| {"messages": [{"content": "How many local minima does the function f(x) = 2|(-3((1(2sin(3\u03c0x - 1) + 2))/(-2(2sin(3\u03c0x - 1) + 2) - 1))^2 + 5((1(2sin(3\u03c0x - 1) + 2))/(-2(2sin(3\u03c0x - 1) + 2) - 1)) + 2)| + 3 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"} | |
| {"messages": [{"content": "Find the x-coordinate of the leftmost local extremum of the function f(x) = -2(-1|(-1cos(3\u03c0((2x + 3)/(3x + 3)) + 2) - 1) - 2| + 3)^2 - 2(-1|(-1cos(3\u03c0((2x + 3)/(3x + 3)) + 2) - 1) - 2| + 3) + 3 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-4", "dataset": "MATH"} | |
| {"messages": [{"content": "Find the x-coordinate of the rightmost local minimum of the function f(x) = -1cos(1\u03c0(-1|((3(1x^2 - 3x + 4))/(1(1x^2 - 3x + 4) - 2)) + 2|) + 2) + 3 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"} | |
| {"messages": [{"content": "Find the x-coordinate of the leftmost local minimum of the function f(x) = 1sin(2\u03c0(5(-3|((3x - 2)/(-1x - 2)) + 3| - 3)^2 - 2(-3|((3x - 2)/(-1x - 2)) + 3| - 3) + 1) - 2) - 3 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-10", "dataset": "MATH"} | |
| {"messages": [{"content": "Find the x-coordinate of the leftmost local minimum of the function f(x) = (1(2|(1sin(3\u03c0(5x^2 + 3x - 2) - 2)) - 1| - 3) - 1)/(2(2|(1sin(3\u03c0(5x^2 + 3x - 2) - 2)) - 1| - 3) + 2) in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-10", "dataset": "MATH"} | |
| {"messages": [{"content": "Find the x-coordinate of the local maximum with the smallest y-value of the function f(x) = -1|(3(-2cos(3\u03c0((-2x)/(-3x + 4)) - 1))^2 + 4(-2cos(3\u03c0((-2x)/(-3x + 4)) - 1)) - 3) - 2| - 3 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"} | |
| {"messages": [{"content": "Find the x-coordinate of the leftmost local maximum of the function f(x) = 1sin(2\u03c0(-1|(5((1x - 3)/(2x - 3))^2 - 4((1x - 3)/(2x - 3))) + 3|) + 2) - 2 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-1", "dataset": "MATH"} | |
| {"messages": [{"content": "Find the x-coordinate of the leftmost local extremum of the function f(x) = 1((2(3|(1sin(1\u03c0x + 3) + 2) + 1| + 2))/(3(3|(1sin(1\u03c0x + 3) + 2) + 1| + 2) - 1))^2 - 2((2(3|(1sin(1\u03c0x + 3) + 2) + 1| + 2))/(3(3|(1sin(1\u03c0x + 3) + 2) + 1| + 2) - 1)) + 2 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-9", "dataset": "MATH"} | |
| {"messages": [{"content": "Find the x-coordinate of the rightmost local minimum of the function f(x) = -3(-1cos(3\u03c0(1|((2x - 1)/(3x + 2)) - 2| + 1)) - 2)^2 + 5(-1cos(3\u03c0(1|((2x - 1)/(3x + 2)) - 2| + 1)) - 2) + 2 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"} | |
| {"messages": [{"content": "Find the x-coordinate of the local extremum with the largest y-value of the function f(x) = (2(-2sin(3\u03c0(1|(-5x^2 + 3x)| - 1) + 2)) + 2)/(3(-2sin(3\u03c0(1|(-5x^2 + 3x)| - 1) + 2)) + 1) in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"} | |
| {"messages": [{"content": "Find the x-coordinate of the local minimum with the smallest y-value of the function f(x) = 1|((-1(4(-1sin(2\u03c0x) - 2)^2 + 2) - 3)/(-3(4(-1sin(2\u03c0x) - 2)^2 + 2) + 2)) - 3| + 3 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-9", "dataset": "MATH"} | |
| {"messages": [{"content": "Find the x-coordinate of the local extremum with the largest y-value of the function f(x) = (3(-5(1|(2cos(1\u03c0x + 3)) - 3| - 2)^2 + 4(1|(2cos(1\u03c0x + 3)) - 3| - 2) - 1) + 3)/(1(-5(1|(2cos(1\u03c0x + 3)) - 3| - 2)^2 + 4(1|(2cos(1\u03c0x + 3)) - 3| - 2) - 1) - 3) in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-10", "dataset": "MATH"} | |
| {"messages": [{"content": "How many local maxima does the function f(x) = -2|(4(3cos(3\u03c0((-1x - 3)/(2x + 3)) - 3) - 2)^2 + 3(3cos(3\u03c0((-1x - 3)/(2x + 3)) - 3) - 2) - 3) + 2| have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"} | |
| {"messages": [{"content": "Find the x-coordinate of the local minimum with the largest y-value of the function f(x) = (-1(2sin(1\u03c0(-3|(3x^2 - 3x - 1) + 3| - 2)) + 1) + 2)/(-1(2sin(1\u03c0(-3|(3x^2 - 3x - 1) + 3| - 2)) + 1)) in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-10", "dataset": "MATH"} | |
| {"messages": [{"content": "Find the x-coordinate of the local minimum of the function f(x) = 1sin(1\u03c0((3(3|(4x^2 + 5x + 1) + 2|) - 1)/(-1(3|(4x^2 + 5x + 1) + 2|) - 3)) + 2) + 1 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-1", "dataset": "MATH"} | |
| {"messages": [{"content": "Find the x-coordinate of the local minimum with the largest y-value of the function f(x) = 1|((1(-1(1cos(1\u03c0x) + 2)^2 - 4(1cos(1\u03c0x) + 2) - 4) + 1)/(3(-1(1cos(1\u03c0x) + 2)^2 - 4(1cos(1\u03c0x) + 2) - 4) - 1)) - 2| - 1 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-8", "dataset": "MATH"} | |
| {"messages": [{"content": "Find the x-coordinate of the local minimum with the smallest y-value of the function f(x) = -2|((2(-5(-2cos(2\u03c0x + 3))^2 + 2(-2cos(2\u03c0x + 3)) - 3))/(-1(-5(-2cos(2\u03c0x + 3))^2 + 2(-2cos(2\u03c0x + 3)) - 3) - 2)) - 3| - 2 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-10", "dataset": "MATH"} | |
| {"messages": [{"content": "Find the x-coordinate of the leftmost local maximum of the function f(x) = 1cos(2\u03c0(-3|(5((1x - 1)/(1x))^2 + 5((1x - 1)/(1x)) - 4) + 1| + 1) + 3) - 1 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-9", "dataset": "MATH"} | |
| {"messages": [{"content": "Find the average of all x-coordinates of local maxima of the function f(x) = 2((-1(-2sin(3\u03c0(-2|x - 2| + 3) + 1) + 1))/(-2(-2sin(3\u03c0(-2|x - 2| + 3) + 1) + 1) - 1))^2 + 4((-1(-2sin(3\u03c0(-2|x - 2| + 3) + 1) + 1))/(-2(-2sin(3\u03c0(-2|x - 2| + 3) + 1) + 1) - 1)) + 4 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"} | |
| {"messages": [{"content": "Find the x-coordinate of the rightmost local extremum of the function f(x) = -2|(4(3cos(2\u03c0((3x - 3)/(-2x)) - 1) - 2)^2 + 4(3cos(2\u03c0((3x - 3)/(-2x)) - 1) - 2) - 5) - 1| + 1 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "9", "dataset": "MATH"} | |
| {"messages": [{"content": "Find the average of all x-coordinates of local maxima of the function f(x) = (-3(-3|(-3sin(3\u03c0(3x^2 - 5x) - 1)) + 3| + 3) - 1)/(-2(-3|(-3sin(3\u03c0(3x^2 - 5x) - 1)) + 3| + 3) - 1) in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"} | |
| {"messages": [{"content": "Find the x-coordinate of the local extremum with the largest y-value of the function f(x) = (1(-2(-1|(-3cos(2\u03c0x + 3) + 3) - 3| + 3)^2 + 3(-1|(-3cos(2\u03c0x + 3) + 3) - 3| + 3) - 4) - 3)/(3(-2(-1|(-3cos(2\u03c0x + 3) + 3) - 3| + 3)^2 + 3(-1|(-3cos(2\u03c0x + 3) + 3) - 3| + 3) - 4) - 1) in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-10", "dataset": "MATH"} | |
| {"messages": [{"content": "How many local extrema (both minima and maxima) does the function f(x) = -1cos(3\u03c0(3|(5((1x + 1)/(3x + 1))^2 - 1((1x + 1)/(3x + 1)) - 3) + 1| + 2) + 2) have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "47", "dataset": "MATH"} | |
