messages listlengths 1 1 | ground_truth stringlengths 3 8 | dataset stringclasses 1
value |
|---|---|---|
[
{
"content": "Calculate the area enclosed between the functions f(x) = -1|(-4(1e^(-2(-1x^2 - 5x - 3)) - 3) + 3) + 2| and g(x) = -1e^(2(-1|(-4x^2 - 1x - 4) + 3| + 2)) - 3 from x = -4.5 to x = -4.4. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.3 | MATH |
[
{
"content": "Calculate the area enclosed between the functions f(x) = -2|(-3sin(1π(-4x^2 + 1x + 1) - 2) - 3) + 1| - 3 and g(x) = -3((-2x)/(-3x - 3)) - 2 from x = 1.6 to x = 1.7000000000000002. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.4 | MATH |
[
{
"content": "Find the area of the region bounded by the curves f(x) = -4(2|(1sin(3πx + 1) - 1)| - 1) + 3, g(x) = -1e^(1((2x - 3)/(2x - 3))) + 2, x = -2.1, and x = -1.8. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1.6 | MATH |
[
{
"content": "Find the area of the region bounded by the curves f(x) = 1(-1cos(2π(2|x + 3| + 3) - 2) + 1)^2 + 3(-1cos(2π(2|x + 3| + 3) - 2) + 1) + 4, g(x) = 3|(3x + 2) - 1| - 3, x = 1.0, and x = 1.4. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": ... | 1.5 | MATH |
[
{
"content": "Calculate the area enclosed between the functions f(x) = 3cos(3π(1(3|x + 3| + 3) - 4)) + 3 and g(x) = (3(1x + 2) - 3)/(1(1x + 2) - 3) from x = 3.4 to x = 3.5. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.5 | MATH |
[
{
"content": "Calculate the area enclosed between the functions f(x) = 1((2(-1(2|x + 2| - 2)^2 - 5(2|x + 2| - 2) - 2) + 3)/(3(-1(2|x + 2| - 2)^2 - 5(2|x + 2| - 2) - 2) + 2)) - 2 and g(x) = -3cos(1π(-2|((3x + 3)/(1x - 2)) - 1| + 1) + 1) + 3 from x = -2.8 to x = -1.2. Round to 1 decimal place.\n\nPresent the answ... | 7.8 | MATH |
[
{
"content": "Find the area of the region bounded by the curves f(x) = -2|(-2(1((1x + 1)/(-1x + 2))^2 - 4((1x + 1)/(-1x + 2)) - 5) - 2) + 2|, g(x) = -1((2(-2|x - 2| - 3) - 3)/(2(-2|x - 2| - 3) - 1))^2 - 5((2(-2|x - 2| - 3) - 3)/(2(-2|x - 2| - 3) - 1)) - 3, x = 1.5, and x = 1.6. Round your answer to 1 decimal pl... | 1.2 | MATH |
[
{
"content": "Find the area of the region bounded by the curves f(x) = -1sin(1π(-3(-1x^2 + 2x - 2) + 5) + 2) - 1, g(x) = (2(-3x - 1) + 1)/(-1(-3x - 1) - 1), x = -2.0, and x = -1.9. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.1 | MATH |
[
{
"content": "Determine the area of the region enclosed by the graphs of f(x) = 3cos(3π(-1((-2(2|x + 3| + 3) + 3)/(1(2|x + 3| + 3))) - 4) - 3) - 1 and g(x) = (2(-3|(1cos(2πx + 3) - 1) - 3|) + 1)/(-2(-3|(1cos(2πx + 3) - 1) - 3|) + 3) between the vertical lines x = -3.3 and x = -2.7. Round to 1 decimal place.\n\n... | 0.9 | MATH |
[
{
"content": "Calculate the area enclosed between the functions f(x) = -1cos(2π((2(2x + 2) + 1)/(3(2x + 2) - 1)) + 2) - 3 and g(x) = -2|(1x^2 - 1x + 5) - 3| + 2 from x = -0.1 to x = 1.6. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 2.2 | MATH |
[
{
"content": "Find the area of the region bounded by the curves f(x) = 4(1((3(3|x - 2| - 1) - 2)/(-1(3|x - 2| - 1) + 3))^2 - 3((3(3|x - 2| - 1) - 2)/(-1(3|x - 2| - 1) + 3)) - 2) + 5, g(x) = 1(-3|(-1x^2 + 1x + 2) + 2|) - 1, x = 2.5, and x = 2.9. Round your answer to 1 decimal place.\n\nPresent the answer in LaTe... | 2.1 | MATH |
[
{
"content": "Find the area of the region bounded by the curves f(x) = -5(-3|(1cos(1πx - 1))| - 1)^2 - 2(-3|(1cos(1πx - 1))| - 1), g(x) = 3cos(1π(1x^2 - 4x + 1) + 1) - 3, x = -4.2, and x = -4.1000000000000005. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
... | 0.2 | MATH |
[
{
"content": "Calculate the area enclosed between the functions f(x) = -3(-3(2|((2x + 1)/(3x - 2)) + 3| - 1) + 4)^2 and g(x) = -4(1((1x + 1)/(-2x - 2))^2 + 1((1x + 1)/(-2x - 2)) + 2) - 2 from x = 0.3 to x = 0.4. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": ... | 0.5 | MATH |
[
{
