) and g(x) = 3cos(2π(5(-3x - 3) - 4) - 1) between the vertical lines x = 1.4 and x = 1.5. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
0.2
|
math
|
train
|
math_algebra_func_area_level_3_3_251
|
algebra_func_area3
|
medium (level 2,3)
| 3 |
{
"role": [
"user"
],
"content": [
"Determine the area of the region enclosed by the graphs of f(x) = 2(5(1(5x^2 - 3x - 2)^2 - 2)^2 + 5(1(5x^2 - 3x - 2)^2 - 2) - 2)^2 + 2(5(1(5x^2 - 3x - 2)^2 - 2)^2 + 5(1(5x^2 - 3x - 2)^2 - 2) - 2) - 1 and g(x) = 3|(-3(-5x^2 + 1x + 2) - 5) - 3| - 3 between the vertical lines x = 1.1 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_3_3_252
|
algebra_func_area3
|
medium (level 2,3)
| 3 |
{
"role": [
"user"
],
"content": [
"Determine the area of the region enclosed by the graphs of f(x) = (-3(3((2(-5x - 2))/(-1(-5x - 2) + 2))^2 + 5((2(-5x - 2))/(-1(-5x - 2) + 2)) - 3) - 1)/(2(3((2(-5x - 2))/(-1(-5x - 2) + 2))^2 + 5((2(-5x - 2))/(-1(-5x - 2) + 2)) - 3) - 1) and g(x) = 2|(1|(-1x + 5) - 3| - 1)| - 3 between the vertical lines x = -0.5 and 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_3_3_253
|
algebra_func_area3
|
medium (level 2,3)
| 3 |
{
"role": [
"user"
],
"content": [
"Find the area of the region bounded by the curves f(x) = 2((1(3|(5x^2 + 1x + 5) - 1| + 1) - 1)/(-3(3|(5x^2 + 1x + 5) - 1| + 1))) + 4, g(x) = 2(3sin(1π((3x - 1)/(-1x)) + 1) - 1)^2 - 2(3sin(1π((3x - 1)/(-1x)) + 1) - 1) + 1, x = 0.1, and x = 0.2. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
1.0
|
math
|
train
|
math_algebra_func_area_level_3_3_254
|
algebra_func_area3
|
medium (level 2,3)
| 3 |
{
"role": [
"user"
],
"content": [
"Determine the area of the region enclosed by the graphs of f(x) = -2(-1sin(1π((-2((3x - 3)/(-2x)) - 3)/(2((3x - 3)/(-2x)) + 1)) + 2) - 2) and g(x) = -4(2sin(3π((1x)/(-3x - 1))) - 2) 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}"
]
}
|
0.7
|
math
|
train
|
math_algebra_func_area_level_3_3_255
|
algebra_func_area3
|
medium (level 2,3)
| 3 |
{
"role": [
"user"
],
"content": [
"Determine the area of the region enclosed by the graphs of f(x) = 3(-3|(4(3sin(3πx) - 3)^2 - 4(3sin(3πx) - 3) - 3) + 2| + 2) - 4 and g(x) = (3(-2|(-5x + 3) - 1| - 2) - 2)/(-2(-2|(-5x + 3) - 1| - 2) - 3) 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}"
]
}
|
0.4
|
math
|
train
|
math_algebra_func_area_level_3_3_256
|
algebra_func_area3
|
medium (level 2,3)
| 3 |
{
"role": [
"user"
],
"content": [
"Determine the area of the region enclosed by the graphs of f(x) = 2sin(1π(1|(-1(-5x - 4) + 5) + 3| - 3)) + 3 and g(x) = (-1((-3(-3cos(3πx + 2) + 1) + 2)/(-2(-3cos(3πx + 2) + 1) - 1)))/(2((-3(-3cos(3πx + 2) + 1) + 2)/(-2(-3cos(3πx + 2) + 1) - 1)) - 3) between the vertical lines x = 4.1 and x = 4.199999999999999. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
0.1
|
math
|
train
|
math_algebra_func_area_level_3_3_257
|
algebra_func_area3
|
medium (level 2,3)
| 3 |
{
"role": [
"user"
],
"content": [
"Calculate the area enclosed between the functions f(x) = 4(1sin(1π(3(1x^2 - 4x) - 1))) - 4 and g(x) = -1cos(2π(-1|(3x^2 - 2x) - 2| - 3) + 3) - 2 from x = 2.8 to x = 3.0. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