| {"messages": [{"content": "Find the x-coordinate of the local minimum with the largest y-value of the function f(x) = (-2(2cos(3\u03c0(2|(-1x^2 + 4x + 4) - 2| + 2) - 1) + 3) + 2)/(2(2cos(3\u03c0(2|(-1x^2 + 4x + 4) - 2| + 2) - 1) + 3) - 3) in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-10", "dataset": "MATH"} | |
| {"messages": [{"content": "Find the x-coordinate of the leftmost local extremum of the function f(x) = -1|(1(-1cos(1\u03c0((-1x + 3)/(2x + 3)) - 1))^2 + 2(-1cos(1\u03c0((-1x + 3)/(2x + 3)) - 1)) - 4) + 3| in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-3", "dataset": "MATH"} | |
| {"messages": [{"content": "Find the x-coordinate of the rightmost local maximum of the function f(x) = 1((1(-1cos(3\u03c0(1|x - 2| - 3)) + 3) - 3)/(2(-1cos(3\u03c0(1|x - 2| - 3)) + 3) - 3))^2 - 2((1(-1cos(3\u03c0(1|x - 2| - 3)) + 3) - 3)/(2(-1cos(3\u03c0(1|x - 2| - 3)) + 3) - 3)) - 4 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"} | |
| {"messages": [{"content": "Find the x-coordinate of the local maximum with the smallest y-value of the function f(x) = 1cos(3\u03c0(3(-2|((3x + 2)/(3x - 2))| - 2)^2 - 1(-2|((3x + 2)/(3x - 2))| - 2))) + 1 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-9", "dataset": "MATH"} | |
| {"messages": [{"content": "Find the x-coordinate of the leftmost local extremum of the function f(x) = 1cos(2\u03c0((3(2(-1|x + 2| + 1)^2 + 5) - 3)/(-1(2(-1|x + 2| + 1)^2 + 5) - 2)) - 1) + 1 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-8", "dataset": "MATH"} | |
| {"messages": [{"content": "Find the x-coordinate of the local maximum with the largest y-value of the function f(x) = -3sin(3\u03c0(-3|((-2(-4x^2 + 1) + 1)/(1(-4x^2 + 1) + 2)) - 3| - 3) - 1) + 3 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-8", "dataset": "MATH"} | |
| {"messages": [{"content": "Find the x-coordinate of the local minimum with the largest y-value of the function f(x) = -3sin(3\u03c0(-1|(5((-3x + 2)/(-2x + 3))^2 + 1((-3x + 2)/(-2x + 3)) - 5)| + 2) - 2) + 3 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-7", "dataset": "MATH"} | |
| {"messages": [{"content": "Find the x-coordinate of the local minimum with the largest y-value of the function f(x) = (1(-3|(-1(3sin(3\u03c0x + 3) + 1)^2 + 4(3sin(3\u03c0x + 3) + 1) - 5)| - 1) + 2)/(3(-3|(-1(3sin(3\u03c0x + 3) + 1)^2 + 4(3sin(3\u03c0x + 3) + 1) - 5)| - 1) - 1) in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-10", "dataset": "MATH"} | |
| {"messages": [{"content": "Find the x-coordinate of the local extremum with the smallest y-value of the function f(x) = (3(-4(-2sin(2\u03c0(3|x - 3| - 3) + 1))^2 + 4(-2sin(2\u03c0(3|x - 3| - 3) + 1)) + 5))/(3(-4(-2sin(2\u03c0(3|x - 3| - 3) + 1))^2 + 4(-2sin(2\u03c0(3|x - 3| - 3) + 1)) + 5) + 1) in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-10", "dataset": "MATH"} | |
| {"messages": [{"content": "Find the x-coordinate of the local minimum with the largest y-value of the function f(x) = -1(-1sin(3\u03c0((-1(-3|x + 2| + 1) + 1)/(-2(-3|x + 2| + 1) - 2)) - 3) + 3)^2 + 3(-1sin(3\u03c0((-1(-3|x + 2| + 1) + 1)/(-2(-3|x + 2| + 1) - 2)) - 3) + 3) - 2 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-4", "dataset": "MATH"} | |
| {"messages": [{"content": "Find the x-coordinate of the rightmost local minimum of the function f(x) = 2|(3(-1cos(1\u03c0((-1x - 3)/(-1x + 2)) - 3) - 3)^2 + 4(-1cos(1\u03c0((-1x - 3)/(-1x + 2)) - 3) - 3)) + 2| in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "7", "dataset": "MATH"} | |
| {"messages": [{"content": "How many local maxima does the function f(x) = (2(-2sin(3\u03c0(2(-2|x - 2| + 1)^2 - 5(-2|x - 2| + 1) - 3))) - 1)/(-1(-2sin(3\u03c0(2(-2|x - 2| + 1)^2 - 5(-2|x - 2| + 1) - 3))) + 2) have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"} | |
| {"messages": [{"content": "Find the x-coordinate of the leftmost local minimum of the function f(x) = 1|(1(2cos(2\u03c0((-1x + 1)/(-3x + 2)) + 3) + 3)^2 + 5(2cos(2\u03c0((-1x + 1)/(-3x + 2)) + 3) + 3) - 1) + 3| + 3 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"} | |
| {"messages": [{"content": "Find the x-coordinate of the local minimum with the smallest y-value of the function f(x) = (-1(2(3|(1sin(1\u03c0x + 2) + 2)| + 3)^2 - 2(3|(1sin(1\u03c0x + 2) + 2)| + 3) + 2) + 1)/(3(2(3|(1sin(1\u03c0x + 2) + 2)| + 3)^2 - 2(3|(1sin(1\u03c0x + 2) + 2)| + 3) + 2) + 2) in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-8", "dataset": "MATH"} | |
| {"messages": [{"content": "Find the x-coordinate of the leftmost local maximum of the function f(x) = 1|(1(-2sin(3\u03c0((-2x - 1)/(1x + 2)) - 3) - 2)^2 + 1(-2sin(3\u03c0((-2x - 1)/(1x + 2)) - 3) - 2) - 3)| + 2 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-9", "dataset": "MATH"} | |
| {"messages": [{"content": "How many local extrema (both minima and maxima) does the function f(x) = 3cos(2\u03c0(2((-2(2|x + 3|))/(-3(2|x + 3|) - 2))^2 - 5((-2(2|x + 3|))/(-3(2|x + 3|) - 2)) - 5) + 1) + 3 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"} | |
| {"messages": [{"content": "Find the average of all x-coordinates of local minima of the function f(x) = -2(-3cos(1\u03c0((1(1|x - 3| - 2))/(-2(1|x - 3| - 2) + 3)) - 1) - 3)^2 + 1 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"} | |
| {"messages": [{"content": "Find the x-coordinate of the local maximum with the largest y-value of the function f(x) = -3(-2sin(2\u03c0(-2|((-3x + 2)/(2x - 1)) - 3| - 3) + 2) + 3)^2 + 5(-2sin(2\u03c0(-2|((-3x + 2)/(2x - 1)) - 3| - 3) + 2) + 3) - 2 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-7", "dataset": "MATH"} | |
| {"messages": [{"content": "Find the x-coordinate of the rightmost local extremum of the function f(x) = 3|((-3(-3(2cos(1\u03c0x - 1) + 1)^2 + 5(2cos(1\u03c0x - 1) + 1) - 5))/(1(-3(2cos(1\u03c0x - 1) + 1)^2 + 5(2cos(1\u03c0x - 1) + 1) - 5))) + 2| - 3 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"} | |
| {"messages": [{"content": "Find the x-coordinate of the local minimum with the largest y-value of the function f(x) = 2(3cos(2\u03c0((-1(1|x + 1| - 1) - 1)/(-1(1|x + 1| - 1) + 2)) + 1) - 3)^2 - 5(3cos(2\u03c0((-1(1|x + 1| - 1) - 1)/(-1(1|x + 1| - 1) + 2)) + 1) - 3) - 1 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-8", "dataset": "MATH"} | |
| {"messages": [{"content": "Find the x-coordinate of the local extremum with the smallest y-value of the function f(x) = 1sin(1\u03c0((3(3(3|x + 3| - 1)^2 - 3(3|x + 3| - 1)) - 3)/(2(3(3|x + 3| - 1)^2 - 3(3|x + 3| - 1)) - 3)) + 2) - 3 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-4", "dataset": "MATH"} | |
| {"messages": [{"content": "Find the x-coordinate of the local maximum with the largest y-value of the function f(x) = 1(3sin(1\u03c0(-1|((-3x - 1)/(1x + 3)) - 3| - 1) + 1))^2 - 5(3sin(1\u03c0(-1|((-3x - 1)/(1x + 3)) - 3| - 1) + 1)) + 4 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-7", "dataset": "MATH"} | |
