| {"messages": [{"content": "Find the area of the region bounded by the curves f(x) = -1|(2cos(1\u03c0((1(-3x^2 + 5x) - 3)/(3(-3x^2 + 5x) - 2)) + 3) + 1) + 1| + 2, g(x) = 1sin(3\u03c0(-3(-3|x - 3| - 2) - 5) + 1), x = 0.2, and x = 0.30000000000000004. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"} | |
| {"messages": [{"content": "Find the area of the region bounded by the curves f(x) = 1|(2e^(-2(1((-2x + 1)/(1x)) - 1))) - 3| - 1, g(x) = (1(-2|(-1sin(1\u03c0x - 1) + 2)| + 2))/(-2(-2|(-1sin(1\u03c0x - 1) + 2)| + 2) + 1), x = 0.3, and x = 0.4. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.1", "dataset": "MATH"} | |
| {"messages": [{"content": "Calculate the area enclosed between the functions f(x) = (1(-2cos(2\u03c0(1|(5x^2 + 5x + 2) - 2| + 3) + 2) + 2) - 1)/(-1(-2cos(2\u03c0(1|(5x^2 + 5x + 2) - 2| + 3) + 2) + 2) + 3) and g(x) = 3(2|(-1x + 3) - 3| + 3)^2 - 3(2|(-1x + 3) - 3| + 3) - 2 from x = 0.7 to x = 0.9. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10.3", "dataset": "MATH"} | |
| {"messages": [{"content": "Calculate the area enclosed between the functions f(x) = 2sin(1\u03c0(-5(1|(-1x - 2) + 3| - 1)^2 + 2(1|(-1x - 2) + 3| - 1) + 2) - 2) + 1 and g(x) = 1(-1|(3cos(1\u03c0x - 3) + 3) - 2| + 1) from x = -4.6 to x = -4.5. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.1", "dataset": "MATH"} | |
| {"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = (-1(-5(4(-1|x| + 3) + 2)^2 + 4(4(-1|x| + 3) + 2) + 1) - 1)/(-2(-5(4(-1|x| + 3) + 2)^2 + 4(4(-1|x| + 3) + 2) + 1) - 1) and g(x) = -3(-3|((3x + 1)/(1x + 3)) + 3| + 2)^2 - 5(-3|((3x + 1)/(1x + 3)) + 3| + 2) + 3 between the vertical lines x = -1.8 and x = -1.5. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.1", "dataset": "MATH"} | |
| {"messages": [{"content": "Find the area of the region bounded by the curves f(x) = 1|((-1(-3(1sin(1\u03c0x) + 1)^2 + 5(1sin(1\u03c0x) + 1) - 3) - 1)/(3(-3(1sin(1\u03c0x) + 1)^2 + 5(1sin(1\u03c0x) + 1) - 3) - 2)) + 2| - 1, g(x) = -1e^(2((-1(-2|x - 3| + 1) - 2)/(-2(-2|x - 3| + 1) + 3))) + 1, x = 3.2, and x = 3.4. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"} | |
| {"messages": [{"content": "Find the area of the region bounded by the curves f(x) = -2(2(3|((-3x + 2)/(3x - 2)) + 1| - 1)^2 - 4(3|((-3x + 2)/(3x - 2)) + 1| - 1) + 2) - 3, g(x) = 3((-1(-1|x - 1| + 2))/(-1(-1|x - 1| + 2) - 1)) - 4, x = -1.8, and x = 3.8. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "84.6", "dataset": "MATH"} | |
| {"messages": [{"content": "Calculate the area enclosed between the functions f(x) = (-2(-1|(2x)| + 1))/(-2(-1|(2x)| + 1) - 2) and g(x) = -3(-3e^(2x) + 2) - 5 from x = 0.1 to x = 1.0. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "29.6", "dataset": "MATH"} | |
| {"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = 3|(-2((2(-3x) + 3)/(2(-3x) + 1))^2 + 1((2(-3x) + 3)/(2(-3x) + 1)) + 1) - 2| - 3 and g(x) = -1(1(1e^(-2x) - 2)^2 - 5(1e^(-2x) - 2) - 3) + 3 between the vertical lines x = -1.0 and x = -0.5. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.7", "dataset": "MATH"} | |
| {"messages": [{"content": "Calculate the area enclosed between the functions f(x) = (-1(1|(-1(-1x + 5)^2 - 5) - 2| - 1) + 3)/(-1(1|(-1(-1x + 5)^2 - 5) - 2| - 1) + 2) and g(x) = 4(1(-3|x - 2| + 2) + 2)^2 - 5(1(-3|x - 2| + 2) + 2) - 4 from x = 2.7 to x = 3.6. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3.7", "dataset": "MATH"} | |
| {"messages": [{"content": "Find the area of the region bounded by the curves f(x) = 2|(4(-5((1x + 2)/(1x + 3))^2 - 4((1x + 2)/(1x + 3)) + 3) - 3) - 3|, g(x) = 3(-2sin(1\u03c0((3x - 1)/(1x))) + 2)^2 - 4(-2sin(1\u03c0((3x - 1)/(1x))) + 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}", "role": "user"}], "ground_truth": "1.8", "dataset": "MATH"} | |
| {"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = 4(1|((2x + 2)/(2x - 1))|)^2 - 2(1|((2x + 2)/(2x - 1))|) - 5 and g(x) = 4(2cos(1\u03c0x - 1) - 2) + 3 between the vertical lines x = -4.2 and x = -3.2. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4.8", "dataset": "MATH"} | |