"content": "Determine the area of the region enclosed by the graphs of f(x) = -1(1(2|((-1x - 1)/(1x - 3)) + 3|) + 3)^2 - 2(1(2|((-1x - 1)/(1x - 3)) + 3|) + 3) - 1 and g(x) = -2((-3(-5x) - 2)/(3(-5x) - 1))^2 - 3((-3(-5x) - 2)/(3(-5x) - 1)) - 3 between the vertical lines x = -0.1 and x = -0.0. Round to 1 decima... | -9.0 | MATH |
[
{
"content": "Find the area of the region bounded by the curves f(x) = 5((-1(-1|(-3x^2 + 4x + 3) - 3| + 3))/(2(-1|(-3x^2 + 4x + 3) - 3| + 3) - 1)) - 3, g(x) = 2|(1(1cos(2πx - 3) - 2)^2 - 3(1cos(2πx - 3) - 2) - 5) + 1| - 2, x = -0.5, and x = 1.8. Round your answer to 1 decimal place.\n\nPresent the answer in LaT... | 43.8 | MATH |
[
{
"content": "Calculate the area enclosed between the functions f(x) = 2(5(-1cos(3π(3|x + 3| - 1) + 2) - 2)^2 + 3(-1cos(3π(3|x + 3| - 1) + 2) - 2) + 1) + 2 and g(x) = 2(-2|(4x - 4) + 1| - 1)^2 + 5(-2|(4x - 4) + 1| - 1) - 5 from x = 1.2 to x = 1.3. Round to 1 decimal place.\n\nPresent the answer in LaTex format:... | 4.0 | MATH |
[
{
"content": "Find the area of the region bounded by the curves f(x) = 1(-1|(1(-3sin(3πx + 2) + 1) + 2) - 3| - 2)^2 - 5(-1|(1(-3sin(3πx + 2) + 1) + 2) - 3| - 2) + 3, g(x) = (-1(2(-1x^2 - 2x)) + 1)/(-2(2(-1x^2 - 2x)) - 2), x = -2.2, and x = 0.2. Round your answer to 1 decimal place.\n\nPresent the answer in LaTe... | 92.9 | MATH |
[
{
"content": "Calculate the area enclosed between the functions f(x) = 1(-5((-2x - 3)/(-2x + 1))^2 - 3((-2x - 3)/(-2x + 1)) - 2) + 1 and g(x) = 3(3x^2 + 3x - 5) - 4 from x = -2.0 to x = -0.1. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 24.8 | MATH |
[
{
"content": "Determine the area of the region enclosed by the graphs of f(x) = 5(-1((-2(-2cos(1πx) + 3) - 2)/(-1(-2cos(1πx) + 3)))^2 - 2((-2(-2cos(1πx) + 3) - 2)/(-1(-2cos(1πx) + 3))) - 5) + 2 and g(x) = (-1(-3|(1x + 3) - 3|) - 2)/(-2(-3|(1x + 3) - 3|) - 1) between the vertical lines x = -0.2 and x = 0.2. Roun... | 55.7 | MATH |
[
{
"content": "Calculate the area enclosed between the functions f(x) = -1(3(3|x + 1|)^2 - 2(3|x + 1|) - 5) + 4 and g(x) = (2(4x^2 - 4x + 4) - 2)/(-1(4x^2 - 4x + 4) + 3) from x = -0.2 to x = 0.3. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 3.0 | MATH |
[
{
"content": "Find the area of the region bounded by the curves f(x) = -1e^(2(5(2|x - 2| - 3)^2 + 5(2|x - 2| - 3) - 2)), g(x) = -1|(5x^2 + 1x + 2) + 2| - 1, x = 2.7, and x = 3.8. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 65.9 | MATH |
[
{
"content": "Find the area of the region bounded by the curves f(x) = (-1(-5(3|x - 2| - 1) - 3) + 3)/(-2(-5(3|x - 2| - 1) - 3) - 1), g(x) = -1|(-5x) + 2| - 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}",
"role": "user"
}
] | 9.4 | MATH |
[
{
"content": "Calculate the area enclosed between the functions f(x) = 1(1|(1e^(-2x) - 1) - 1| - 1)^2 - 3 and g(x) = -1((3x - 2)/(2x))^2 - 4((3x - 2)/(2x)) - 2 from x = 0.2 to x = 0.7. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1.4 | MATH |
[
{
"content": "Determine the area of the region enclosed by the graphs of f(x) = (-1(-1(-2(-3|x + 1|)^2 - 3(-3|x + 1|) - 1) + 1) + 1)/(2(-1(-2(-3|x + 1|)^2 - 3(-3|x + 1|) - 1) + 1) + 1) and g(x) = 2|(-2(-2x^2 + 4x - 1) - 3)| - 2 between the vertical lines x = -0.0 and x = 2.0. Round to 1 decimal place.\n\nPresen... | 11.6 | MATH |
[
{
"content": "Determine the area of the region enclosed by the graphs of f(x) = -2(-1cos(2π(4((3x - 1)/(-1x - 2)) - 4) - 3) - 3)^2 - 4(-1cos(2π(4((3x - 1)/(-1x - 2)) - 4) - 3) - 3) and g(x) = -2(-4((-3x + 1)/(-2x))^2 - 4((-3x + 1)/(-2x)) + 4) + 2 between the vertical lines x = 0.2 and x = 0.3. Round to 1 decima... | 0.4 | MATH |
[
{
"content": "Find the area of the region bounded by the curves f(x) = -3|(-2((-2(4x^2 + 4x))/(3(4x^2 + 4x) - 1)) - 3) - 3| + 3, g(x) = -3sin(2π((-3(-1|x + 3| - 3) - 1)/(-2(-1|x + 3| - 3) - 3)) + 1) + 3, x = -1.1, and x = -1.0. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed... | 13.0 | MATH |