| {"messages": [{"content": "How many local extrema (both minima and maxima) does the function f(x) = -4((-1(1sin(2\u03c0(2|x - 1| + 1)) + 2) - 3)/(2(1sin(2\u03c0(2|x - 1| + 1)) + 2) - 3))^2 + 3((-1(1sin(2\u03c0(2|x - 1| + 1)) + 2) - 3)/(2(1sin(2\u03c0(2|x - 1| + 1)) + 2) - 3)) - 5 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "161", "dataset": "MATH"} | |
| {"messages": [{"content": "Find the x-coordinate of the local maximum with the largest y-value of the function f(x) = (-2(-2|(3(3sin(2\u03c0x - 1) + 3)^2 + 3(3sin(2\u03c0x - 1) + 3) - 5) - 2| + 1) - 1)/(1(-2|(3(3sin(2\u03c0x - 1) + 3)^2 + 3(3sin(2\u03c0x - 1) + 3) - 5) - 2| + 1)) in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-10", "dataset": "MATH"} | |
| {"messages": [{"content": "Find the x-coordinate of the leftmost local maximum of the function f(x) = -2cos(1\u03c0(1(2|((2x + 2)/(2x - 1)) - 3| + 1)^2 + 3(2|((2x + 2)/(2x - 1)) - 3| + 1) + 5) + 1) - 1 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-7", "dataset": "MATH"} | |
| {"messages": [{"content": "Find the x-coordinate of the local maximum with the smallest y-value of the function f(x) = (-1(2|(1(2cos(1\u03c0x - 3) - 2)^2 + 5(2cos(1\u03c0x - 3) - 2) + 1) - 1| + 1) + 1)/(2(2|(1(2cos(1\u03c0x - 3) - 2)^2 + 5(2cos(1\u03c0x - 3) - 2) + 1) - 1| + 1) + 2) in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-8", "dataset": "MATH"} | |
| {"messages": [{"content": "Find the x-coordinate of the local minimum with the smallest y-value of the function f(x) = -4(-2|((1(3cos(1\u03c0x) - 1) + 3)/(1(3cos(1\u03c0x) - 1) + 1)) - 1| + 2)^2 + 3(-2|((1(3cos(1\u03c0x) - 1) + 3)/(1(3cos(1\u03c0x) - 1) + 1)) - 1| + 2) - 4 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-9", "dataset": "MATH"} | |
| {"messages": [{"content": "Find the x-coordinate of the leftmost local extremum of the function f(x) = (-1(-2(2cos(2\u03c0(-2|x - 1| - 1) - 3) - 3)^2 + 2(2cos(2\u03c0(-2|x - 1| - 1) - 3) - 3) - 1) - 1)/(-2(-2(2cos(2\u03c0(-2|x - 1| - 1) - 3) - 3)^2 + 2(2cos(2\u03c0(-2|x - 1| - 1) - 3) - 3) - 1) + 3) in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-10", "dataset": "MATH"} | |
| {"messages": [{"content": "Find the average of all x-coordinates of local extrema of the function f(x) = 5(-3sin(1\u03c0((3(-2|x - 1| + 2))/(-3(-2|x - 1| + 2) - 1)) - 1) + 2)^2 + 5(-3sin(1\u03c0((3(-2|x - 1| + 2))/(-3(-2|x - 1| + 2) - 1)) - 1) + 2) + 1 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"} | |
| {"messages": [{"content": "Find the average of all x-coordinates of local extrema of the function f(x) = 1sin(1\u03c0((3(-5(-3|x| + 2)^2 + 4(-3|x| + 2) + 3) + 3)/(-1(-5(-3|x| + 2)^2 + 4(-3|x| + 2) + 3) + 3)) + 1) + 3 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"} | |
| {"messages": [{"content": "Find the average of all x-coordinates of local minima of the function f(x) = -1|(-1((2(2sin(2\u03c0x) - 2) + 3)/(3(2sin(2\u03c0x) - 2) + 3))^2 - 1((2(2sin(2\u03c0x) - 2) + 3)/(3(2sin(2\u03c0x) - 2) + 3)) - 5) - 2| + 2 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"} | |
| {"messages": [{"content": "Find the x-coordinate of the rightmost local extremum of the function f(x) = -1sin(1\u03c0(3|((3(-3x^2 - 1x + 1) + 1)/(3(-3x^2 - 1x + 1))) - 3| - 3) + 1) - 2 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"} | |
| {"messages": [{"content": "Find the x-coordinate of the local maximum with the largest y-value of the function f(x) = (2(4(2cos(2\u03c0(-2|x| - 2) + 3) + 3)^2 - 4(2cos(2\u03c0(-2|x| - 2) + 3) + 3) + 5) - 2)/(3(4(2cos(2\u03c0(-2|x| - 2) + 3) + 3)^2 - 4(2cos(2\u03c0(-2|x| - 2) + 3) + 3) + 5)) in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-10", "dataset": "MATH"} | |
| {"messages": [{"content": "Find the average of all x-coordinates of local minima of the function f(x) = (-1(-1|(1cos(1\u03c0(-1x^2 - 3x - 4) + 2) - 1) - 3| - 1) - 3)/(2(-1|(1cos(1\u03c0(-1x^2 - 3x - 4) + 2) - 1) - 3| - 1) + 3) in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"} | |
| {"messages": [{"content": "Find the x-coordinate of the leftmost local extremum of the function f(x) = -3sin(2\u03c0(3(-1|((-2x - 2)/(-3x - 3)) + 1| - 3)^2 - 5) + 1) + 1 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-4", "dataset": "MATH"} | |
| {"messages": [{"content": "Find the x-coordinate of the local maximum with the smallest y-value of the function f(x) = 2|(-5((-1(-1sin(3\u03c0x + 1) + 1) + 2)/(-3(-1sin(3\u03c0x + 1) + 1) - 2))^2 + 1((-1(-1sin(3\u03c0x + 1) + 1) + 2)/(-3(-1sin(3\u03c0x + 1) + 1) - 2)) + 4) + 2| + 2 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-10", "dataset": "MATH"} | |
| {"messages": [{"content": "How many local extrema (both minima and maxima) does the function f(x) = 5(2cos(2\u03c0((-1(3|x + 2| + 2) + 2)/(-2(3|x + 2| + 2) + 1)) - 2) - 1)^2 - 1(2cos(2\u03c0((-1(3|x + 2| + 2) + 2)/(-2(3|x + 2| + 2) + 1)) - 2) - 1) + 4 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "6", "dataset": "MATH"} | |
| {"messages": [{"content": "Find the x-coordinate of the local maximum with the largest y-value of the function f(x) = -1sin(2\u03c0((1(-2|(-1x^2 + 2x + 4) - 1|) + 3)/(2(-2|(-1x^2 + 2x + 4) - 1|) - 1)) + 3) + 3 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-2", "dataset": "MATH"} | |
| {"messages": [{"content": "Find the x-coordinate of the leftmost local minimum of the function f(x) = 4(3|(-3cos(3\u03c0((3x + 2)/(3x)) - 3) - 1) - 2| + 1)^2 - 3(3|(-3cos(3\u03c0((3x + 2)/(3x)) - 3) - 1) - 2| + 1) in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-2", "dataset": "MATH"} | |
| {"messages": [{"content": "Find the average of all x-coordinates of local minima of the function f(x) = (-3(-4(1sin(1\u03c0(-3|x + 3| + 2) - 3) - 1)^2 - 4(1sin(1\u03c0(-3|x + 3| + 2) - 3) - 1) + 2) - 2)/(-2(-4(1sin(1\u03c0(-3|x + 3| + 2) - 3) - 1)^2 - 4(1sin(1\u03c0(-3|x + 3| + 2) - 3) - 1) + 2) - 3) in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"} | |
| {"messages": [{"content": "Find the average of all x-coordinates of local maxima of the function f(x) = 1(-3|((-3(-1sin(3\u03c0x - 1) + 3) + 3)/(-3(-1sin(3\u03c0x - 1) + 3) - 1)) - 3| - 1)^2 + 1(-3|((-3(-1sin(3\u03c0x - 1) + 3) + 3)/(-3(-1sin(3\u03c0x - 1) + 3) - 1)) - 3| - 1) + 2 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"} | |
| {"messages": [{"content": "Find the x-coordinate of the local extremum with the largest y-value of the function f(x) = (2(2|(-5(-1cos(3\u03c0x - 1) - 3)^2 + 2(-1cos(3\u03c0x - 1) - 3) - 1) - 3|) - 2)/(1(2|(-5(-1cos(3\u03c0x - 1) - 3)^2 + 2(-1cos(3\u03c0x - 1) - 3) - 1) - 3|)) in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-10", "dataset": "MATH"} | |
| {"messages": [{"content": "Find the average of all x-coordinates of local extrema of the function f(x) = (-2(3cos(2\u03c0(-5(1|x + 2| - 1)^2 - 2(1|x + 2| - 1) - 2) + 2) - 3) + 2)/(-3(3cos(2\u03c0(-5(1|x + 2| - 1)^2 - 2(1|x + 2| - 1) - 2) + 2) - 3) - 2) in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"} | |
| {"messages": [{"content": "Find the average of all x-coordinates of local maxima of the function f(x) = 1|(1((2(3sin(1\u03c0x - 2)) - 1)/(1(3sin(1\u03c0x - 2)) + 1))^2 - 2((2(3sin(1\u03c0x - 2)) - 1)/(1(3sin(1\u03c0x - 2)) + 1)) + 3) - 2| + 3 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"} | |