| {"messages": [{"content": "Find the area of the region bounded by the curves f(x) = -4(-2(3|((1x - 2)/(2x - 3)) - 2| + 2)^2 - 2(3|((1x - 2)/(2x - 3)) - 2| + 2) - 4), g(x) = 1|(-4((-2x - 3)/(-1x))^2) + 2| + 1, x = 1.3, and x = 1.4000000000000001. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4.6", "dataset": "MATH"} | |
| {"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = 2(1((2x + 3)/(3x - 2))^2 + 5((2x + 3)/(3x - 2)) + 3) - 5 and g(x) = (-2(-2cos(1\u03c0x + 2) - 2) + 3)/(2(-2cos(1\u03c0x + 2) - 2) + 3) between the vertical lines x = 2.8 and x = 4.0. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "42.3", "dataset": "MATH"} | |
| {"messages": [{"content": "Find the area of the region bounded by the curves f(x) = (3(2|(1(-3x)^2 - 4(-3x) + 5) + 1| + 3) + 1)/(2(2|(1(-3x)^2 - 4(-3x) + 5) + 1| + 3) - 1), g(x) = -3((-1(-1x^2 + 5x - 3) + 3)/(3(-1x^2 + 5x - 3) - 2)) - 4, x = 0.7, and x = 4.3. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "42.6", "dataset": "MATH"} | |
| {"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = -2|(1((-1x + 1)/(-1x)) + 3) - 1| + 2 and g(x) = 5(5x^2 + 2x - 1) - 4 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}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"} | |
| {"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = (1(-1cos(1\u03c0(-2x^2 + 5x + 5) + 2)) - 1)/(-2(-1cos(1\u03c0(-2x^2 + 5x + 5) + 2)) + 1) and g(x) = -3|((-2x - 3)/(-2x + 3))| + 1 between the vertical lines x = -1.2 and x = -1.0999999999999999. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.3", "dataset": "MATH"} | |
| {"messages": [{"content": "Find the area of the region bounded by the curves f(x) = (-1(3sin(3\u03c0(-1x + 4) + 3) + 1) - 1)/(3(3sin(3\u03c0(-1x + 4) + 3) + 1) - 2), g(x) = 2e^(1(-3x)), x = 3.7, and x = 3.9. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"} | |
| {"messages": [{"content": "Find the area of the region bounded by the curves f(x) = 1((-2(-1(-2|x + 2| + 1)) - 1)/(-1(-1(-2|x + 2| + 1))))^2 + 5((-2(-1(-2|x + 2| + 1)) - 1)/(-1(-1(-2|x + 2| + 1)))) - 4, g(x) = -1cos(2\u03c0(-4(2|x + 2| - 1)^2 + 2(2|x + 2| - 1) - 2) + 3) + 3, x = -2.4, and x = -1.6. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4.9", "dataset": "MATH"} | |
| {"messages": [{"content": "Find the area of the region bounded by the curves f(x) = 3((2(-2|(-2e^(-1x) + 2)| - 3) - 2)/(-3(-2|(-2e^(-1x) + 2)| - 3) - 3))^2 + 4((2(-2|(-2e^(-1x) + 2)| - 3) - 2)/(-3(-2|(-2e^(-1x) + 2)| - 3) - 3)) + 2, g(x) = 1cos(1\u03c0((-3(-1x + 2) - 1)/(2(-1x + 2) - 1)) - 2) + 1, x = 2.0, and x = 2.3. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"} | |
| {"messages": [{"content": "Calculate the area enclosed between the functions f(x) = -3|(-5(-2((2x)/(2x - 3))^2 - 1((2x)/(2x - 3)) + 4) + 4) - 1| + 3 and g(x) = -1|(-4(-3x + 3)^2 + 3(-3x + 3) + 5) - 2| + 3 from x = 0.9 to x = 1.0. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.2", "dataset": "MATH"} | |
| {"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = 5(-1cos(3\u03c0((-1x)/(-1x + 2))) + 1) - 5 and g(x) = -4((3x - 3)/(3x + 3)) + 4 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}", "role": "user"}], "ground_truth": "0.4", "dataset": "MATH"} | |
| {"messages": [{"content": "Calculate the area enclosed between the functions f(x) = 2(-1sin(1\u03c0(-1|x - 3| - 2) + 3) + 3) - 1 and g(x) = -2(-4x)^2 - 3(-4x) + 5 from x = 0.0 to x = 0.5. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.7", "dataset": "MATH"} | |
| {"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = 2|(3(1cos(3\u03c0((-2x - 3)/(-1x + 2)) + 2) + 1)^2 - 4(1cos(3\u03c0((-2x - 3)/(-1x + 2)) + 2) + 1) - 5) + 2| and g(x) = 2e^(-2((3(-5x + 2))/(-2(-5x + 2) - 2))) - 2 between the vertical lines x = 0.3 and x = 0.4. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"} | |
| {"messages": [{"content": "Find the area of the region bounded by the curves f(x) = 2|(3(5x)^2 + 3(5x) - 3) - 3| - 1, g(x) = 1|(-3e^(2x) - 2) + 2|, x = 0.1, and x = 0.3. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.5", "dataset": "MATH"} | |