[
{
"content": "Determine the area of the region enclosed by the graphs of f(x) = 1(1|(-5(-1sin(2πx - 3)) + 4) - 2| - 2)^2 - 2(1|(-5(-1sin(2πx - 3)) + 4) - 2| - 2) - 2 and g(x) = (-1(1|(3x^2 + 5x + 3) + 2| - 2) - 2)/(-2(1|(3x^2 + 5x + 3) + 2| - 2) + 3) between the vertical lines x = 1.1 and x = 1.4. Round to 1 de... | 0.9 | MATH |
[
{
"content": "Determine the area of the region enclosed by the graphs of f(x) = (-2(-5(2sin(3π(3x + 5)) - 2)^2 - 1(2sin(3π(3x + 5)) - 2) - 1) - 3)/(2(-5(2sin(3π(3x + 5)) - 2)^2 - 1(2sin(3π(3x + 5)) - 2) - 1) + 3) and g(x) = -2|((-1(-3x^2 - 4x + 2) - 1)/(2(-3x^2 - 4x + 2) - 3)) + 3| between the vertical lines x ... | 2.7 | MATH |
[
{
"content": "Determine the area of the region enclosed by the graphs of f(x) = (-1(-3sin(1π(2(-1x + 1)^2 + 5(-1x + 1) - 1) - 2) + 3) + 3)/(-1(-3sin(1π(2(-1x + 1)^2 + 5(-1x + 1) - 1) - 2) + 3) - 1) and g(x) = 3e^(1((-3(-3|x| + 3) + 2)/(-2(-3|x| + 3) - 2))) - 3 between the vertical lines x = -1.0 and x = -0.9. R... | 0.1 | MATH |
[
{
"content": "Calculate the area enclosed between the functions f(x) = 1(-2|((-3x - 3)/(-3x + 2)) + 2| - 2)^2 + 5(-2|((-3x - 3)/(-3x + 2)) + 2| - 2) + 2 and g(x) = (-1(-3|x - 2|))/(3(-3|x - 2|) - 2) from x = -0.3 to x = 0.3. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",... | 1.5 | MATH |
[
{
"content": "Determine the area of the region enclosed by the graphs of f(x) = 1(-2|((-2x - 3)/(-2x + 3)) + 2| - 1) - 4 and g(x) = -3(3sin(2πx + 2) + 1)^2 + 1(3sin(2πx + 2) + 1) between the vertical lines x = -1.5 and x = -1.3. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answe... | 1.2 | MATH |
[
{
"content": "Calculate the area enclosed between the functions f(x) = (2(-1(2sin(3πx + 3) - 1)^2 + 2(2sin(3πx + 3) - 1) + 4) + 1)/(3(-1(2sin(3πx + 3) - 1)^2 + 2(2sin(3πx + 3) - 1) + 4) - 2) and g(x) = (2(3|x - 1| + 2) + 1)/(-2(3|x - 1| + 2) - 3) from x = 0.0 to x = 0.3. Round to 1 decimal place.\n\nPresent the... | 0.7 | MATH |
[
{
"content": "Find the area of the region bounded by the curves f(x) = (-3(-3|(-1x - 3) - 2| + 1) + 3)/(1(-3|(-1x - 3) - 2| + 1)), g(x) = -1|(-4x - 4) - 1| + 3, x = -4.5, and x = -2.9. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 3.7 | MATH |
[
{
"content": "Determine the area of the region enclosed by the graphs of f(x) = 1(-3|(-2sin(1πx - 1) - 1) + 1| - 3) - 3 and g(x) = -1|(-3x^2 + 2x + 2) + 1| between the vertical lines x = -1.6 and x = 2.2. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
... | 27.5 | MATH |
[
{
"content": "Determine the area of the region enclosed by the graphs of f(x) = 3(1((2x + 2)/(-2x + 3)) - 5)^2 - 1(1((2x + 2)/(-2x + 3)) - 5) + 2 and g(x) = 3|(-3sin(2πx + 3) + 2) + 1| + 2 between the vertical lines x = 1.0 and x = 1.2. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Yo... | 2.0 | MATH |
[
{
"content": "Find the area of the region bounded by the curves f(x) = -2|((-3(2cos(2πx - 1) - 3))/(1(2cos(2πx - 1) - 3) + 2)) - 3| - 2, g(x) = -4(2cos(3πx - 3) - 2)^2 - 4(2cos(3πx - 3) - 2) - 5, x = -0.7, and x = -0.6. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your an... | 34.5 | MATH |
[
{
"content": "Determine the area of the region enclosed by the graphs of f(x) = (2(2(3cos(3πx) + 2)) + 3)/(-3(2(3cos(3πx) + 2)) + 4) and g(x) = -1cos(2π(4x + 5) + 1) + 3 between the vertical lines x = -2.9 and x = -2.4. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
... | 2.7 | MATH |
[
{
"content": "Find the area of the region bounded by the curves f(x) = (3(-4(-2cos(1π(-2x - 4) - 1) + 1)^2 - 4) - 3)/(-3(-4(-2cos(1π(-2x - 4) - 1) + 1)^2 - 4) - 2), g(x) = (-3(-1|(-4x - 1) + 1| + 2) + 2)/(-3(-1|(-4x - 1) + 1| + 2) + 1), x = -0.4, and x = 0.4. Round your answer to 1 decimal place.\n\nPresent the... | 1.3 | MATH |
[
{