| {"messages": [{"content": "Find the x-coordinate of the rightmost local minimum of the function f(x) = (-3(1sin(1\u03c0(5(-3|x - 1| - 2)^2 - 2(-3|x - 1| - 2) + 5) + 2) + 2) + 3)/(2(1sin(1\u03c0(5(-3|x - 1| - 2)^2 - 2(-3|x - 1| - 2) + 5) + 2) + 2) + 1) in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"} | |
| {"messages": [{"content": "Find the average of all x-coordinates of local maxima of the function f(x) = -4(-2|((-2(-2sin(3\u03c0x + 2) + 3) + 3)/(2(-2sin(3\u03c0x + 2) + 3) - 1)) + 2| - 3)^2 + 4(-2|((-2(-2sin(3\u03c0x + 2) + 3) + 3)/(2(-2sin(3\u03c0x + 2) + 3) - 1)) + 2| - 3) in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"} | |
| {"messages": [{"content": "Find the x-coordinate of the rightmost local minimum of the function f(x) = 1((2(-2cos(1\u03c0(-2|x| - 3) + 3)) - 1)/(2(-2cos(1\u03c0(-2|x| - 3) + 3)) - 3))^2 + 3((2(-2cos(1\u03c0(-2|x| - 3) + 3)) - 1)/(2(-2cos(1\u03c0(-2|x| - 3) + 3)) - 3)) in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"} | |
| {"messages": [{"content": "Find the average of all x-coordinates of local extrema of the function f(x) = -1sin(1\u03c0(4((-3(3|x - 3| - 3) - 3)/(-2(3|x - 3| - 3) - 2))^2 + 4) + 3) + 2 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"} | |
| {"messages": [{"content": "Find the x-coordinate of the leftmost local maximum of the function f(x) = (-2(-1sin(2\u03c0(3|(4x^2 - 2x) - 3| + 2) - 2) + 1) + 2)/(-1(-1sin(2\u03c0(3|(4x^2 - 2x) - 3| + 2) - 2) + 1) + 3) in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-10", "dataset": "MATH"} | |
| {"messages": [{"content": "Find the x-coordinate of the leftmost local maximum of the function f(x) = 3|(4(3cos(2\u03c0((-1x + 2)/(-3x)) - 3) - 1)^2 - 1(3cos(2\u03c0((-1x + 2)/(-3x)) - 3) - 1) - 2) + 1| - 3 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-5", "dataset": "MATH"} | |
| {"messages": [{"content": "Find the x-coordinate of the leftmost local extremum of the function f(x) = -2(1sin(1\u03c0((3(-3|x|) + 1)/(-3(-3|x|) + 2))) - 3)^2 + 2(1sin(1\u03c0((3(-3|x|) + 1)/(-3(-3|x|) + 2))) - 3) - 2 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"} | |
| {"messages": [{"content": "Find the x-coordinate of the local maximum with the smallest y-value of the function f(x) = (-3(-2sin(3\u03c0(-2|(-3x^2 + 4x - 4) + 3|) + 2) - 3) + 1)/(1(-2sin(3\u03c0(-2|(-3x^2 + 4x - 4) + 3|) + 2) - 3) + 2) in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"} | |
| {"messages": [{"content": "Find the average of all x-coordinates of local minima of the function f(x) = 2|(-5(-2sin(1\u03c0((1x - 1)/(1x + 1))) - 1)^2 + 4(-2sin(1\u03c0((1x - 1)/(1x + 1))) - 1) - 1)| - 1 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-1", "dataset": "MATH"} | |
| {"messages": [{"content": "Find the x-coordinate of the leftmost local extremum of the function f(x) = -1|(-1((-3(3sin(3\u03c0x - 2)) + 3)/(2(3sin(3\u03c0x - 2)) - 1))^2 + 1((-3(3sin(3\u03c0x - 2)) + 3)/(2(3sin(3\u03c0x - 2)) - 1)) - 3) + 3| + 1 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-10", "dataset": "MATH"} | |
| {"messages": [{"content": "Find the x-coordinate of the rightmost local extremum of the function f(x) = 1(1|((-1(-1cos(3\u03c0x - 1) - 2) + 2)/(-3(-1cos(3\u03c0x - 1) - 2) - 2))| + 2)^2 - 1(1|((-1(-1cos(3\u03c0x - 1) - 2) + 2)/(-3(-1cos(3\u03c0x - 1) - 2) - 2))| + 2) - 2 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"} | |
| {"messages": [{"content": "Find the x-coordinate of the local minimum with the smallest y-value of the function f(x) = -2|(-3sin(3\u03c0((2(5x^2 + 3x + 5) - 1)/(-2(5x^2 + 3x + 5) - 2)))) + 3| - 2 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-1", "dataset": "MATH"} | |
| {"messages": [{"content": "Find the x-coordinate of the local minimum with the smallest y-value of the function f(x) = 1(3cos(2\u03c0(-3|((-2x)/(-3x - 1)) + 1| + 3)) - 3)^2 + 4(3cos(2\u03c0(-3|((-2x)/(-3x - 1)) + 1| + 3)) - 3) - 3 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-4", "dataset": "MATH"} | |
| {"messages": [{"content": "How many local extrema (both minima and maxima) does the function f(x) = 2sin(3\u03c0((-2(-1(-2|x - 3| - 3)^2 + 3(-2|x - 3| - 3) + 2) + 1)/(-3(-1(-2|x - 3| - 3)^2 + 3(-2|x - 3| - 3) + 2) - 3)) - 2) + 2 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"} | |
| {"messages": [{"content": "Find the x-coordinate of the local minimum with the smallest y-value of the function f(x) = 1cos(3\u03c0((-3(-5(1|x + 2| - 1)^2 - 4(1|x + 2| - 1) + 1) + 1)/(1(-5(1|x + 2| - 1)^2 - 4(1|x + 2| - 1) + 1) - 3)) + 1) in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-4", "dataset": "MATH"} | |
| {"messages": [{"content": "Find the average of all x-coordinates of local minima of the function f(x) = 5(-1|((2(-2sin(1\u03c0x - 2) + 2) + 1)/(2(-2sin(1\u03c0x - 2) + 2))) + 2| - 2)^2 + 4 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"} | |
| {"messages": [{"content": "Find the x-coordinate of the local extremum with the largest y-value of the function f(x) = -1|(-1(-2cos(1\u03c0((3x - 2)/(1x + 2)) - 2) + 3)^2 - 1(-2cos(1\u03c0((3x - 2)/(1x + 2)) - 2) + 3) - 4) + 3| + 2 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-7", "dataset": "MATH"} | |
| {"messages": [{"content": "Find the average of all x-coordinates of local extrema of the function f(x) = -2((1(3sin(2\u03c0(3|x - 3| + 3)) - 3) + 2)/(-2(3sin(2\u03c0(3|x - 3| + 3)) - 3) + 3))^2 - 4((1(3sin(2\u03c0(3|x - 3| + 3)) - 3) + 2)/(-2(3sin(2\u03c0(3|x - 3| + 3)) - 3) + 3)) - 5 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"} | |
| {"messages": [{"content": "How many local maxima does the function f(x) = -1|(-4(2cos(3\u03c0((1x + 3)/(1x - 2)) + 2))^2 - 1(2cos(3\u03c0((1x + 3)/(1x - 2)) + 2)) + 2) - 2| - 3 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"} | |
| {"messages": [{"content": "Find the x-coordinate of the leftmost local maximum of the function f(x) = (2(-1sin(1\u03c0(-3|(-1x^2 + 2x - 5) + 3| - 1) - 1) - 2))/(-2(-1sin(1\u03c0(-3|(-1x^2 + 2x - 5) + 3| - 1) - 1) - 2) - 2) in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-10", "dataset": "MATH"} | |
| {"messages": [{"content": "Find the x-coordinate of the leftmost local extremum of the function f(x) = (-1(5(1sin(2\u03c0(-2|x - 3| + 3) + 1) + 1)^2 + 1(1sin(2\u03c0(-2|x - 3| + 3) + 1) + 1)) - 1)/(3(5(1sin(2\u03c0(-2|x - 3| + 3) + 1) + 1)^2 + 1(1sin(2\u03c0(-2|x - 3| + 3) + 1) + 1))) in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-10", "dataset": "MATH"} | |
| {"messages": [{"content": "Find the average of all x-coordinates of local maxima of the function f(x) = -1sin(1\u03c0(1|((1(1x^2 + 5x + 4) - 1)/(2(1x^2 + 5x + 4) + 2)) - 3| + 1)) - 3 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-3", "dataset": "MATH"} | |
| {"messages": [{"content": "Find the average of all x-coordinates of local minima of the function f(x) = -1cos(1\u03c0(-1|(-4((3x - 2)/(-3x))^2 - 2) + 1| + 2) + 2) in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"} | |