| {"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = (-1(-2|(1(2x + 1)^2 - 5(2x + 1) + 1) - 1| + 2) + 2)/(3(-2|(1(2x + 1)^2 - 5(2x + 1) + 1) - 1| + 2) - 1) and g(x) = (-2(-3sin(3\u03c0(-2|x + 3| + 3) - 3) - 3) + 2)/(-3(-3sin(3\u03c0(-2|x + 3| + 3) - 3) - 3) - 1) between the vertical lines x = -0.4 and x = 1.9. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5.8", "dataset": "MATH"} | |
| {"messages": [{"content": "Calculate the area enclosed between the functions f(x) = -2cos(3\u03c0(1(-2|((-3x + 3)/(2x - 1)) + 2|) - 3) - 3) and g(x) = 1|(5(-1x + 4)^2 - 5(-1x + 4) - 3) - 1| - 3 from x = 2.2 to x = 3.0. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.9", "dataset": "MATH"} | |
| {"messages": [{"content": "Find the area of the region bounded by the curves f(x) = -3|(5((-3(-4x + 3) - 1)/(-3(-4x + 3) - 3))^2 + 2((-3(-4x + 3) - 1)/(-3(-4x + 3) - 3)) - 4)| - 2, g(x) = 1(-1(3cos(1\u03c0x + 2) - 3)^2 - 1(3cos(1\u03c0x + 2) - 3) + 4) - 5, x = -0.2, and x = 0.8. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15.8", "dataset": "MATH"} | |
| {"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = (-2(-3(-3|x + 3| + 1) + 3) + 2)/(2(-3(-3|x + 3| + 1) + 3) + 2) and g(x) = -1((-2x - 2)/(-3x + 4))^2 - 1((-2x - 2)/(-3x + 4)) + 1 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}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"} | |
| {"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = (-3(3(2|(1x^2 + 5x + 3)| + 2) - 4) - 3)/(3(3(2|(1x^2 + 5x + 3)| + 2) - 4)) and g(x) = -3|(-1(-4x^2 - 5x - 5) - 2)| + 3 between the vertical lines x = -0.7 and x = -0.6. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"} | |
| {"messages": [{"content": "Find the area of the region bounded by the curves f(x) = -1sin(3\u03c0(1(1|x - 2| - 2) + 5) - 2), g(x) = -3(-4x^2 + 2x + 1) + 3, x = 0.1, and x = 0.5. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.4", "dataset": "MATH"} | |
| {"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = 2|(4(3((1x + 3)/(-1x - 3)) + 3)^2 + 5(3((1x + 3)/(-1x - 3)) + 3) + 1) - 1| + 2 and g(x) = (3(5(3cos(1\u03c0x - 3) + 1) - 1) + 1)/(-1(5(3cos(1\u03c0x - 3) + 1) - 1) + 2) between the vertical lines x = 1.5 and x = 2.4. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3.6", "dataset": "MATH"} | |
| {"messages": [{"content": "Calculate the area enclosed between the functions f(x) = (-2(-3cos(1\u03c0(1|x - 3| - 3)) - 3) - 3)/(-3(-3cos(1\u03c0(1|x - 3| - 3)) - 3) + 4) and g(x) = -3sin(1\u03c0(1|x + 2| - 2) - 2) - 1 from x = -4.5 to x = -3.8. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.7", "dataset": "MATH"} | |
| {"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = 3|(1(2cos(1\u03c0x - 3) + 3)^2 + 1(2cos(1\u03c0x - 3) + 3) + 5)| + 2 and g(x) = 3(2x - 3)^2 - 3(2x - 3) - 2 between the vertical lines x = -0.6 and x = 0.2. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "9.6", "dataset": "MATH"} | |
| {"messages": [{"content": "Find the area of the region bounded by the curves f(x) = -5(-3(3|(2e^(1x) - 3) - 2|)^2 - 1(3|(2e^(1x) - 3) - 2|) + 1) + 2, g(x) = -1e^(-2(-3(1|x + 1| - 3) - 1)) - 1, x = 0.9, and x = 1.0. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.9", "dataset": "MATH"} | |
| {"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = 2((-1(-1e^(2(2|x + 3| - 2)) - 1))/(1(-1e^(2(2|x + 3| - 2)) - 1) - 3))^2 + 5((-1(-1e^(2(2|x + 3| - 2)) - 1))/(1(-1e^(2(2|x + 3| - 2)) - 1) - 3)) - 1 and g(x) = -4(-1(3|x + 2|)^2 + 5(3|x + 2|) + 2) + 4 between the vertical lines x = -3.7 and x = -0.3. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "59.1", "dataset": "MATH"} | |
| {"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = -2sin(2\u03c0(-1|((-1x + 3)/(-1x + 3)) + 3| + 1) - 1) + 3 and g(x) = (1(1cos(1\u03c0x + 3) + 2) + 1)/(-1(1cos(1\u03c0x + 3) + 2) + 2) between the vertical lines x = -2.3 and x = -1.6. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.3", "dataset": "MATH"} | |