"content": "Calculate the area enclosed between the functions f(x) = 2e^(-1(-2|(-5((1x + 2)/(-1x - 3))^2) + 1| - 2)) - 1 and g(x) = 5(-2(3sin(1πx + 2) + 2) + 5)^2 - 2(-2(3sin(1πx + 2) + 2) + 5) + 4 from x = -0.8 to x = -0.3. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}... | 17.4 | MATH |
[
{
"content": "Determine the area of the region enclosed by the graphs of f(x) = -3e^(1(1(3x^2 - 4x - 1) - 4)) + 1 and g(x) = 3sin(3π((2x - 2)/(-2x + 1)) + 2) - 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}",
"role": "u... | 0.2 | MATH |
[
{
"content": "Calculate the area enclosed between the functions f(x) = 4((-1(-5(1|x + 2| + 1) - 5) + 2)/(3(-5(1|x + 2| + 1) - 5) + 3))^2 - 4((-1(-5(1|x + 2| + 1) - 5) + 2)/(3(-5(1|x + 2| + 1) - 5) + 3)) - 3 and g(x) = (-2(4(-3|x + 1| + 2) - 4) - 1)/(-1(4(-3|x + 1| + 2) - 4)) from x = -1.4 to x = -0.6. Round to ... | 6.7 | MATH |
[
{
"content": "Calculate the area enclosed between the functions f(x) = (1(2(1sin(2πx) - 1)^2 - 3(1sin(2πx) - 1) - 1) + 1)/(-2(2(1sin(2πx) - 1)^2 - 3(1sin(2πx) - 1) - 1) + 3) and g(x) = (-2(-1sin(3πx - 3)) - 3)/(-2(-1sin(3πx - 3)) + 3) from x = -2.0 to x = -1.9. Round to 1 decimal place.\n\nPresent the answer in... | 1.6 | MATH |
[
{
"content": "Find the area of the region bounded by the curves f(x) = 1(3|((-2(-2sin(1πx + 3) + 1) - 1)/(2(-2sin(1πx + 3) + 1) - 3)) - 2| - 3) - 4, g(x) = 1((1(-2e^(1x) - 1))/(-1(-2e^(1x) - 1)))^2 - 3, x = -2.8, and x = -2.1. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{... | 0.8 | MATH |
[
{
"content": "Calculate the area enclosed between the functions f(x) = -3|(-3cos(1π(2x^2 + 2x + 1)) + 1) + 1| + 1 and g(x) = 1(-2e^(1x) + 1) - 2 from x = -2.5 to x = -2.4. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.1 | MATH |
[
{
"content": "Determine the area of the region enclosed by the graphs of f(x) = -5(3e^(-1(-2|x + 1| + 1))) + 5 and g(x) = -3sin(3π(-4x^2 + 3) - 2) between the vertical lines x = -1.1 and x = -1.0. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.2 | MATH |
[
{
"content": "Calculate the area enclosed between the functions f(x) = -2sin(3π(-3(-1|x - 2| + 1) + 1) + 2) + 3 and g(x) = 3(-5x^2 + 2x + 2) - 5 from x = 0.0 to x = 0.2. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.4 | MATH |
[
{
"content": "Find the area of the region bounded by the curves f(x) = 2|(-3((1x + 3)/(1x + 2))^2 + 4((1x + 3)/(1x + 2)) + 3) - 2| - 2, g(x) = -1sin(3π(3|x + 3| - 2)) - 1, x = -0.3, and x = -0.2. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "use... | 0.1 | MATH |
[
{
"content": "Calculate the area enclosed between the functions f(x) = -2((-2(1e^(2(-2|x + 2| + 1)) + 2) + 1)/(-2(1e^(2(-2|x + 2| + 1)) + 2) - 1))^2 + 3((-2(1e^(2(-2|x + 2| + 1)) + 2) + 1)/(-2(1e^(2(-2|x + 2| + 1)) + 2) - 1)) + 3 and g(x) = -2(-3|(-2e^(1x) - 1) + 3| + 3) - 1 from x = -2.6 to x = 0.6. Round to 1... | 12.8 | MATH |
[
{
"content": "Calculate the area enclosed between the functions f(x) = (-3(1|(1x^2 - 1x - 5) + 2| + 2) - 1)/(-3(1|(1x^2 - 1x - 5) + 2| + 2) + 4) and g(x) = 5(-3cos(1πx - 1) + 1)^2 + 4(-3cos(1πx - 1) + 1) - 2 from x = 0.1 to x = 0.5. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your a... | 2.3 | MATH |
[
{
"content": "Calculate the area enclosed between the functions f(x) = 1((3(1(-2|x + 2| - 1) - 3) + 1)/(-1(1(-2|x + 2| - 1) - 3) + 2))^2 + 1((3(1(-2|x + 2| - 1) - 3) + 1)/(-1(1(-2|x + 2| - 1) - 3) + 2)) + 2 and g(x) = 3|(-1(4x^2 - 3x - 2) + 2) + 1| + 1 from x = -0.7 to x = 1.4. Round to 1 decimal place.\n\nPres... | 17.1 | MATH |
[
{
"content": "Determine the area of the region enclosed by the graphs of f(x) = 1(-2|((3(3x) - 3)/(-2(3x) + 3)) + 1| + 3)^2 - 1(-2|((3(3x) - 3)/(-2(3x) + 3)) + 1| + 3) + 1 and g(x) = 1cos(1π(1|(-1x + 2) - 1|)) + 3 between the vertical lines x = 3.6 and x = 4.4. Round to 1 decimal place.\n\nPresent the answer in... | 0.3 | MATH |