| {"messages": [{"content": "How many local maxima does the function f(x) = 2|(4((2(-1sin(3\u03c0x + 2) + 2) + 1)/(-1(-1sin(3\u03c0x + 2) + 2) + 2))^2 - 3) - 3| + 1 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"} | |
| {"messages": [{"content": "Find the x-coordinate of the leftmost local maximum of the function f(x) = 2sin(1\u03c0(-2|((1(-1x^2 - 3x - 1) + 1)/(1(-1x^2 - 3x - 1))) + 3| + 2)) in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-4", "dataset": "MATH"} | |
| {"messages": [{"content": "Find the x-coordinate of the local minimum with the largest y-value of the function f(x) = 1|((-1(1(3sin(2\u03c0x + 2) - 3)^2 - 4(3sin(2\u03c0x + 2) - 3) + 3) - 1)/(3(1(3sin(2\u03c0x + 2) - 3)^2 - 4(3sin(2\u03c0x + 2) - 3) + 3) - 2)) - 2| + 2 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-10", "dataset": "MATH"} | |
| {"messages": [{"content": "Find the x-coordinate of the local extremum with the smallest y-value of the function f(x) = 2|(-1sin(2\u03c0(-5((-1x - 2)/(2x - 1))^2 - 1((-1x - 2)/(2x - 1)) + 4))) + 2| + 3 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-1", "dataset": "MATH"} | |
| {"messages": [{"content": "Find the x-coordinate of the leftmost local minimum of the function f(x) = 2cos(2\u03c0((1(2(3|x - 2| - 1)^2 + 4(3|x - 2| - 1)))/(3(2(3|x - 2| - 1)^2 + 4(3|x - 2| - 1)) + 1)) - 2) - 3 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"} | |
| {"messages": [{"content": "Find the x-coordinate of the local minimum with the smallest y-value of the function f(x) = -1((3(-2|(-2cos(1\u03c0x) - 1) + 3|) + 3)/(-1(-2|(-2cos(1\u03c0x) - 1) + 3|) + 3))^2 - 4((3(-2|(-2cos(1\u03c0x) - 1) + 3|) + 3)/(-1(-2|(-2cos(1\u03c0x) - 1) + 3|) + 3)) + 3 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-8", "dataset": "MATH"} | |
| {"messages": [{"content": "Find the x-coordinate of the local extremum with the smallest y-value of the function f(x) = -1cos(3\u03c0((-3(4(-2|x|)^2 + 2(-2|x|) - 4) - 1)/(3(4(-2|x|)^2 + 2(-2|x|) - 4)))) + 1 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-1", "dataset": "MATH"} | |
| {"messages": [{"content": "Find the x-coordinate of the local minimum with the largest y-value of the function f(x) = -1cos(1\u03c0(-3(-2|((3x + 1)/(2x + 2)) + 3| + 2)^2 + 1(-2|((3x + 1)/(2x + 2)) + 3| + 2) - 4) - 3) + 3 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-1", "dataset": "MATH"} | |
| {"messages": [{"content": "How many local extrema (both minima and maxima) does the function f(x) = 3|(3sin(3\u03c0((3(-5x^2 - 4x - 5) + 2)/(-2(-5x^2 - 4x - 5) + 3)) + 1) + 1) + 3| - 1 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5", "dataset": "MATH"} | |
| {"messages": [{"content": "Find the x-coordinate of the local maximum with the largest y-value of the function f(x) = -3(-2sin(3\u03c0(1|((3x + 3)/(-3x + 1)) + 2|) - 2) - 1)^2 + 1(-2sin(3\u03c0(1|((3x + 3)/(-3x + 1)) + 2|) - 2) - 1) - 4 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-4", "dataset": "MATH"} | |
| {"messages": [{"content": "How many local extrema (both minima and maxima) does the function f(x) = (-3(5(3cos(2\u03c0(-3|x + 1| - 2) + 1) - 1)^2 + 2(3cos(2\u03c0(-3|x + 1| - 2) + 1) - 1) - 3) - 2)/(-2(5(3cos(2\u03c0(-3|x + 1| - 2) + 1) - 1)^2 + 2(3cos(2\u03c0(-3|x + 1| - 2) + 1) - 1) - 3) + 1) have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "241", "dataset": "MATH"} | |
| {"messages": [{"content": "Find the x-coordinate of the leftmost local extremum of the function f(x) = -1|(3cos(1\u03c0((1(-3x^2 - 3x - 1) - 3)/(-3(-3x^2 - 3x - 1) - 3)) + 3) + 2) - 2| + 2 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-1", "dataset": "MATH"} | |
| {"messages": [{"content": "Find the x-coordinate of the local minimum with the smallest y-value of the function f(x) = (2(-1cos(3\u03c0(-2(1|x - 3| - 2)^2 - 2(1|x - 3| - 2)) - 3)) - 2)/(-1(-1cos(3\u03c0(-2(1|x - 3| - 2)^2 - 2(1|x - 3| - 2)) - 3)) + 2) in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-10", "dataset": "MATH"} | |
| {"messages": [{"content": "Find the x-coordinate of the local maximum with the smallest y-value of the function f(x) = -4(1cos(2\u03c0((2(-1|x - 2| + 3) - 1)/(-2(-1|x - 2| + 3) + 3)) - 3) + 3)^2 - 1(1cos(2\u03c0((2(-1|x - 2| + 3) - 1)/(-2(-1|x - 2| + 3) + 3)) - 3) + 3) - 4 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-1", "dataset": "MATH"} | |
| {"messages": [{"content": "Find the x-coordinate of the leftmost local extremum of the function f(x) = 2(-2|(2cos(2\u03c0((2x + 2)/(1x - 3)) + 2) - 1) - 2| - 2)^2 + 5(-2|(2cos(2\u03c0((2x + 2)/(1x - 3)) + 2) - 1) - 2| - 2) + 3 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-7", "dataset": "MATH"} | |
| {"messages": [{"content": "How many local maxima does the function f(x) = -3cos(3\u03c0((-2(-3|(2x^2 - 3x - 4)| - 2) + 1)/(-3(-3|(2x^2 - 3x - 4)| - 2)))) + 3 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"} | |
| {"messages": [{"content": "Find the average of all x-coordinates of local minima of the function f(x) = 1(1cos(1\u03c0(-2|((1x - 3)/(1x - 2)) - 3|) + 1) + 1)^2 + 2(1cos(1\u03c0(-2|((1x - 3)/(1x - 2)) - 3|) + 1) + 1) + 1 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"} | |
| {"messages": [{"content": "Find the x-coordinate of the local maximum with the largest y-value of the function f(x) = -4(2cos(1\u03c0(-1|((-2x + 3)/(-3x + 1)) + 2| - 2) + 1))^2 + 3(2cos(1\u03c0(-1|((-2x + 3)/(-3x + 1)) + 2| - 2) + 1)) + 5 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-8", "dataset": "MATH"} | |
| {"messages": [{"content": "Find the x-coordinate of the rightmost local maximum of the function f(x) = 2(-3cos(2\u03c0((-1(-3|x| + 1) - 2)/(3(-3|x| + 1))) + 3) + 2)^2 - 3 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"} | |
| {"messages": [{"content": "Find the x-coordinate of the rightmost local extremum of the function f(x) = (1(-2cos(1\u03c0(-2|(-2x^2 - 4x - 2) - 3| + 1) + 3)) + 3)/(2(-2cos(1\u03c0(-2|(-2x^2 - 4x - 2) - 3| + 1) + 3)) + 3) in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"} | |
| {"messages": [{"content": "Find the x-coordinate of the local minimum with the largest y-value of the function f(x) = 1cos(3\u03c0(-1(3|((-1x - 1)/(-2x + 3))| + 2)^2 + 5(3|((-1x - 1)/(-2x + 3))| + 2) - 3) - 2) + 1 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-3", "dataset": "MATH"} | |
| {"messages": [{"content": "Find the x-coordinate of the rightmost local extremum of the function f(x) = 3sin(2\u03c0(-5(-1|((-1x - 3)/(1x + 2)) + 1| + 3)^2 + 1(-1|((-1x - 3)/(1x + 2)) + 1| + 3) - 1) + 3) - 2 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8", "dataset": "MATH"} | |
| {"messages": [{"content": "Find the x-coordinate of the local maximum with the smallest y-value of the function f(x) = -2|((2(1sin(1\u03c0(-3x^2 - 5x - 5) + 3) + 1) + 3)/(-2(1sin(1\u03c0(-3x^2 - 5x - 5) + 3) + 1) + 3)) + 2| - 1 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-10", "dataset": "MATH"} | |