0.9
|
math
|
train
|
math_algebra_func_area_level_3_3_258
|
algebra_func_area3
|
medium (level 2,3)
| 3 |
{
"role": [
"user"
],
"content": [
"Find the area of the region bounded by the curves f(x) = 3((-1(3|(-3|x + 2|) - 2| - 2) + 2)/(2(3|(-3|x + 2|) - 2| - 2) + 3)) + 1, g(x) = (-1(1(-3sin(2πx + 3) - 3)^2 - 1(-3sin(2πx + 3) - 3) + 5) - 1)/(3(1(-3sin(2πx + 3) - 3)^2 - 1(-3sin(2πx + 3) - 3) + 5) - 1), x = 2.4, and x = 3.1. 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_3_3_259
|
algebra_func_area3
|
medium (level 2,3)
| 3 |
{
"role": [
"user"
],
"content": [
"Calculate the area enclosed between the functions f(x) = -3((1(1(-2x - 2) + 3) + 3)/(-3(1(-2x - 2) + 3) + 1)) + 1 and g(x) = (-2(1sin(3π(-2x + 4) - 2) - 3))/(-1(1sin(3π(-2x + 4) - 2) - 3) - 1) from x = -1.3 to x = -1.1. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
0.1
|
math
|
train
|
math_algebra_func_area_level_3_3_260
|
algebra_func_area3
|
medium (level 2,3)
| 3 |
{
"role": [
"user"
],
"content": [
"Find the area of the region bounded by the curves f(x) = 1(-3sin(2π((-2(-2|x - 1| + 1) + 3)/(-1(-2|x - 1| + 1) + 2)) - 2)) + 1, g(x) = 3|(-3((1x + 2)/(-3x - 3)) + 1) - 3| - 3, x = -2.5, and x = -0.5. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
141.8
|
math
|
train
|
math_algebra_func_area_level_3_3_261
|
algebra_func_area3
|
medium (level 2,3)
| 3 |
{
"role": [
"user"
],
"content": [
"Determine the area of the region enclosed by the graphs of f(x) = -2(-4(-2|(-2e^(-2x)) - 2|)) - 4 and g(x) = 4((1(-1sin(1πx + 3)) + 1)/(-2(-1sin(1πx + 3)))) - 4 between the vertical lines x = 2.1 and x = 3.0. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
24.0
|
math
|
train
|
math_algebra_func_area_level_3_3_262
|
algebra_func_area3
|
medium (level 2,3)
| 3 |
{
"role": [
"user"
],
"content": [
"Calculate the area enclosed between the functions f(x) = 3(5(2e^(2((1x + 1)/(-2x - 1))) - 1) - 2)^2 - 3(5(2e^(2((1x + 1)/(-2x - 1))) - 1) - 2) + 5 and g(x) = -3cos(3π(4((-2x - 2)/(2x + 1))^2 + 1((-2x - 2)/(2x + 1))) + 3) + 3 from x = -1.3 to x = -1.1. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
0.2
|
math
|
train
|
math_algebra_func_area_level_3_3_263
|
algebra_func_area3
|
medium (level 2,3)
| 3 |
{
"role": [
"user"
],
"content": [
"Calculate the area enclosed between the functions f(x) = -1(-1(-2|(3x - 3) - 1| + 3) + 3) + 5 and g(x) = 3sin(3π(-5(3|x + 2| - 3) + 5)) + 1 from x = 1.7 to x = 1.8. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
0.2
|
math
|
train
|
math_algebra_func_area_level_3_3_264
|
algebra_func_area3
|
medium (level 2,3)
| 3 |
{
"role": [
"user"
],
"content": [
"Determine the area of the region enclosed by the graphs of f(x) = -3sin(1π((-1((2(-4x - 4) - 2)/(3(-4x - 4) + 1)) + 3)/(3((2(-4x - 4) - 2)/(3(-4x - 4) + 1)) + 3)) - 3) and g(x) = (-1(-1(-3e^(-1x) + 3) + 2) + 3)/(2(-1(-3e^(-1x) + 3) + 2) + 1) 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}"
]
}
|
0.2
|
math
|
train