[
{
"content": "Determine the area of the region enclosed by the graphs of f(x) = 4(3|((3(3x^2 + 3x - 5) - 3)/(-1(3x^2 + 3x - 5) - 3)) + 2| + 2) + 4 and g(x) = (-3(-1|(-2x - 3) - 1|))/(-2(-1|(-2x - 3) - 1|) - 1) between the vertical lines x = -2.3 and x = -1.7. Round to 1 decimal place.\n\nPresent the answer in L... | 41.5 | MATH |
[
{
"content": "Determine the area of the region enclosed by the graphs of f(x) = 1(-2((-2(-1|x|) - 3)/(-1(-1|x|) + 2)) - 1)^2 + 1(-2((-2(-1|x|) - 3)/(-1(-1|x|) + 2)) - 1) and g(x) = (-3(-2(-2|x + 1| + 2)^2 - 4(-2|x + 1| + 2) + 4) - 1)/(-1(-2(-2|x + 1| + 2)^2 - 4(-2|x + 1| + 2) + 4) - 3) between the vertical line... | 11.9 | MATH |
[
{
"content": "Calculate the area enclosed between the functions f(x) = -1|(-1(-4((-2x)/(-3x - 3))^2 - 1((-2x)/(-3x - 3)) - 4) - 5) + 2| - 3 and g(x) = -3|(-5((3x + 1)/(1x + 2))^2 - 5((3x + 1)/(1x + 2)) + 2) + 3| + 1 from x = -1.2 to x = -0.7. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\bo... | -24.8 | MATH |
[
{
"content": "Find the area of the region bounded by the curves f(x) = 3|((3(-1e^(1(1x + 2)) + 3) - 1)/(-1(-1e^(1(1x + 2)) + 3))) - 2| - 3, g(x) = (-1(4(-1|x - 2| - 2) - 2) + 3)/(1(4(-1|x - 2| - 2) - 2) + 2), x = -1.0, and x = -0.9. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\... | 22.7 | MATH |
[
{
"content": "Determine the area of the region enclosed by the graphs of f(x) = 1|((3(3x^2 - 5x - 2) - 2)/(-3(3x^2 - 5x - 2) - 3)) - 1| + 3 and g(x) = (-1(-3|x + 3| + 2) - 2)/(2(-3|x + 3| + 2) - 1) between the vertical lines x = -3.6 and x = -2.4. Round to 1 decimal place.\n\nPresent the answer in LaTex format:... | 32.2 | MATH |
[
{
"content": "Determine the area of the region enclosed by the graphs of f(x) = (-2(3(2|(-2x + 5) - 3|)^2 + 4(2|(-2x + 5) - 3|) + 1) - 2)/(3(3(2|(-2x + 5) - 3|)^2 + 4(2|(-2x + 5) - 3|) + 1) + 2) and g(x) = -5(-1(-2|x - 3| + 2)^2 + 1) - 1 between the vertical lines x = 2.5 and x = 3.5. Round to 1 decimal place.\... | 6.3 | MATH |
[
{
"content": "Find the area of the region bounded by the curves f(x) = 2cos(1π(-5((1(-3x^2 + 4x + 3) + 3)/(-2(-3x^2 + 4x + 3) - 3)) - 3) + 2) + 1, g(x) = (1(2sin(3π(-1|x - 2| - 2) + 3)) + 2)/(-1(2sin(3π(-1|x - 2| - 2) + 3)) - 3), x = 2.0, and x = 2.1. Round your answer to 1 decimal place.\n\nPresent the answer ... | 0.2 | MATH |
[
{
"content": "Calculate the area enclosed between the functions f(x) = -4(-2((1x + 1)/(3x - 2))^2 - 1((1x + 1)/(3x - 2)) + 3) + 1 and g(x) = 3|(-4x + 3) - 2| - 2 from x = 0.4 to x = 1.2. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -21.0 | MATH |
[
{
"content": "Calculate the area enclosed between the functions f(x) = (-1(-1(5(3|x + 2|)^2 + 1(3|x + 2|)) + 5) - 1)/(3(-1(5(3|x + 2|)^2 + 1(3|x + 2|)) + 5) + 3) and g(x) = -4(2e^(2((-2x - 2)/(1x - 2))) - 1)^2 - 1(2e^(2((-2x - 2)/(1x - 2))) - 1) + 1 from x = -3.9 to x = -1.2. Round to 1 decimal place.\n\nPresen... | 2.0 | MATH |
[
{
"content": "Determine the area of the region enclosed by the graphs of f(x) = -3|(-1(5((2x + 1)/(3x + 2))^2 + 3)) - 3| - 3 and g(x) = (-3(1(-1sin(3πx + 3) + 2)^2 + 2(-1sin(3πx + 3) + 2) - 5) - 1)/(-2(1(-1sin(3πx + 3) + 2)^2 + 2(-1sin(3πx + 3) + 2) - 5) - 1) between the vertical lines x = 1.8 and x = 1.9. Roun... | 2.8 | MATH |
[
{
"content": "Calculate the area enclosed between the functions f(x) = (1(-3|(-3x^2 + 3x + 3) + 3| + 2) - 2)/(2(-3|(-3x^2 + 3x + 3) + 3| + 2) - 1) and g(x) = -1(-3sin(1πx - 3) + 3)^2 - 3(-3sin(1πx - 3) + 3) + 2 from x = -2.7 to x = -2.4. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Y... | 0.3 | MATH |
[
{
"content": "Calculate the area enclosed between the functions f(x) = (-3(2e^(1(-1x^2 - 4x)) - 3) - 2)/(2(2e^(1(-1x^2 - 4x)) - 3) + 2) and g(x) = (2(1x^2 - 5x + 4))/(2(1x^2 - 5x + 4)) from x = -4.0 to x = -0.0. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": ... | 11.4 | MATH |