| {"messages": [{"content": "Find the x-coordinate of the local extremum with the largest y-value of the function f(x) = -3((1(1|(2sin(2\u03c0x - 3) + 3) + 1| - 3) + 1)/(-3(1|(2sin(2\u03c0x - 3) + 3) + 1| - 3) + 2))^2 + 3((1(1|(2sin(2\u03c0x - 3) + 3) + 1| - 3) + 1)/(-3(1|(2sin(2\u03c0x - 3) + 3) + 1| - 3) + 2)) + 1 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-10", "dataset": "MATH"} | |
| {"messages": [{"content": "Find the x-coordinate of the local maximum with the smallest y-value of the function f(x) = -3cos(2\u03c0(-2|((-3(-2x^2 + 1x + 1) + 1)/(1(-2x^2 + 1x + 1) - 2)) + 1| + 3) + 2) + 3 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"} | |
| {"messages": [{"content": "How many local maxima does the function f(x) = 5((2(2sin(1\u03c0(-1|x + 3| - 1) + 3) + 1) + 2)/(-3(2sin(1\u03c0(-1|x + 3| - 1) + 3) + 1) - 1))^2 + 3((2(2sin(1\u03c0(-1|x + 3| - 1) + 3) + 1) + 2)/(-3(2sin(1\u03c0(-1|x + 3| - 1) + 3) + 1) - 1)) - 4 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"} | |
| {"messages": [{"content": "Find the x-coordinate of the rightmost local extremum of the function f(x) = (-2(-2cos(3\u03c0(4(3|x + 1| - 1)^2 + 2) + 1) + 1) - 1)/(-3(-2cos(3\u03c0(4(3|x + 1| - 1)^2 + 2) + 1) + 1) - 1) in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"} | |
| {"messages": [{"content": "Find the average of all x-coordinates of local extrema of the function f(x) = -1(2|((1(-3cos(2\u03c0x) - 2) - 3)/(2(-3cos(2\u03c0x) - 2) - 3)) - 3| - 3)^2 - 2(2|((1(-3cos(2\u03c0x) - 2) - 3)/(2(-3cos(2\u03c0x) - 2) - 3)) - 3| - 3) + 5 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"} | |
| {"messages": [{"content": "Find the x-coordinate of the local maximum with the largest y-value of the function f(x) = 3(1|((1(-3sin(3\u03c0x - 3) - 2) - 1)/(-3(-3sin(3\u03c0x - 3) - 2) - 1)) + 2| - 3)^2 + 4(1|((1(-3sin(3\u03c0x - 3) - 2) - 1)/(-3(-3sin(3\u03c0x - 3) - 2) - 1)) + 2| - 3) + 1 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-10", "dataset": "MATH"} | |
| {"messages": [{"content": "Find the x-coordinate of the local extremum with the largest y-value of the function f(x) = 2|(-4(1sin(2\u03c0((-3x)/(1x)) + 2) + 1)^2 - 4(1sin(2\u03c0((-3x)/(1x)) + 2) + 1) - 5) + 2| in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-2", "dataset": "MATH"} | |
| {"messages": [{"content": "Find the x-coordinate of the leftmost local minimum of the function f(x) = -3(2|(1cos(2\u03c0((3x + 1)/(-2x - 1)) - 1) - 1) + 3| + 2)^2 + 4(2|(1cos(2\u03c0((3x + 1)/(-2x - 1)) - 1) - 1) + 3| + 2) + 2 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-1", "dataset": "MATH"} | |
| {"messages": [{"content": "Find the x-coordinate of the local minimum with the smallest y-value of the function f(x) = -2sin(3\u03c0(4((2(3|x - 2|))/(2(3|x - 2|) - 3))^2 - 3((2(3|x - 2|))/(2(3|x - 2|) - 3)) - 3) + 3) + 2 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-4", "dataset": "MATH"} | |
| {"messages": [{"content": "How many local extrema (both minima and maxima) does the function f(x) = 3|(3(1sin(2\u03c0((3x - 1)/(-1x - 2)) - 1) - 2)^2 - 4(1sin(2\u03c0((3x - 1)/(-1x - 2)) - 1) - 2) + 4) - 1| have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "74", "dataset": "MATH"} | |
| {"messages": [{"content": "Find the x-coordinate of the local maximum with the smallest y-value of the function f(x) = -4(2|((3(-2cos(1\u03c0x) - 3) - 3)/(3(-2cos(1\u03c0x) - 3) - 2)) - 1| - 1)^2 + 4(2|((3(-2cos(1\u03c0x) - 3) - 3)/(3(-2cos(1\u03c0x) - 3) - 2)) - 1| - 1) - 4 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-9", "dataset": "MATH"} | |
| {"messages": [{"content": "Find the average of all x-coordinates of local minima of the function f(x) = 3cos(2\u03c0((-3(-5(2|x - 3| - 2)^2 + 4(2|x - 3| - 2)) + 3)/(-1(-5(2|x - 3| - 2)^2 + 4(2|x - 3| - 2)) - 3))) + 3 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"} | |
| {"messages": [{"content": "Find the x-coordinate of the leftmost local minimum of the function f(x) = (-1(1|(1(-2sin(2\u03c0x) + 3)^2 + 3(-2sin(2\u03c0x) + 3) - 3) + 1| + 3) + 1)/(-1(1|(1(-2sin(2\u03c0x) + 3)^2 + 3(-2sin(2\u03c0x) + 3) - 3) + 1| + 3) - 2) in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-10", "dataset": "MATH"} | |
| {"messages": [{"content": "Find the x-coordinate of the local minimum with the largest y-value of the function f(x) = (-3(3|(-1cos(1\u03c0(4x^2 - 1x + 2) - 1)) - 2| - 1) + 1)/(-1(3|(-1cos(1\u03c0(4x^2 - 1x + 2) - 1)) - 2| - 1) - 1) in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"} | |
| {"messages": [{"content": "Find the average of all x-coordinates of local minima of the function f(x) = -3|(2sin(2\u03c0(1((1x - 3)/(-3x - 2))^2 - 1((1x - 3)/(-3x - 2)) + 2) + 1) + 3) - 1| - 1 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-1", "dataset": "MATH"} | |
| {"messages": [{"content": "Find the x-coordinate of the leftmost local extremum of the function f(x) = -3|(-1(-1sin(1\u03c0((3x - 1)/(3x - 2))) + 2)^2 + 4(-1sin(1\u03c0((3x - 1)/(3x - 2))) + 2) - 5) - 2| + 1 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"} | |
| {"messages": [{"content": "Find the average of all x-coordinates of local minima of the function f(x) = -3(-1sin(2\u03c0(2|((-1x + 2)/(1x)) + 1| + 2) + 1) - 1)^2 - 2 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"} | |
| {"messages": [{"content": "How many local extrema (both minima and maxima) does the function f(x) = -2sin(1\u03c0(-2|(-4((-1x + 2)/(2x + 1))^2 + 5((-1x + 2)/(2x + 1)) + 2)| - 1) + 1) - 2 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "87", "dataset": "MATH"} | |
| {"messages": [{"content": "Find the x-coordinate of the leftmost local maximum of the function f(x) = -1cos(3\u03c0(3((2(2|x + 3|) - 2)/(-2(2|x + 3|) - 1))^2 + 4((2(2|x + 3|) - 2)/(-2(2|x + 3|) - 1))) + 2) + 2 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-8", "dataset": "MATH"} | |
| {"messages": [{"content": "Find the x-coordinate of the local maximum with the smallest y-value of the function f(x) = (1(1(2|(1cos(3\u03c0x + 2)) + 2| - 3)^2 + 2) - 3)/(2(1(2|(1cos(3\u03c0x + 2)) + 2| - 3)^2 + 2) - 3) in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-10", "dataset": "MATH"} | |
| {"messages": [{"content": "Find the average of all x-coordinates of local minima of the function f(x) = 1sin(3\u03c0(-1|(2((1x + 2)/(1x))^2 + 5((1x + 2)/(1x))) + 3| - 2) + 3) + 2 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"} | |
| {"messages": [{"content": "Find the average of all x-coordinates of local maxima of the function f(x) = 2(-3cos(3\u03c0((2(-2|x|) - 3)/(1(-2|x|) + 3))))^2 - 1(-3cos(3\u03c0((2(-2|x|) - 3)/(1(-2|x|) + 3)))) - 3 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"} | |
| {"messages": [{"content": "Find the average of all x-coordinates of local extrema of the function f(x) = -1((1(-1sin(1\u03c0(-3|x| - 3) + 1) + 3) - 3)/(-1(-1sin(1\u03c0(-3|x| - 3) + 1) + 3) - 3))^2 + 3((1(-1sin(1\u03c0(-3|x| - 3) + 1) + 3) - 3)/(-1(-1sin(1\u03c0(-3|x| - 3) + 1) + 3) - 3)) - 4 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"} | |