|
math_algebra_func_area_level_3_3_265
|
algebra_func_area3
|
medium (level 2,3)
| 3 |
{
"role": [
"user"
],
"content": [
"Find the area of the region bounded by the curves f(x) = 1|(-1(4(-2e^(-1x) + 1) - 4)^2 - 5(4(-2e^(-1x) + 1) - 4) + 1) - 2| + 1, g(x) = (-2(2(-2x - 2)^2 - 2(-2x - 2) - 4) - 1)/(-1(2(-2x - 2)^2 - 2(-2x - 2) - 4) + 2), x = -0.3, and x = 0.5. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
16.0
|
math
|
train
|
math_algebra_func_area_level_3_3_266
|
algebra_func_area3
|
medium (level 2,3)
| 3 |
{
"role": [
"user"
],
"content": [
"Calculate the area enclosed between the functions f(x) = 2((2(-1|(2x^2 - 2x + 5) - 3| - 3) + 1)/(-3(-1|(2x^2 - 2x + 5) - 3| - 3) - 2)) + 2 and g(x) = 3sin(1π(2(-3x^2 + 5x - 4)^2 + 4(-3x^2 + 5x - 4) + 3) - 3) + 2 from x = -2.7 to x = -2.6. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
0.2
|
math
|
train
|
math_algebra_func_area_level_3_3_267
|
algebra_func_area3
|
medium (level 2,3)
| 3 |
{
"role": [
"user"
],
"content": [
"Determine the area of the region enclosed by the graphs of f(x) = 1((-2((-3((-3x + 3)/(-1x + 3)) + 1)/(2((-3x + 3)/(-1x + 3)) + 2)) + 2)/(3((-3((-3x + 3)/(-1x + 3)) + 1)/(2((-3x + 3)/(-1x + 3)) + 2)) + 1)) + 4 and g(x) = 4((1(5x^2 - 3x - 1) - 1)/(3(5x^2 - 3x - 1) + 2)) + 3 between the vertical lines x = -0.2 and x = 0.6. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
23.0
|
math
|
train
|
math_algebra_func_area_level_3_3_268
|
algebra_func_area3
|
medium (level 2,3)
| 3 |
{
"role": [
"user"
],
"content": [
"Find the area of the region bounded by the curves f(x) = -1|(1((-1(-4x^2 + 5x + 5) - 2)/(1(-4x^2 + 5x + 5) + 3)) - 3)| - 2, g(x) = -1|(1cos(3π((3x + 2)/(-2x - 1)) + 3) + 2) + 3| - 2, x = 2.2, and x = 2.3000000000000003. 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_3_3_269
|
algebra_func_area3
|
medium (level 2,3)
| 3 |
{
"role": [
"user"
],
"content": [
"Find the area of the region bounded by the curves f(x) = -4(-2cos(2π((3(-2x + 3) + 2)/(-1(-2x + 3) + 2)) + 3) - 3), g(x) = (-2(3cos(2π((-1x - 1)/(-2x - 1)) - 2) - 3) + 2)/(-2(3cos(2π((-1x - 1)/(-2x - 1)) - 2) - 3) - 1), x = -0.5, and x = -0.4. 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_3_3_270
|
algebra_func_area3
|
medium (level 2,3)
| 3 |
{
"role": [
"user"
],
"content": [
"Find the area of the region bounded by the curves f(x) = (2(2|((3(-1|x + 1| - 1) + 1)/(1(-1|x + 1| - 1) + 1)) - 1| + 1))/(-2(2|((3(-1|x + 1| - 1) + 1)/(1(-1|x + 1| - 1) + 1)) - 1| + 1)), g(x) = -1((-2(2cos(2πx + 2)) + 2)/(-3(2cos(2πx + 2)) - 2))^2 - 1, x = -1.5, and x = -1.2. 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_3_3_271
|
algebra_func_area3
|
medium (level 2,3)
| 3 |
{
"role": [
"user"
],
"content": [
"Find the area of the region bounded by the curves f(x) = 2((2(3(-4x^2 + 1x - 5) - 3))/(-3(3(-4x^2 + 1x - 5) - 3) + 2))^2 - 3((2(3(-4x^2 + 1x - 5) - 3))/(-3(3(-4x^2 + 1x - 5) - 3) + 2)) - 4, g(x) = -5((1(-2x^2 + 2x - 2) + 2)/(1(-2x^2 + 2x - 2) - 2)), x = -0.4, and x = 1.4. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
2.2
|
math
|