[
{
"content": "Determine the area of the region enclosed by the graphs of f(x) = 3|((2(3(-4x - 2)^2 - 1(-4x - 2) - 1) - 2)/(-3(3(-4x - 2)^2 - 1(-4x - 2) - 1) - 3))| - 2 and g(x) = -3cos(1π((3(3x^2 + 5x - 5) + 1)/(-2(3x^2 + 5x - 5) + 1)) + 3) + 2 between the vertical lines x = -2.5 and x = -2.4. Round to 1 decima... | 0.2 | MATH |
[
{
"content": "Find the area of the region bounded by the curves f(x) = -1|(4(1((2x + 3)/(2x - 1))^2 - 4((2x + 3)/(2x - 1)) - 2) - 4) - 1| + 2, g(x) = -1((2(2sin(3πx - 1) + 1) - 1)/(-1(2sin(3πx - 1) + 1) + 3)) + 4, x = -1.0, and x = -0.5. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex forma... | 2.5 | MATH |
[
{
"content": "Determine the area of the region enclosed by the graphs of f(x) = (-2(-4(-4(1cos(3πx + 2))^2 + 5(1cos(3πx + 2)) - 1) - 4) + 3)/(3(-4(-4(1cos(3πx + 2))^2 + 5(1cos(3πx + 2)) - 1) - 4)) and g(x) = 3((-1(1x^2 + 2) + 1)/(-1(1x^2 + 2))) + 4 between the vertical lines x = -2.0 and x = -0.4. Round to 1 de... | 11.0 | MATH |
[
{
"content": "Find the area of the region bounded by the curves f(x) = (3(-2cos(3π(-2x^2 - 1x + 1) - 2) + 1) - 2)/(-1(-2cos(3π(-2x^2 - 1x + 1) - 2) + 1) + 2), g(x) = 3e^(-1(-4x - 2)) - 2, x = 0.2, and x = 0.5. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
... | 32.8 | MATH |
[
{
"content": "Find the area of the region bounded by the curves f(x) = (-1(1(-1|(-3x + 4) - 1|)^2 + 4(-1|(-3x + 4) - 1|)) - 3)/(1(1(-1|(-3x + 4) - 1|)^2 + 4(-1|(-3x + 4) - 1|))), g(x) = 5(-2|(3x - 4) + 1| + 3)^2 - 4(-2|(3x - 4) + 1| + 3) - 3, x = 0.4, and x = 0.7. Round your answer to 1 decimal place.\n\nPresen... | 0.7 | MATH |
[
{
"content": "Calculate the area enclosed between the functions f(x) = (-3(2(-3x - 5)^2 - 1(-3x - 5) - 5))/(2(2(-3x - 5)^2 - 1(-3x - 5) - 5) - 1) and g(x) = -3((-1x - 1)/(-3x - 3)) from x = -2.2 to x = -1.3. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "use... | 0.3 | MATH |
[
{
"content": "Find the area of the region bounded by the curves f(x) = 3|((1(-3sin(3πx) + 3) - 1)/(1(-3sin(3πx) + 3) + 3)) - 2| - 3, g(x) = 2(-2|x| + 2) - 2, x = -0.2, and x = 0.0. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.0 | MATH |
[
{
"content": "Determine the area of the region enclosed by the graphs of f(x) = 1((-2(4(2|x - 1| - 3)^2 + 5(2|x - 1| - 3) - 4) + 2)/(-3(4(2|x - 1| - 3)^2 + 5(2|x - 1| - 3) - 4) + 4)) and g(x) = (2(-2(-1x^2 + 3x - 3) + 5) - 3)/(1(-2(-1x^2 + 3x - 3) + 5)) between the vertical lines x = -0.8 and x = 0.5. Round to ... | 1.8 | MATH |
[
{
"content": "Calculate the area enclosed between the functions f(x) = (1(-4(-1|(-2x^2 + 5x + 4) + 1| + 1) - 4) + 3)/(-3(-4(-1|(-2x^2 + 5x + 4) + 1| + 1) - 4)) and g(x) = -2cos(3π(-5(-3|x - 3| + 1)^2 + 5(-3|x - 3| + 1) - 1) - 2) + 1 from x = 2.2 to x = 2.3000000000000003. Round to 1 decimal place.\n\nPresent th... | 0.2 | MATH |
[
{
"content": "Calculate the area enclosed between the functions f(x) = -3e^(-1(2(3x + 4)^2 + 4(3x + 4) + 1)) - 1 and g(x) = -2(2|x - 1| - 3) + 1 from x = -1.9 to x = -1.4. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1.7 | MATH |
[
{
"content": "Calculate the area enclosed between the functions f(x) = 1|((1(-4(5x - 5)^2) - 2)/(2(-4(5x - 5)^2) + 1)) - 1| - 1 and g(x) = (3(-2sin(2π(-2|x + 2| + 2) + 1) + 1) - 3)/(-1(-2sin(2π(-2|x + 2| + 2) + 1) + 1) + 2) from x = -3.6 to x = -3.3. Round to 1 decimal place.\n\nPresent the answer in LaTex form... | 0.4 | MATH |
[
{
"content": "Calculate the area enclosed between the functions f(x) = -4(1sin(2π(2((2x - 1)/(1x + 1)) - 4) + 1))^2 + 5(1sin(2π(2((2x - 1)/(1x + 1)) - 4) + 1)) + 2 and g(x) = (2(-1cos(2π(-3|x + 3|) + 3) + 2))/(-3(-1cos(2π(-3|x + 3|) + 3) + 2)) from x = -1.2 to x = -1.0999999999999999. Round to 1 decimal place.\... | 0.4 | MATH |
[
{