| {"messages": [{"content": "Find the average of all x-coordinates of local minima of the function f(x) = (-1(5(1cos(2\u03c0(1|x + 3| - 1) - 2) + 2)^2 - 2(1cos(2\u03c0(1|x + 3| - 1) - 2) + 2) + 3) - 1)/(-3(5(1cos(2\u03c0(1|x + 3| - 1) - 2) + 2)^2 - 2(1cos(2\u03c0(1|x + 3| - 1) - 2) + 2) + 3)) in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"} | |
| {"messages": [{"content": "Find the x-coordinate of the local maximum with the smallest y-value of the function f(x) = -5(1|((-3(1cos(3\u03c0x + 1)))/(-2(1cos(3\u03c0x + 1)) + 3)) - 3| + 1)^2 - 1(1|((-3(1cos(3\u03c0x + 1)))/(-2(1cos(3\u03c0x + 1)) + 3)) - 3| + 1) + 4 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-10", "dataset": "MATH"} | |
| {"messages": [{"content": "Find the x-coordinate of the rightmost local maximum of the function f(x) = -5((2(1cos(2\u03c0(-1|x - 3| - 1) + 3) + 3) + 2)/(1(1cos(2\u03c0(-1|x - 3| - 1) + 3) + 3)))^2 + 4((2(1cos(2\u03c0(-1|x - 3| - 1) + 3) + 3) + 2)/(1(1cos(2\u03c0(-1|x - 3| - 1) + 3) + 3))) - 4 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "9", "dataset": "MATH"} | |
| {"messages": [{"content": "How many local maxima does the function f(x) = (-1(2sin(3\u03c0(1|(1x^2 + 3x) + 1| - 1)) - 2) - 1)/(2(2sin(3\u03c0(1|(1x^2 + 3x) + 1| - 1)) - 2)) have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"} | |
| {"messages": [{"content": "Find the x-coordinate of the local extremum with the smallest y-value of the function f(x) = 1|(2((-2(1sin(2\u03c0x - 2) - 2))/(1(1sin(2\u03c0x - 2) - 2) + 2))^2 + 4((-2(1sin(2\u03c0x - 2) - 2))/(1(1sin(2\u03c0x - 2) - 2) + 2)) + 4) + 3| in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-9", "dataset": "MATH"} | |
| {"messages": [{"content": "Find the x-coordinate of the local maximum with the largest y-value of the function f(x) = 2cos(2\u03c0(5(3|((3x + 3)/(2x + 1)) - 2| + 1)^2 + 1) - 1) in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-9", "dataset": "MATH"} | |
| {"messages": [{"content": "Find the x-coordinate of the rightmost local extremum of the function f(x) = (-1(-2sin(1\u03c0(-3(3|x - 1| + 2)^2 - 4(3|x - 1| + 2) - 3) + 3) - 2) + 1)/(-1(-2sin(1\u03c0(-3(3|x - 1| + 2)^2 - 4(3|x - 1| + 2) - 3) + 3) - 2) + 2) in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"} | |
| {"messages": [{"content": "Find the x-coordinate of the leftmost local minimum of the function f(x) = 1sin(2\u03c0(5((1(3|x - 2| - 1) - 1)/(3(3|x - 2| - 1) + 2))^2 + 1((1(3|x - 2| - 1) - 1)/(3(3|x - 2| - 1) + 2)) - 3)) - 3 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-4", "dataset": "MATH"} | |
| {"messages": [{"content": "Find the x-coordinate of the leftmost local minimum of the function f(x) = 2sin(2\u03c0((-2(-1|(-5x^2 + 1x + 4) - 1| + 1) + 2)/(-3(-1|(-5x^2 + 1x + 4) - 1| + 1) + 1)) + 2) in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-1", "dataset": "MATH"} | |
| {"messages": [{"content": "How many local extrema (both minima and maxima) does the function f(x) = 4((3(1|(2cos(2\u03c0x + 2)) - 3| - 1) + 3)/(3(1|(2cos(2\u03c0x + 2)) - 3| - 1) - 2))^2 + 2((3(1|(2cos(2\u03c0x + 2)) - 3| - 1) + 3)/(3(1|(2cos(2\u03c0x + 2)) - 3| - 1) - 2)) + 1 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "80", "dataset": "MATH"} | |
| {"messages": [{"content": "Find the x-coordinate of the local maximum with the smallest y-value of the function f(x) = -2|(-1sin(3\u03c0((-1(5x^2 - 2x - 3) + 3)/(-3(5x^2 - 2x - 3) - 2)) + 1) - 3)| + 2 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-1", "dataset": "MATH"} | |
| {"messages": [{"content": "How many local extrema (both minima and maxima) does the function f(x) = 2|((-3(-3sin(1\u03c0(-3x^2 + 1x) - 3) - 1))/(-1(-3sin(1\u03c0(-3x^2 + 1x) - 3) - 1) + 2)) + 2| - 1 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "510", "dataset": "MATH"} | |
| {"messages": [{"content": "Find the x-coordinate of the local minimum with the smallest y-value of the function f(x) = 2sin(2\u03c0(-2|((-3(2x^2 - 2x - 3) - 1)/(-3(2x^2 - 2x - 3))) + 3| - 1) + 2) + 1 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-1", "dataset": "MATH"} | |
| {"messages": [{"content": "Find the x-coordinate of the local minimum with the smallest y-value of the function f(x) = -1cos(1\u03c0(-1(-3|((3x - 1)/(3x + 1)) + 3| - 2)^2 + 4(-3|((3x - 1)/(3x + 1)) + 3| - 2) - 1) - 2) - 1 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-8", "dataset": "MATH"} | |
| {"messages": [{"content": "Find the average of all x-coordinates of local minima of the function f(x) = 4(-2cos(1\u03c0((1(2|x + 1|) + 2)/(-1(2|x + 1|) - 1))) + 1)^2 - 1(-2cos(1\u03c0((1(2|x + 1|) + 2)/(-1(2|x + 1|) - 1))) + 1) - 5 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-1", "dataset": "MATH"} | |
| {"messages": [{"content": "Find the x-coordinate of the rightmost local minimum of the function f(x) = (1(2cos(2\u03c0(3(3|x + 3| - 3)^2 - 4(3|x + 3| - 3) - 1)) + 2) - 3)/(3(2cos(2\u03c0(3(3|x + 3| - 3)^2 - 4(3|x + 3| - 3) - 1)) + 2) + 1) in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"} | |
| {"messages": [{"content": "Find the x-coordinate of the local maximum with the smallest y-value of the function f(x) = -1(1|((2(2cos(1\u03c0x + 2)) - 3)/(3(2cos(1\u03c0x + 2)) + 1)) - 1| + 2)^2 + 5(1|((2(2cos(1\u03c0x + 2)) - 3)/(3(2cos(1\u03c0x + 2)) + 1)) - 1| + 2) + 4 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-9", "dataset": "MATH"} | |
| {"messages": [{"content": "Find the average of all x-coordinates of local extrema of the function f(x) = -4((2(-1sin(1\u03c0(-1|x + 2| - 1) + 1) + 1) - 1)/(1(-1sin(1\u03c0(-1|x + 2| - 1) + 1) + 1) + 3))^2 - 4((2(-1sin(1\u03c0(-1|x + 2| - 1) + 1) + 1) - 1)/(1(-1sin(1\u03c0(-1|x + 2| - 1) + 1) + 1) + 3)) + 1 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"} | |
| {"messages": [{"content": "Find the x-coordinate of the leftmost local extremum of the function f(x) = -2cos(3\u03c0(2((-2(-2|x - 2| - 2) - 3)/(3(-2|x - 2| - 2)))^2 - 2((-2(-2|x - 2| - 2) - 3)/(3(-2|x - 2| - 2))) + 1)) - 3 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-7", "dataset": "MATH"} | |
| {"messages": [{"content": "How many local maxima does the function f(x) = 1((1(-1sin(1\u03c0(2|x - 1|) + 1) + 3) + 1)/(-1(-1sin(1\u03c0(2|x - 1|) + 1) + 3) + 3))^2 + 5((1(-1sin(1\u03c0(2|x - 1|) + 1) + 3) + 1)/(-1(-1sin(1\u03c0(2|x - 1|) + 1) + 3) + 3)) + 2 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"} | |
| {"messages": [{"content": "Find the x-coordinate of the leftmost local maximum of the function f(x) = 2cos(3\u03c0(1|(3((1x - 2)/(3x + 3))^2 + 3((1x - 2)/(3x + 3)) + 2) - 1| - 1)) - 2 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-9", "dataset": "MATH"} | |
| {"messages": [{"content": "Find the x-coordinate of the rightmost local minimum of the function f(x) = 4(1sin(1\u03c0(1|((3x - 1)/(1x)) - 1| - 1) + 2))^2 - 5(1sin(1\u03c0(1|((3x - 1)/(1x)) - 1| - 1) + 2)) - 1 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"} | |
| {"messages": [{"content": "Find the average of all x-coordinates of local minima of the function f(x) = 1(-1cos(1\u03c0(-1|((-2x - 3)/(1x - 3)) + 3| - 1)) + 3)^2 - 1(-1cos(1\u03c0(-1|((-2x - 3)/(1x - 3)) + 3| - 1)) + 3) - 5 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"} | |