| {"messages": [{"content": "Calculate the area enclosed between the functions f(x) = 1|(-2sin(1\u03c0(-1x^2 + 3x + 3) + 3) - 2) + 2| + 2 and g(x) = -1(-1|x + 3| - 3) - 3 from x = 0.3 to x = 0.5. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.1", "dataset": "MATH"} | |
| {"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = (2(-3e^(1(-3|(-4x^2 + 3x)| + 3)) + 3))/(-2(-3e^(1(-3|(-4x^2 + 3x)| + 3)) + 3) + 3) and g(x) = 3|(4((-1x - 3)/(3x - 2)) - 3) + 3| - 2 between the vertical lines x = -3.0 and x = -0.3. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8.9", "dataset": "MATH"} | |
| {"messages": [{"content": "Calculate the area enclosed between the functions f(x) = 1|((1(1sin(1\u03c0(-2x^2 - 2x - 1) + 1) - 1))/(-2(1sin(1\u03c0(-2x^2 - 2x - 1) + 1) - 1) + 3)) - 3| + 1 and g(x) = 2(-5(1cos(2\u03c0x - 3) - 1) - 4)^2 + 3(-5(1cos(2\u03c0x - 3) - 1) - 4) - 3 from x = -1.4 to x = -1.3. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"} | |
| {"messages": [{"content": "Find the area of the region bounded by the curves f(x) = -2sin(3\u03c0(5(3|((-2x + 1)/(-1x + 2))| + 2) - 3) - 1) + 1, g(x) = 2cos(3\u03c0(4(1|x + 2| - 3)^2 - 1(1|x + 2| - 3) - 1) + 1) - 2, x = -2.4, and x = -2.3. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.4", "dataset": "MATH"} | |
| {"messages": [{"content": "Calculate the area enclosed between the functions f(x) = 1|(1e^(1(2((3x)/(-2x - 2)) + 1)) + 2) - 3| - 2 and g(x) = (1(1(3e^(2x) - 3) - 3) - 2)/(3(1(3e^(2x) - 3) - 3) + 3) from x = -0.1 to x = 0.3. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3.8", "dataset": "MATH"} | |
| {"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = -2sin(1\u03c0(3|(-3x - 3) - 1| - 3) + 1) + 3 and g(x) = 2|((-3x - 1)/(-3x - 3)) - 3| - 2 between the vertical lines x = 1.7 and x = 1.9. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.3", "dataset": "MATH"} | |
| {"messages": [{"content": "Find the area of the region bounded by the curves f(x) = -4(2|(-5x^2 + 1x + 4) - 3| - 2) + 5, g(x) = -3|(3x - 5)|, x = -1.0, and x = 0.9. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "35.3", "dataset": "MATH"} | |
| {"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = 1(2cos(3\u03c0(-3|x - 1| - 3) - 1))^2 + 1(2cos(3\u03c0(-3|x - 1| - 3) - 1)) - 1 and g(x) = 3sin(3\u03c0(2x - 1) + 1) + 2 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}", "role": "user"}], "ground_truth": "0.1", "dataset": "MATH"} | |
| {"messages": [{"content": "Find the area of the region bounded by the curves f(x) = (-1(-3(3|x - 2| + 3)^2 - 4(3|x - 2| + 3) - 2) + 1)/(3(-3(3|x - 2| + 3)^2 - 4(3|x - 2| + 3) - 2) - 2), g(x) = 1|(-4x + 3) + 2| - 2, x = 0.8, and x = 1.7. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.7", "dataset": "MATH"} | |
| {"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = -3(3((1(3|x|))/(-3(3|x|) + 2))^2 - 4((1(3|x|))/(-3(3|x|) + 2))) - 4 and g(x) = -1(3((-1x + 2)/(-2x - 3))^2 + 5((-1x + 2)/(-2x - 3)) + 4) + 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}", "role": "user"}], "ground_truth": "0.4", "dataset": "MATH"} | |
| {"messages": [{"content": "Find the area of the region bounded by the curves f(x) = 1(-1((2x + 1)/(-2x + 3))^2 - 5((2x + 1)/(-2x + 3)) - 2), g(x) = 2cos(2\u03c0(-1|x - 1| + 3) - 2), x = -1.4, and x = -1.0. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.3", "dataset": "MATH"} | |
| {"messages": [{"content": "Calculate the area enclosed between the functions f(x) = 2|(1(1x^2 + 4x - 2) - 3) - 2| - 2 and g(x) = (-1(3cos(3\u03c0x - 1) + 2) - 1)/(2(3cos(3\u03c0x - 1) + 2)) from x = 1.9 to x = 2.4. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "6.0", "dataset": "MATH"} | |
| {"messages": [{"content": "Calculate the area enclosed between the functions f(x) = -3(1|((1x - 2)/(-2x + 3)) - 1| - 1) + 2 and g(x) = -2|(2cos(1\u03c0x - 1) + 2) - 3| - 3 from x = 1.4 to x = 1.5. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15.9", "dataset": "MATH"} | |