"content": "Determine the area of the region enclosed by the graphs of f(x) = (1(2|(3x^2 + 2x - 1) + 1| + 1) - 2)/(-2(2|(3x^2 + 2x - 1) + 1| + 1) + 1) and g(x) = -2cos(2π(1x - 3) - 1) + 2 between the vertical lines x = -0.7 and x = -0.0. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed... | 1.7 | MATH |
[
{
"content": "Find the area of the region bounded by the curves f(x) = 1(1((-2x + 2)/(2x))^2 + 1((-2x + 2)/(2x))) + 3, g(x) = -2|(2x^2 - 5x - 1) - 2| + 3, x = 3.0, and x = 3.1. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.1 | MATH |
[
{
"content": "Determine the area of the region enclosed by the graphs of f(x) = -2cos(3π(-4(-4((3x + 3)/(-1x - 2))^2 - 5((3x + 3)/(-1x - 2)) + 3) + 2) - 3) - 1 and g(x) = 1(4(-2|x + 2| + 1)^2 + 5(-2|x + 2| + 1) - 5) - 1 between the vertical lines x = -1.9 and x = -1.8. Round to 1 decimal place.\n\nPresent the a... | 0.1 | MATH |
[
{
"content": "Calculate the area enclosed between the functions f(x) = 1((-2(-3|x + 2| + 2) - 3)/(2(-3|x + 2| + 2) - 1))^2 - 5((-2(-3|x + 2| + 2) - 3)/(2(-3|x + 2| + 2) - 1)) + 3 and g(x) = -3((2x - 1)/(-1x)) + 3 from x = -2.6 to x = -1.4. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed... | 2.6 | MATH |
[
{
"content": "Determine the area of the region enclosed by the graphs of f(x) = -3|(-2(-3cos(3πx - 3) - 1) + 2) + 1| + 2 and g(x) = -5(3x + 1)^2 - 5(3x + 1) - 5 between the vertical lines x = -0.8 and x = -0.6. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "... | 1.1 | MATH |
[
{
"content": "Find the area of the region bounded by the curves f(x) = -1|((-1(-2(-3x^2 + 3x + 1) - 2) + 2)/(-2(-2(-3x^2 + 3x + 1) - 2) - 2)) - 1| + 1, g(x) = -3cos(1π(-2|(4x^2 + 1) - 1| - 3) + 2) + 2, x = 4.8, and x = 4.8999999999999995. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex form... | 0.2 | MATH |
[
{
"content": "Calculate the area enclosed between the functions f(x) = -2((-3(-3x) - 3)/(2(-3x) + 3))^2 + 2((-3(-3x) - 3)/(2(-3x) + 3)) - 2 and g(x) = (2(-3|x + 1| + 3) + 1)/(3(-3|x + 1| + 3) + 1) from x = -2.1 to x = 0.1. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
... | 19.2 | MATH |
[
{
"content": "Calculate the area enclosed between the functions f(x) = -1(1|(1e^(-1x) + 2) + 3| - 2)^2 + 2(1|(1e^(-1x) + 2) + 3| - 2) and g(x) = (3(2cos(1πx - 3) + 2) - 2)/(3(2cos(1πx - 3) + 2) - 1) from x = 2.2 to x = 3.8. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
... | 6.9 | MATH |
[
{
"content": "Calculate the area enclosed between the functions f(x) = -3|(5(-2((1x - 1)/(-2x - 2))^2 + 3((1x - 1)/(-2x - 2))) + 2) + 1| + 2 and g(x) = (-1(-3|(1x - 5) + 2| - 2) + 2)/(3(-3|(1x - 5) + 2| - 2) + 2) from x = -0.5 to x = 1.7. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{... | 26.0 | MATH |
[
{
"content": "Calculate the area enclosed between the functions f(x) = 4(4(-3|x + 3| - 1)^2 + 5(-3|x + 3| - 1) - 5) - 4 and g(x) = (1(1cos(3πx + 3)))/(3(1cos(3πx + 3)) + 1) from x = -3.3 to x = -3.2. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1.1 | MATH |
[
{
"content": "Determine the area of the region enclosed by the graphs of f(x) = 1((-2(3x^2 + 1x - 1) - 1)/(-1(3x^2 + 1x - 1) - 1)) + 5 and g(x) = (-3(3x + 5) + 3)/(1(3x + 5) + 2) between the vertical lines x = -0.4 and x = 0.1. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer... | 61.8 | MATH |
[
{
"content": "Calculate the area enclosed between the functions f(x) = 3|(4((1x + 1)/(3x + 3))^2 - 2((1x + 1)/(3x + 3)) - 1) - 3| + 1 and g(x) = 2|(-1x^2 - 1x + 5)| - 2 from x = -4.1 to x = 3.1. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 62.0 | MATH |
[
{
"content": "Calculate the area enclosed between the functions f(x) = 1cos(3π(2|(-1(-1x - 2)^2 + 3(-1x - 2) + 2) + 3| + 1) + 3) + 2 and g(x) = (-3(1(2|x + 1| + 1) + 4) + 3)/(-1(1(2|x + 1| + 1) + 4) - 2) from x = 3.5 to x = 3.6. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answe... | 0.1 | MATH |
[
{