train
|
math_algebra_func_area_level_3_3_272
|
algebra_func_area3
|
medium (level 2,3)
| 3 |
{
"role": [
"user"
],
"content": [
"Calculate the area enclosed between the functions f(x) = -2(3|(2|(-3cos(2πx + 2) + 2) + 2| - 2)| - 1) - 5 and g(x) = -2|(4((1x + 3)/(3x)) - 4)| + 1 from x = 0.1 to x = 0.6. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
14.0
|
math
|
train
|
math_algebra_func_area_level_3_3_273
|
algebra_func_area3
|
medium (level 2,3)
| 3 |
{
"role": [
"user"
],
"content": [
"Determine the area of the region enclosed by the graphs of f(x) = (-2(2|(-1sin(1π(-3x - 5) + 2) + 1) - 2| - 3))/(2(2|(-1sin(1π(-3x - 5) + 2) + 1) - 2| - 3) + 3) and g(x) = -3(-5(-3x - 3)^2 + 5(-3x - 3) - 4) between the vertical lines x = -1.1 and x = -0.8. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
4.7
|
math
|
train
|
math_algebra_func_area_level_3_3_274
|
algebra_func_area3
|
medium (level 2,3)
| 3 |
{
"role": [
"user"
],
"content": [
"Determine the area of the region enclosed by the graphs of f(x) = -3(-3cos(2π((3((2x - 3)/(3x + 1)) + 3)/(1((2x - 3)/(3x + 1)))) - 3) - 1)^2 - 2(-3cos(2π((3((2x - 3)/(3x + 1)) + 3)/(1((2x - 3)/(3x + 1)))) - 3) - 1) + 4 and g(x) = -1sin(1π(-1((3x + 2)/(1x + 2)) - 4)) - 1 between the vertical lines x = 2.2 and x = 2.3000000000000003. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
1.0
|
math
|
train
|
math_algebra_func_area_level_3_3_275
|
algebra_func_area3
|
medium (level 2,3)
| 3 |
{
"role": [
"user"
],
"content": [
"Determine the area of the region enclosed by the graphs of f(x) = -5(1sin(1π(1|(-2|x + 2| + 2)| - 3) - 2)) + 5 and g(x) = 2e^(1(-4(-2x - 3) + 5)) between the vertical lines x = -2.9 and x = -2.8. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
0.1
|
math
|
train
|
math_algebra_func_area_level_3_3_276
|
algebra_func_area3
|
medium (level 2,3)
| 3 |
{
"role": [
"user"
],
"content": [
"Find the area of the region bounded by the curves f(x) = 1|((2(2cos(1π(3x - 5)) + 2) + 3)/(-1(2cos(1π(3x - 5)) + 2) + 3)) + 3| - 2, g(x) = 2|(3(-4x^2 - 1x - 5)^2 + 5(-4x^2 - 1x - 5) + 1) - 1| - 2, x = -0.4, and x = -0.2. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
43.7
|
math
|
train
|
math_algebra_func_area_level_3_3_277
|
algebra_func_area3
|
medium (level 2,3)
| 3 |
{
"role": [
"user"
],
"content": [
"Find the area of the region bounded by the curves f(x) = -1(-2|(1(1cos(2πx + 1) - 1)^2 - 1(1cos(2πx + 1) - 1) - 3) - 3| - 3) - 4, g(x) = -1sin(3π(-1|(-5x^2 + 1x - 4) - 1| - 2)) - 1, x = -4.7, and x = -4.6. 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_3_3_278
|
algebra_func_area3
|
medium (level 2,3)
| 3 |
{
"role": [
"user"
],
"content": [
"Find the area of the region bounded by the curves f(x) = 3cos(2π(-3(1(4x - 5) - 2) - 3) + 1) + 2, g(x) = -2|(2|(3cos(1πx + 3) + 2) - 2| - 3) - 2| + 2, x = 0.2, and x = 0.30000000000000004. 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_3_3_279
|
algebra_func_area3
|
medium (level 2,3)
| 3 |
{
"role": [
"user"
],
"content": [