| {"messages": [{"content": "Find the area of the region bounded by the curves f(x) = 1|((-1(3sin(3\u03c0(1x - 3) - 1) - 3))/(2(3sin(3\u03c0(1x - 3) - 1) - 3))) + 3| - 1, g(x) = (2(2(-4x^2 - 2x + 4) - 2) - 3)/(-1(2(-4x^2 - 2x + 4) - 2) + 2), x = -1.0, and x = 0.5. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "9.4", "dataset": "MATH"} | |
| {"messages": [{"content": "Find the area of the region bounded by the curves f(x) = 3((1(3x^2 + 4x - 1) + 3)/(1(3x^2 + 4x - 1) - 2)), g(x) = 2sin(3\u03c0(-2|x - 3| - 2)) - 1, x = -0.5, and x = -0.3. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.3", "dataset": "MATH"} | |
| {"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = 1((-3(1(-2|x + 1| + 1) - 5) - 1)/(1(1(-2|x + 1| + 1) - 5) - 3))^2 + 1((-3(1(-2|x + 1| + 1) - 5) - 1)/(1(1(-2|x + 1| + 1) - 5) - 3)) + 4 and g(x) = (-1(1(-2|x - 2| + 2)^2 + 5(-2|x - 2| + 2) + 5) - 3)/(-2(1(-2|x - 2| + 2)^2 + 5(-2|x - 2| + 2) + 5) - 1) between the vertical lines x = 0.2 and x = 3.8. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "20.4", "dataset": "MATH"} | |
| {"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = 1|(-3(-1x + 2)^2 + 4(-1x + 2) + 4) + 1| - 1 and g(x) = 1sin(3\u03c0(3x^2 + 1) - 3) + 2 between the vertical lines x = 3.1 and x = 3.2. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.1", "dataset": "MATH"} | |
| {"messages": [{"content": "Find the area of the region bounded by the curves f(x) = (3(-2|(-4(-1x)^2 - 1(-1x)) + 3| - 2) + 1)/(-2(-2|(-4(-1x)^2 - 1(-1x)) + 3| - 2) - 1), g(x) = 3sin(2\u03c0(3((1x - 2)/(-1x - 3)) - 2) - 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"}], "ground_truth": "0.2", "dataset": "MATH"} | |
| {"messages": [{"content": "Find the area of the region bounded by the curves f(x) = -2(1((3(2|x - 2| - 3) + 1)/(-2(2|x - 2| - 3) + 3))^2 - 4((3(2|x - 2| - 3) + 1)/(-2(2|x - 2| - 3) + 3))) + 3, g(x) = 1|((1(4x^2 - 5x - 5) - 2)/(1(4x^2 - 5x - 5))) - 2| + 1, x = -0.0, and x = 0.8. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4.0", "dataset": "MATH"} | |
| {"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = -3(2sin(2\u03c0(3|x - 2| - 3) - 1) - 2) + 5 and g(x) = (-1(-2cos(2\u03c0x + 3) + 1) - 1)/(-3(-2cos(2\u03c0x + 3) + 1) + 4) between the vertical lines x = 2.2 and x = 2.8. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8.0", "dataset": "MATH"} | |
| {"messages": [{"content": "Calculate the area enclosed between the functions f(x) = (-3(-3cos(3\u03c0(4(4x^2 - 1) + 4) + 3) + 1))/(2(-3cos(3\u03c0(4(4x^2 - 1) + 4) + 3) + 1) + 3) and g(x) = 3((2(1|x - 3|) + 3)/(-3(1|x - 3|))) - 3 from x = 0.4 to x = 0.5. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.8", "dataset": "MATH"} | |
| {"messages": [{"content": "Calculate the area enclosed between the functions f(x) = (3(3cos(2\u03c0(4(3|x - 2| + 1)^2 + 2(3|x - 2| + 1) + 2)) - 1))/(1(3cos(2\u03c0(4(3|x - 2| + 1)^2 + 2(3|x - 2| + 1) + 2)) - 1) + 2) and g(x) = -2|(-1sin(3\u03c0((-2x - 1)/(-3x + 1)))) + 3| from x = -0.4 to x = -0.30000000000000004. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.7", "dataset": "MATH"} | |
| {"messages": [{"content": "Find the area of the region bounded by the curves f(x) = -1(-3(3cos(1\u03c0((2x - 3)/(-3x + 2))) + 2)^2 - 1(3cos(1\u03c0((2x - 3)/(-3x + 2))) + 2) - 2) + 4, g(x) = (2(-3(5x^2 + 2x - 1) + 2) + 3)/(-1(-3(5x^2 + 2x - 1) + 2)), x = -0.8, and x = 0.4. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "30.8", "dataset": "MATH"} | |
| {"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = 3(1cos(3\u03c0((-2x - 3)/(1x + 2)) + 2) + 1)^2 + 1(1cos(3\u03c0((-2x - 3)/(1x + 2)) + 2) + 1) and g(x) = 2sin(3\u03c0(-1x^2 - 3x - 4) + 1) + 3 between the vertical lines x = -2.0 and x = -1.9. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.4", "dataset": "MATH"} | |
| {"messages": [{"content": "Calculate the area enclosed between the functions f(x) = (-1(1|(-2x^2 + 2x + 4) - 3| - 1) + 1)/(1(1|(-2x^2 + 2x + 4) - 3| - 1) + 3) and g(x) = (-1(-2x^2 - 2x) - 3)/(-1(-2x^2 - 2x) + 2) from x = -1.4 to x = 1.5. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3.6", "dataset": "MATH"} | |