"content": "Calculate the area enclosed between the functions f(x) = (-1(2(-1sin(3π(1|x - 2|) + 1) + 1)) - 2)/(3(2(-1sin(3π(1|x - 2|) + 1) + 1)) + 3) and g(x) = -2e^(-2((-1(1|x - 1| - 2))/(2(1|x - 1| - 2) - 1))) + 1 from x = -1.1 to x = 3.1. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\b... | 8.9 | MATH |
[
{
"content": "Calculate the area enclosed between the functions f(x) = -4(-4(1|x| - 2) - 3)^2 + 4(-4(1|x| - 2) - 3) + 5 and g(x) = -2cos(2π(-1x - 3) - 3) from x = -0.9 to x = 0.8. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 49.2 | MATH |
[
{
"content": "Calculate the area enclosed between the functions f(x) = (3(-2sin(1π(1(2x^2 + 4x + 2) - 2) + 3) - 1) + 2)/(1(-2sin(1π(1(2x^2 + 4x + 2) - 2) + 3) - 1) + 1) and g(x) = 3cos(2π(-1(3|x - 1| - 2) + 4)) + 1 from x = -3.8 to x = -3.6. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\box... | 1.1 | MATH |
[
{
"content": "Find the area of the region bounded by the curves f(x) = (-1(3(-2|(-2x + 1) - 1| - 1)^2 + 5(-2|(-2x + 1) - 1| - 1) - 2) - 3)/(-2(3(-2|(-2x + 1) - 1| - 1)^2 + 5(-2|(-2x + 1) - 1| - 1) - 2) - 3), g(x) = -2cos(2π(2|((1x + 1)/(3x)) - 1| - 1) + 3) - 1, x = -0.1, and x = 0.0. Round your answer to 1 deci... | 0.1 | MATH |
[
{
"content": "Calculate the area enclosed between the functions f(x) = 3(-5(-1|((2x - 2)/(-2x + 1)) - 1| + 3)^2 + 2(-1|((2x - 2)/(-2x + 1)) - 1| + 3) + 4) - 2 and g(x) = -1|((2(4x - 1) + 2)/(-1(4x - 1) + 2)) - 3| + 1 from x = 0.7 to x = 0.8. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\box... | 59.6 | MATH |
[
{
"content": "Determine the area of the region enclosed by the graphs of f(x) = -3(-3|((1(3x^2 + 3x - 3) - 1)/(2(3x^2 + 3x - 3) + 1))| - 2) - 2 and g(x) = -4((-2(1|x + 2| + 3) - 1)/(1(1|x + 2| + 3) + 1)) - 1 between the vertical lines x = -1.7 and x = 0.7. Round to 1 decimal place.\n\nPresent the answer in LaTe... | 48.3 | MATH |
[
{
"content": "Determine the area of the region enclosed by the graphs of f(x) = -1sin(1π(5(2|x - 3| - 3) + 3) + 3) - 2 and g(x) = (-2(5x + 4) + 1)/(3(5x + 4) + 2) between the vertical lines x = -1.3 and x = -1.2. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role":... | 0.0 | MATH |
[
{
"content": "Determine the area of the region enclosed by the graphs of f(x) = 1(1cos(3π((-2x + 1)/(1x - 3)) + 2) + 3)^2 - 2(1cos(3π((-2x + 1)/(1x - 3)) + 2) + 3) + 4 and g(x) = -3sin(2π((2x + 1)/(-2x + 1)) + 1) + 2 between the vertical lines x = 3.1 and x = 3.2. Round to 1 decimal place.\n\nPresent the answer... | 0.3 | MATH |
[
{
"content": "Find the area of the region bounded by the curves f(x) = -5(2|((-2(5x^2 + 2x - 1) - 3)/(-3(5x^2 + 2x - 1) + 1)) - 1| - 2) - 3, g(x) = 1((1(-1|x - 2| + 3) - 2)/(-1(-1|x - 2| + 3) + 3)), x = -0.9, and x = 0.5. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your ... | 62.2 | MATH |
[
{
"content": "Calculate the area enclosed between the functions f(x) = 3((-1(3|(3x^2 - 4x - 2)|) + 3)/(3(3|(3x^2 - 4x - 2)|) + 2)) - 5 and g(x) = (3(2(-3cos(2πx - 1) - 1)^2 + 5(-3cos(2πx - 1) - 1) + 3) - 2)/(2(2(-3cos(2πx - 1) - 1)^2 + 5(-3cos(2πx - 1) - 1) + 3) - 1) from x = -3.0 to x = -2.1. Round to 1 decima... | 6.9 | MATH |
[
{
"content": "Calculate the area enclosed between the functions f(x) = 3cos(2π((1(4(1|x + 1| - 2) + 3) - 1)/(2(4(1|x + 1| - 2) + 3) + 3))) - 3 and g(x) = -4(1|((-1x + 3)/(-3x + 1)) - 1| - 2)^2 - 4(1|((-1x + 3)/(-3x + 1)) - 1| - 2) - 5 from x = -0.2 to x = -0.1. Round to 1 decimal place.\n\nPresent the answer in... | 0.2 | MATH |
[
{
"content": "Find the area of the region bounded by the curves f(x) = (-1(-1sin(1π(2|(2x^2 - 2x - 2) + 3| + 3) + 1) - 2))/(1(-1sin(1π(2|(2x^2 - 2x - 2) + 3| + 3) + 1) - 2) + 2), g(x) = -2|(-3(5x^2 + 2x - 2) + 4) - 3| + 2, x = -1.3, and x = -1.2. Round your answer to 1 decimal place.\n\nPresent the answer in La... | 3.3 | MATH |
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