"Calculate the area enclosed between the functions f(x) = 1sin(1π(1(2((2x + 1)/(3x + 2))) - 1) - 1) and g(x) = (-3(-1|(1x^2 - 3x - 2)| + 3) - 2)/(3(-1|(1x^2 - 3x - 2)| + 3) + 3) 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
|
train
|
math_algebra_func_area_level_3_3_280
|
algebra_func_area3
|
medium (level 2,3)
| 3 |
{
"role": [
"user"
],
"content": [
"Find the area of the region bounded by the curves f(x) = (-1((-2(-1cos(2π(4x^2 + 2x + 3) - 3) + 1) - 3)/(3(-1cos(2π(4x^2 + 2x + 3) - 3) + 1) - 2)) + 1)/(-3((-2(-1cos(2π(4x^2 + 2x + 3) - 3) + 1) - 3)/(3(-1cos(2π(4x^2 + 2x + 3) - 3) + 1) - 2))), g(x) = 4(-3((2x - 3)/(3x + 3))^2 - 2((2x - 3)/(3x + 3)) + 1)^2 - 4(-3((2x - 3)/(3x + 3))^2 - 2((2x - 3)/(3x + 3)) + 1) - 1, x = 1.0, and x = 1.1. 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_3_3_281
|
algebra_func_area3
|
medium (level 2,3)
| 3 |
{
"role": [
"user"
],
"content": [
"Find the area of the region bounded by the curves f(x) = 1(-3(1(3sin(1πx + 1) + 2)^2 + 3(3sin(1πx + 1) + 2) + 3) + 2) + 4, g(x) = (3(-1(-1x^2 - 5x + 4)^2 - 4(-1x^2 - 5x + 4) - 1) - 3)/(3(-1(-1x^2 - 5x + 4)^2 - 4(-1x^2 - 5x + 4) - 1) + 1), x = 0.7, and x = 1.0. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
4.0
|
math
|
train
|
math_algebra_func_area_level_3_3_282
|
algebra_func_area3
|
medium (level 2,3)
| 3 |
{
"role": [
"user"
],
"content": [
"Find the area of the region bounded by the curves f(x) = 3(3(3e^(-1((-3x + 1)/(1x + 3))) - 1) + 1)^2 + 3(3(3e^(-1((-3x + 1)/(1x + 3))) - 1) + 1) - 2, g(x) = -3cos(2π(2((2x - 2)/(3x + 1))^2 + 4((2x - 2)/(3x + 1)) + 4) - 3) + 1, x = -1.6, and x = -1.5. 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_3_3_283
|
algebra_func_area3
|
medium (level 2,3)
| 3 |
{
"role": [
"user"
],
"content": [
"Calculate the area enclosed between the functions f(x) = -2((2((-1(4x - 2) + 2)/(3(4x - 2) + 1)) + 3)/(-2((-1(4x - 2) + 2)/(3(4x - 2) + 1)) + 3)) + 1 and g(x) = -1sin(2π(-3((2x)/(-3x - 1))^2 - 2((2x)/(-3x - 1)) - 5) + 1) + 1 from x = -0.5 to x = -0.4. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
0.1
|
math
|
train
|
math_algebra_func_area_level_3_3_284
|
algebra_func_area3
|
medium (level 2,3)
| 3 |
{
"role": [
"user"
],
"content": [
"Determine the area of the region enclosed by the graphs of f(x) = -1(1|(-1|(-1|x - 3| - 1) + 1| - 3) + 3|) - 2 and g(x) = -4(-4((3x + 1)/(2x + 3))^2 + 2((3x + 1)/(2x + 3)) + 2) + 3 between the vertical lines x = -0.3 and x = 0.3. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
0.4
|
math
|
train
|
math_algebra_func_area_level_3_3_285
|
algebra_func_area3
|
medium (level 2,3)
| 3 |
{
"role": [
"user"
],
"content": [
"Determine the area of the region enclosed by the graphs of f(x) = 5(-1|(-1|(4x^2 - 1x - 4) + 1| + 1) + 1| + 3) - 5 and g(x) = 3|(-2sin(1π(4x + 5) + 3) + 2)| - 1 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}"
]
}
|
0.7
|
math
|
train
|
math_algebra_func_area_level_3_3_286
|
algebra_func_area3
|
medium (level 2,3)
| 3 |
{
"role": [
"user"
],
"content": [