| {"messages": [{"content": "Calculate the area enclosed between the functions f(x) = (3(4(2|(3x^2 + 5x - 5) + 1| - 3) - 5) - 1)/(3(4(2|(3x^2 + 5x - 5) + 1| - 3) - 5) - 1) and g(x) = (-1(3(2x - 5)^2 + 5(2x - 5) - 4) + 2)/(3(3(2x - 5)^2 + 5(2x - 5) - 4)) from x = 1.3 to x = 2.8. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4.1", "dataset": "MATH"} | |
| {"messages": [{"content": "Calculate the area enclosed between the functions f(x) = 2|(3((-1(3x) + 1)/(3(3x)))^2 - 5) + 1| + 1 and g(x) = (3(2|(2x - 2) - 3| - 1) + 2)/(-1(2|(2x - 2) - 3| - 1) - 1) from x = 2.5 to x = 2.6. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5.7", "dataset": "MATH"} | |
| {"messages": [{"content": "Calculate the area enclosed between the functions f(x) = 1((-1(-1|(1cos(3\u03c0x + 1) - 3) + 2| - 3) - 2)/(2(-1|(1cos(3\u03c0x + 1) - 3) + 2| - 3) - 1))^2 + 2((-1(-1|(1cos(3\u03c0x + 1) - 3) + 2| - 3) - 2)/(2(-1|(1cos(3\u03c0x + 1) - 3) + 2| - 3) - 1)) - 3 and g(x) = 1(3sin(3\u03c0(1|x - 2| + 2) - 3)) - 2 from x = -4.3 to x = -4.0. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.3", "dataset": "MATH"} | |
| {"messages": [{"content": "Find the area of the region bounded by the curves f(x) = -5((3(-1sin(1\u03c0(-1|x - 3| - 2) + 3) + 3) + 2)/(3(-1sin(1\u03c0(-1|x - 3| - 2) + 3) + 3) - 1)) - 1, g(x) = (2(-2|(-2x - 4)| + 1) - 2)/(-3(-2|(-2x - 4)| + 1) + 1), x = -2.2, and x = -1.8. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8.4", "dataset": "MATH"} | |
| {"messages": [{"content": "Calculate the area enclosed between the functions f(x) = 4(-3cos(2\u03c0(-3((1x - 1)/(-3x - 1))^2 + 2((1x - 1)/(-3x - 1)) - 2)) + 1) - 4 and g(x) = -3e^(-1(3((-2x - 1)/(-1x)) + 5)) from x = -1.0 to x = -0.9. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.8", "dataset": "MATH"} | |
| {"messages": [{"content": "Calculate the area enclosed between the functions f(x) = 1|(4(4((-3x)/(-1x - 2))^2 - 3((-3x)/(-1x - 2)) + 3) + 2) - 2| - 1 and g(x) = -4(-1(-2cos(1\u03c0x + 1) - 1)^2 + 4(-2cos(1\u03c0x + 1) - 1) - 2) - 3 from x = 1.1 to x = 2.1. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "39.2", "dataset": "MATH"} | |
| {"messages": [{"content": "Find the area of the region bounded by the curves f(x) = -1(2|(2sin(1\u03c0(1x^2 + 4x + 3)) - 2) - 2|) + 4, g(x) = 5(-1e^(2(-3x^2 + 5x + 5))) - 2, x = 4.5, and x = 4.6. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.3", "dataset": "MATH"} | |
| {"messages": [{"content": "Find the area of the region bounded by the curves f(x) = -2|(3(5((-2x + 3)/(1x - 3))^2 - 1) - 3) - 2| + 2, g(x) = -3|(-1((-1x - 2)/(2x - 1)) + 5)| + 1, x = 0.3, and x = 2.0. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "88.0", "dataset": "MATH"} | |
| {"messages": [{"content": "Find the area of the region bounded by the curves f(x) = 2|(-4(5x + 4)^2 - 5(5x + 4) + 1) - 3| - 2, g(x) = (2(-4x^2 - 4x + 1) + 3)/(-2(-4x^2 - 4x + 1) + 3), x = -1.1, and x = -0.1. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "62.4", "dataset": "MATH"} | |
| {"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = -1((3(-2|x - 1| - 1) + 3)/(-2(-2|x - 1| - 1) + 1)) + 4 and g(x) = 5(3e^(-1x) - 1)^2 - 3(3e^(-1x) - 1) - 2 between the vertical lines x = 0.2 and x = 3.8. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11.6", "dataset": "MATH"} | |
| {"messages": [{"content": "Find the area of the region bounded by the curves f(x) = -3sin(1\u03c0(-4(1x - 4)^2 + 5(1x - 4) + 4) - 1) + 1, g(x) = (-3(-2x - 5) + 1)/(1(-2x - 5)), x = -2.8, and x = -2.6999999999999997. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"} | |
| {"messages": [{"content": "Calculate the area enclosed between the functions f(x) = (-1(-1|(4(1x^2 + 5x) - 1) + 2|) + 2)/(2(-1|(4(1x^2 + 5x) - 1) + 2|) + 1) and g(x) = 3|(-1((2x + 1)/(1x - 2))^2 - 5((2x + 1)/(1x - 2)) + 3) + 1| + 2 from x = -4.9 to x = -0.1. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "47.1", "dataset": "MATH"} | |