"Find the area of the region bounded by the curves f(x) = -2|(3((-2(-4x^2 + 2x - 4) - 2)/(3(-4x^2 + 2x - 4) + 1))^2 + 3((-2(-4x^2 + 2x - 4) - 2)/(3(-4x^2 + 2x - 4) + 1)) + 1)| - 1, g(x) = -5(-1cos(2π(-3|x - 1| + 1) - 1) + 1)^2 + 1(-1cos(2π(-3|x - 1| + 1) - 1) + 1) + 2, x = -4.9, and x = -4.7. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
1.5
|
math
|
train
|
math_algebra_func_area_level_3_3_287
|
algebra_func_area3
|
medium (level 2,3)
| 3 |
{
"role": [
"user"
],
"content": [
"Determine the area of the region enclosed by the graphs of f(x) = (3(-3(4(-2|x - 3| + 1)^2 - 5(-2|x - 3| + 1) + 1) - 2) + 3)/(-1(-3(4(-2|x - 3| + 1)^2 - 5(-2|x - 3| + 1) + 1) - 2) - 1) and g(x) = -5(1|((3x + 2)/(-2x + 3)) - 2| - 1)^2 - 4(1|((3x + 2)/(-2x + 3)) - 2| - 1) + 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}"
]
}
|
3.6
|
math
|
train
|
math_algebra_func_area_level_3_3_288
|
algebra_func_area3
|
medium (level 2,3)
| 3 |
{
"role": [
"user"
],
"content": [
"Determine the area of the region enclosed by the graphs of f(x) = 4(2|((-2(-3|x - 3| + 1) + 3)/(1(-3|x - 3| + 1))) + 3|) + 4 and g(x) = 5(2cos(3π(-5x + 5) + 3) + 3) between the vertical lines x = -3.0 and x = -2.9. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
0.8
|
math
|
train
|
math_algebra_func_area_level_3_3_289
|
algebra_func_area3
|
medium (level 2,3)
| 3 |
{
"role": [
"user"
],
"content": [
"Find the area of the region bounded by the curves f(x) = 3(1((3(3sin(3πx + 2)) + 1)/(1(3sin(3πx + 2)) + 1)) + 4) + 3, g(x) = -3(-2e^(1((-1x - 1)/(-1x + 3))) + 2) - 1, x = -0.9, and x = -0.5. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
13.0
|
math
|
train
|
math_algebra_func_area_level_3_3_290
|
algebra_func_area3
|
medium (level 2,3)
| 3 |
{
"role": [
"user"
],
"content": [
"Find the area of the region bounded by the curves f(x) = -2((3(4((-2x - 1)/(-1x))^2 + 5) - 3)/(-3(4((-2x - 1)/(-1x))^2 + 5) - 3))^2 - 5((3(4((-2x - 1)/(-1x))^2 + 5) - 3)/(-3(4((-2x - 1)/(-1x))^2 + 5) - 3)) + 2, g(x) = 1((-1(-1|x - 3| + 3) - 1)/(2(-1|x - 3| + 3) + 1))^2 + 2((-1(-1|x - 3| + 3) - 1)/(2(-1|x - 3| + 3) + 1)) - 4, x = -0.6, and x = -0.4. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
5.8
|
math
|
train
|
math_algebra_func_area_level_3_3_291
|
algebra_func_area3
|
medium (level 2,3)
| 3 |
{
"role": [
"user"
],
"content": [
"Find the area of the region bounded by the curves f(x) = 1(-3(-5(3x - 3) + 4) - 3)^2 - 5(-3(-5(3x - 3) + 4) - 3) + 4, g(x) = -1e^(-2(2|(2|x| - 2) + 1|)), x = 1.4, and x = 1.5. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
0.8
|
math
|
train
|
math_algebra_func_area_level_3_3_292
|
algebra_func_area3
|
medium (level 2,3)
| 3 |
{
"role": [
"user"
],
"content": [
"Determine the area of the region enclosed by the graphs of f(x) = -2(-1|(-2(-3|x| - 1)^2 + 2) - 1| + 3) and g(x) = (-2(2cos(1π((1x + 1)/(-2x + 3)) + 1) + 1) + 2)/(-1(2cos(1π((1x + 1)/(-2x + 3)) + 1) + 1) - 1) between the vertical lines x = -0.1 and x = 0.1. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
0.3
|
math
|
train
|
math_algebra_func_area_level_3_3_293
|
algebra_func_area3
|
medium (level 2,3)
| 3 |
{
"role": [
"user"
],
"content": [
"Find the area of the region bounded by the curves f(x) = -1|(3(1(1x^2 + 5x - 1) - 3) - 5) + 1| - 3, g(x) = -4(1|((2x - 3)/(1x)) + 1| - 1)^2 + 1, x = -4.3, and x = -2.7. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
3.3
|
math
|
train
|
math_algebra_func_area_level_3_3_294
|
algebra_func_area3
|
medium (level 2,3)
| 3 |
{
"role": [
"user"
],
"content": [
"Find the area of the region bounded by the curves f(x) = 5(3|(-2sin(3π((-3x - 1)/(-3x - 1)) - 2) - 1) - 2| + 2) + 4, g(x) = -4(-3|(-5x^2 + 2x - 1) - 3|) + 2, x = -0.6, and x = 1.0. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
41.4
|
math
|
train
|
math_algebra_func_area_level_3_3_295
|
algebra_func_area3
|
medium (level 2,3)
| 3 |
{
"role": [
"user"
],
"content": [
"Determine the area of the region enclosed by the graphs of f(x) = -1((1((-2(2|x - 1| - 3) + 2)/(-1(2|x - 1| - 3) + 2)) - 2)/(1((-2(2|x - 1| - 3) + 2)/(-1(2|x - 1| - 3) + 2)))) and g(x) = 2|(-5(-1|x| - 3) - 5) - 1| + 1 between the vertical lines x = -1.0 and x = 3.0. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
134.2
|
math
|
train
|
math_algebra_func_area_level_3_3_296
|
algebra_func_area3
|
medium (level 2,3)
| 3 |
{
"role": [
"user"
],
"content": [
"Find the area of the region bounded by the curves f(x) = (-2(-2cos(2π(-5(-3x^2 + 5x)^2 - 4(-3x^2 + 5x) + 2) - 1) - 1))/(-2(-2cos(2π(-5(-3x^2 + 5x)^2 - 4(-3x^2 + 5x) + 2) - 1) - 1) - 1), g(x) = 4(-3(-2cos(3πx - 3) + 2) + 5) - 3, x = -0.5, and x = -0.2. 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_3_3_297
|
algebra_func_area3
|
medium (level 2,3)
| 3 |
{
"role": [
"user"
],
"content": [
"Determine the area of the region enclosed by the graphs of f(x) = 5((-2(4(-5x - 5)^2 - 5(-5x - 5) + 5) - 1)/(-2(4(-5x - 5)^2 - 5(-5x - 5) + 5) - 3)) + 3 and g(x) = 1(-3|(-2x^2 - 5x - 3) + 3|)^2 + 2(-3|(-2x^2 - 5x - 3) + 3|) - 2 between the vertical lines x = -2.8 and x = -2.2. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
4.8
|
math
|
train
|
math_algebra_func_area_level_3_3_298
|
algebra_func_area3
|
medium (level 2,3)
| 3 |
{
"role": [
"user"
],
"content": [
"Calculate the area enclosed between the functions f(x) = -3(4(1|(3cos(3πx + 1) + 3)| - 1)^2 - 3(1|(3cos(3πx + 1) + 3)| - 1) - 4) + 4 and g(x) = -5(1((-2x - 2)/(3x - 2))^2 + 5((-2x - 2)/(3x - 2)) - 3)^2 - 3(1((-2x - 2)/(3x - 2))^2 + 5((-2x - 2)/(3x - 2)) - 3) + 2 from x = -1.3 to x = -0.9. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
16.4
|
math
|
train
|
math_algebra_func_area_level_3_3_299
|
algebra_func_area3
|
medium (level 2,3)
| 3 |
{
"role": [
"user"
],
"content": [
"Determine the area of the region enclosed by the graphs of f(x) = -3((-3(-5(-3sin(3πx + 1) - 2) + 2) - 3)/(3(-5(-3sin(3πx + 1) - 2) + 2) - 1))^2 - 2((-3(-5(-3sin(3πx + 1) - 2) + 2) - 3)/(3(-5(-3sin(3πx + 1) - 2) + 2) - 1)) + 3 and g(x) = 2sin(1π(3|((2x - 2)/(-3x + 2)) - 1| + 2) - 3) - 1 between the vertical lines x = 4.5 and x = 4.6. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
0.3
|
math
|
train
|
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