| {"messages": [{"content": "Find the area of the region bounded by the curves f(x) = 2(-1|(-1e^(-1x) + 2) - 2| - 1) + 1, g(x) = 2(2sin(2\u03c0x + 2) - 3)^2 + 4(2sin(2\u03c0x + 2) - 3) - 3, x = 0.1, and x = 0.7. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10.0", "dataset": "MATH"} | |
| {"messages": [{"content": "Calculate the area enclosed between the functions f(x) = (1(2|(-1x^2 - 1x + 1) + 3| - 1) - 3)/(-3(2|(-1x^2 - 1x + 1) + 3| - 1) + 2) and g(x) = -2sin(3\u03c0(-5x^2 - 1x + 2) - 2) - 1 from x = -4.9 to x = -4.800000000000001. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.1", "dataset": "MATH"} | |
| {"messages": [{"content": "Find the area of the region bounded by the curves f(x) = (1(-1|(-1(-2x^2 - 5x) - 1) + 3| + 3) + 1)/(3(-1|(-1(-2x^2 - 5x) - 1) + 3| + 3) + 1), g(x) = -1sin(2\u03c0(3|(1x + 1) + 1| + 1)) + 3, x = -2.7, and x = 0.2. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "7.3", "dataset": "MATH"} | |
| {"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = 4(-3sin(2\u03c0((-1x + 2)/(3x - 2)) - 1) + 2) - 1 and g(x) = 1(-2sin(2\u03c0x + 2) - 3)^2 - 2(-2sin(2\u03c0x + 2) - 3) + 5 between the vertical lines x = 0.6 and x = 0.7. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.1", "dataset": "MATH"} | |
| {"messages": [{"content": "Find the area of the region bounded by the curves f(x) = -3cos(3\u03c0(2((3(-2x^2 + 2x + 5) + 2)/(-2(-2x^2 + 2x + 5) - 3)) + 1) + 1) + 3, g(x) = -2cos(2\u03c0(2((1x + 1)/(3x + 2))^2 - 1) - 2), x = -0.6, and x = -0.5. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.1", "dataset": "MATH"} | |
| {"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = 3e^(2(3|((-1x + 2)/(-2x)) + 1|)) - 1 and g(x) = 2((-3x)/(-1x)) - 3 between the vertical lines x = 0.6 and x = 0.7. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.1", "dataset": "MATH"} | |
| {"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = 1|((1(4(-2x^2 - 1x - 5) - 3) + 3)/(3(4(-2x^2 - 1x - 5) - 3) + 2)) + 2| - 1 and g(x) = 1cos(2\u03c0(1(2|x - 2| + 2) - 5) + 1) + 2 between the vertical lines x = -2.6 and x = -2.2. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.4", "dataset": "MATH"} | |
| {"messages": [{"content": "Calculate the area enclosed between the functions f(x) = (2(4(1|x + 2|) - 5))/(-3(4(1|x + 2|) - 5) - 2) and g(x) = 1|((-3x - 3)/(-3x + 1)) - 3| + 1 from x = -3.1 to x = -0.9. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11.8", "dataset": "MATH"} | |
| {"messages": [{"content": "Find the area of the region bounded by the curves f(x) = 5(-3((3(3|x + 1| - 2) - 3)/(1(3|x + 1| - 2)))^2 + 2((3(3|x + 1| - 2) - 3)/(1(3|x + 1| - 2))) + 3) + 2, g(x) = 3|(2((3x + 2)/(2x - 1)) + 1)| + 2, x = -0.0, and x = 0.1. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.5", "dataset": "MATH"} | |
| {"messages": [{"content": "Find the area of the region bounded by the curves f(x) = 1|((1(5(1x^2 + 2x) - 4) - 3)/(1(5(1x^2 + 2x) - 4) + 3)) - 3| - 2, g(x) = (2(-3(-1sin(1\u03c0x - 2) + 2)^2 + 2(-1sin(1\u03c0x - 2) + 2)) - 2)/(-2(-3(-1sin(1\u03c0x - 2) + 2)^2 + 2(-1sin(1\u03c0x - 2) + 2)) + 1), x = -1.9, and x = -1.3. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"} | |
| {"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = 3cos(3\u03c0((1(-1x^2 - 1x + 4) + 3)/(2(-1x^2 - 1x + 4))) - 3) + 2 and g(x) = (3(2|x + 1| - 2) + 1)/(-1(2|x + 1| - 2) + 2) between the vertical lines x = -2.4 and x = -2.3. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"} | |
| {"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = (3(1(3|x - 3| + 2) - 5) - 2)/(3(1(3|x - 3| + 2) - 5)) and g(x) = 1|(-2cos(1\u03c0x - 3)) - 1| - 3 between the vertical lines x = 1.9 and x = 4.1. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10.4", "dataset": "MATH"} | |
| {"messages": [{"content": "Find the area of the region bounded by the curves f(x) = (1(-1|(-4x^2 + 4x - 5) - 3| - 2) + 1)/(-1(-1|(-4x^2 + 4x - 5) - 3| - 2) - 1), g(x) = -1(2|x + 3| - 2)^2 + 4(2|x + 3| - 2), x = -2.1, and x = 0.1. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "7.5", "dataset": "MATH"} | |
| {"messages": [{"content": "Find the area of the region bounded by the curves f(x) = 2|((-1(2x - 4) + 1)/(-1(2x - 4) - 1)) - 3| + 3, g(x) = 4(-5x^2 + 4x + 4) - 4, x = -0.3, and x = 1.1. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "9.8", "dataset": "MATH"} | |
| {"messages": [{"content": "Calculate the area enclosed between the functions f(x) = -1|((3(-1(-3x - 2)^2) + 1)/(1(-1(-3x - 2)^2) - 2)) - 2| and g(x) = -3cos(2\u03c0(4(2|x - 2| - 2)^2 + 5(2|x - 2| - 2) - 5) - 3) + 2 from x = -4.2 to x = -4.1. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.3", "dataset": "MATH"} | |
| {"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = -2((-2(1cos(2\u03c0(3|x| + 2) - 3) - 1) + 2)/(3(1cos(2\u03c0(3|x| + 2) - 3) - 1) - 1)) - 4 and g(x) = 4(1(-1|x - 2|) + 3)^2 - 5(1(-1|x - 2|) + 3) - 1 between the vertical lines x = -0.0 and x = 0.1. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"} | |
| {"messages": [{"content": "Calculate the area enclosed between the functions f(x) = -3|((3(3cos(3\u03c0x + 1) + 1) + 1)/(-2(3cos(3\u03c0x + 1) + 1) + 3)) + 1| - 1 and g(x) = 1cos(3\u03c0(-3x^2 - 3x - 3)) - 1 from x = 3.6 to x = 3.7. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"} | |
| {"messages": [{"content": "Calculate the area enclosed between the functions f(x) = 1|((-3(-1(-1x + 1)^2 + 5(-1x + 1) + 5) + 2)/(-3(-1(-1x + 1)^2 + 5(-1x + 1) + 5))) + 3| + 1 and g(x) = 1|((-2(3x^2 + 3x + 5) + 3)/(2(3x^2 + 3x + 5) - 1)) - 2| + 1 from x = -4.8 to x = -4.7. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"} | |
| {"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = -3|(5((-2(4x^2 - 5x - 2) + 1)/(-3(4x^2 - 5x - 2) + 1)) - 3) + 3| + 2 and g(x) = (-1(-1(2e^(-2x) - 1) - 1) + 2)/(1(-1(2e^(-2x) - 1) - 1) + 1) 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}", "role": "user"}], "ground_truth": "6.5", "dataset": "MATH"} | |
| {"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = -1(-3cos(2\u03c0((1(3|x + 3| - 3) + 3)/(2(3|x + 3| - 3) + 1)) + 3) + 3) - 4 and g(x) = 2((-1(3|x + 1| - 3) + 1)/(2(3|x + 1| - 3) + 2)) between the vertical lines x = -1.6 and x = -0.5. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5.9", "dataset": "MATH"} | |
| {"messages": [{"content": "Find the area of the region bounded by the curves f(x) = (-1(-5(-1|(-5x^2 - 3x - 2) - 2| + 3) - 2) + 3)/(1(-5(-1|(-5x^2 - 3x - 2) - 2| + 3) - 2) + 2), g(x) = (-1(-1(3e^(-1x) + 1) - 3) - 1)/(-2(-1(3e^(-1x) + 1) - 3) - 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}", "role": "user"}], "ground_truth": "0.1", "dataset": "MATH"} | |
| {"messages": [{"content": "Find the area of the region bounded by the curves f(x) = (1(-2(-4x)^2 - 4(-4x) - 2) + 3)/(2(-2(-4x)^2 - 4(-4x) - 2) + 3), g(x) = -1(-3|x + 2| + 2)^2 - 3(-3|x + 2| + 2) + 2, x = -2.5, and x = -1.5. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4.0", "dataset": "MATH"} | |
| {"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = 3|(2(2x^2 - 1x - 2) - 5)| - 3 and g(x) = (-1(3x^2 + 1x + 1) - 1)/(3(3x^2 + 1x + 1) + 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": "user"}], "ground_truth": "0.2", "dataset": "MATH"} | |
| {"messages": [{"content": "Find the area of the region bounded by the curves f(x) = 3cos(3\u03c0(1(-2(-1|x - 2| + 3)^2 + 5(-1|x - 2| + 3)) - 1) - 1), g(x) = (2(2|(-1x^2 - 2) + 1| + 1) + 2)/(-2(2|(-1x^2 - 2) + 1| + 1) - 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}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"} | |
| {"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = -4(-3|(3sin(1\u03c0((-1x + 3)/(1x - 2)) + 3)) + 1| - 2) + 4 and g(x) = 2|(-3((2x + 3)/(-1x))^2 - 3((2x + 3)/(-1x)) - 5) + 1| between the vertical lines x = 2.1 and x = 2.2. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.4", "dataset": "MATH"} | |
| {"messages": [{"content": "Calculate the area enclosed between the functions f(x) = 1|((3(-4x + 3) - 3)/(1(-4x + 3) + 3)) + 2| - 1 and g(x) = (2(-2e^(1x) - 3))/(3(-2e^(1x) - 3) - 1) from x = 0.6 to x = 1.0. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.3", "dataset": "MATH"} | |