| {"messages": [{"content": "Find the x-coordinate of the local maximum with the largest y-value of the function f(x) = -1sin(3\u03c0(-2|(3((-1x - 2)/(-3x))^2 - 4((-1x - 2)/(-3x)) - 3) + 3| - 1)) - 1 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-4", "dataset": "MATH"} | |
| {"messages": [{"content": "Find the x-coordinate of the local minimum with the largest y-value of the function f(x) = (1(1|(1cos(1\u03c0(3x^2 + 3x + 5) + 2) - 2) - 3| - 1) + 2)/(3(1|(1cos(1\u03c0(3x^2 + 3x + 5) + 2) - 2) - 3| - 1)) in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-10", "dataset": "MATH"} | |
| {"messages": [{"content": "Find the average of all x-coordinates of local maxima of the function f(x) = -3|((1(1sin(3\u03c0(-4x^2 + 1x - 1) + 1) + 3) + 2)/(1(1sin(3\u03c0(-4x^2 + 1x - 1) + 1) + 3) - 3)) - 2| - 2 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"} | |
| {"messages": [{"content": "Find the x-coordinate of the local minimum with the largest y-value of the function f(x) = (-2(3(-1sin(3\u03c0(-3|x + 3| + 3) + 3) + 2)^2 - 4(-1sin(3\u03c0(-3|x + 3| + 3) + 3) + 2) - 5) - 2)/(-2(3(-1sin(3\u03c0(-3|x + 3| + 3) + 3) + 2)^2 - 4(-1sin(3\u03c0(-3|x + 3| + 3) + 3) + 2) - 5) - 1) in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-10", "dataset": "MATH"} | |
| {"messages": [{"content": "Find the x-coordinate of the leftmost local maximum of the function f(x) = -5(3sin(3\u03c0((2(1|x + 1| - 3) - 3)/(-3(1|x + 1| - 3) - 1)) + 2) + 1)^2 + 2 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-7", "dataset": "MATH"} | |
| {"messages": [{"content": "How many local extrema (both minima and maxima) does the function f(x) = 1|((-2(-1(-3sin(3\u03c0x - 2) + 3)^2 - 2(-3sin(3\u03c0x - 2) + 3) + 2) + 2)/(3(-1(-3sin(3\u03c0x - 2) + 3)^2 - 2(-3sin(3\u03c0x - 2) + 3) + 2) + 1)) - 2| - 3 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "90", "dataset": "MATH"} | |
| {"messages": [{"content": "Find the x-coordinate of the leftmost local minimum of the function f(x) = (3(2|(1(2cos(1\u03c0x + 1) + 3)^2 - 3(2cos(1\u03c0x + 1) + 3) + 1)| + 2) - 3)/(-1(2|(1(2cos(1\u03c0x + 1) + 3)^2 - 3(2cos(1\u03c0x + 1) + 3) + 1)| + 2)) in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-10", "dataset": "MATH"} | |
| {"messages": [{"content": "Find the x-coordinate of the rightmost local minimum of the function f(x) = 2|(1sin(3\u03c0((3(-5x^2 + 5x - 1) - 1)/(-2(-5x^2 + 5x - 1) - 1)) + 3) + 2) + 1| + 3 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"} | |
| {"messages": [{"content": "Find the x-coordinate of the rightmost local extremum of the function f(x) = 2sin(2\u03c0((-1(-2(2|x + 1| - 2)^2 + 4(2|x + 1| - 2) - 1) - 1)/(2(-2(2|x + 1| - 2)^2 + 4(2|x + 1| - 2) - 1) - 3))) + 3 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"} | |
| {"messages": [{"content": "Find the x-coordinate of the local minimum of the function f(x) = -1(-2cos(1\u03c0((3(-1|x| + 1) + 3)/(-1(-1|x| + 1) - 1)) + 3) + 2)^2 - 3(-2cos(1\u03c0((3(-1|x| + 1) + 3)/(-1(-1|x| + 1) - 1)) + 3) + 2) + 2 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"} | |
| {"messages": [{"content": "Find the x-coordinate of the local maximum with the smallest y-value of the function f(x) = 2sin(1\u03c0(2|(-4((-3x)/(2x + 3))^2 + 2)| - 1) - 3) in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"} | |
| {"messages": [{"content": "Find the x-coordinate of the rightmost local maximum of the function f(x) = 2|(-2cos(2\u03c0((3(-3x^2 + 1x - 1))/(-3(-3x^2 + 1x - 1) - 2)) - 3) - 3) - 2| + 2 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"} | |
| {"messages": [{"content": "Find the x-coordinate of the rightmost local extremum of the function f(x) = 1|(1sin(1\u03c0((-1(-5x^2 - 3x + 3) - 1)/(3(-5x^2 - 3x + 3) + 2)) - 1) - 3) + 3| - 1 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"} | |
| {"messages": [{"content": "Find the x-coordinate of the local minimum with the largest y-value of the function f(x) = (-2(2cos(1\u03c0(3(-2|x - 1|)^2 + 5(-2|x - 1|) + 1) - 1) - 3) - 1)/(3(2cos(1\u03c0(3(-2|x - 1|)^2 + 5(-2|x - 1|) + 1) - 1) - 3) - 2) in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"} | |
| {"messages": [{"content": "Find the x-coordinate of the leftmost local maximum of the function f(x) = 1cos(1\u03c0(-4(3|((1x)/(-2x - 3)) - 3| - 3)^2 - 5(3|((1x)/(-2x - 3)) - 3| - 3) + 2) + 2) + 1 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-10", "dataset": "MATH"} | |
| {"messages": [{"content": "Find the x-coordinate of the rightmost local minimum of the function f(x) = 1cos(1\u03c0(5((2(1|x + 3| + 1))/(-1(1|x + 3| + 1) + 3))^2 - 3((2(1|x + 3| + 1))/(-1(1|x + 3| + 1) + 3)) + 1) + 3) - 1 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "9", "dataset": "MATH"} | |
| {"messages": [{"content": "How many local minima does the function f(x) = 1|(-4(3sin(1\u03c0((1x - 3)/(-3x - 1))) - 1)^2 - 1(3sin(1\u03c0((1x - 3)/(-3x - 1))) - 1) + 2)| have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"} | |
| {"messages": [{"content": "Find the x-coordinate of the local maximum with the smallest y-value of the function f(x) = 1|(-1(-1cos(1\u03c0((-2x)/(2x - 1)) + 3) - 2)^2 - 3(-1cos(1\u03c0((-2x)/(2x - 1)) + 3) - 2) + 2) + 1| + 2 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"} | |
| {"messages": [{"content": "Find the x-coordinate of the leftmost local minimum of the function f(x) = -4(-3|(2sin(2\u03c0((3x + 2)/(3x)) + 2) + 1)| + 2)^2 + 2(-3|(2sin(2\u03c0((3x + 2)/(3x)) + 2) + 1)| + 2) + 2 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-10", "dataset": "MATH"} | |
| {"messages": [{"content": "Find the x-coordinate of the rightmost local minimum of the function f(x) = 1|(-1((-2(3cos(2\u03c0x - 2) + 3) - 3)/(2(3cos(2\u03c0x - 2) + 3) + 1))^2 + 4((-2(3cos(2\u03c0x - 2) + 3) - 3)/(2(3cos(2\u03c0x - 2) + 3) + 1)) + 4) - 2| + 1 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "9", "dataset": "MATH"} | |
| {"messages": [{"content": "Find the x-coordinate of the rightmost local maximum of the function f(x) = -5(2cos(1\u03c0(-3|((-1x - 1)/(-1x + 2)) + 2|) - 3))^2 + 1(2cos(1\u03c0(-3|((-1x - 1)/(-1x + 2)) + 2|) - 3)) - 1 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8", "dataset": "MATH"} | |
| {"messages": [{"content": "Find the x-coordinate of the leftmost local minimum of the function f(x) = -1|(1sin(3\u03c0((-2(4x^2 - 3x + 1) - 3)/(3(4x^2 - 3x + 1) + 2)) - 1) - 1) + 1| - 1 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-1", "dataset": "MATH"} | |
| {"messages": [{"content": "Find the x-coordinate of the local minimum with the smallest y-value of the function f(x) = -1(-2|((1(-3sin(1\u03c0x) - 1))/(3(-3sin(1\u03c0x) - 1) - 2)) - 2|)^2 - 4(-2|((1(-3sin(1\u03c0x) - 1))/(3(-3sin(1\u03c0x) - 1) - 2)) - 2|) in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-8", "dataset": "MATH"} | |
| {"messages": [{"content": "Find the x-coordinate of the leftmost local extremum of the function f(x) = (1(-2(-1|(-2cos(3\u03c0x - 2) - 1) - 3| - 2)^2 - 3(-1|(-2cos(3\u03c0x - 2) - 1) - 3| - 2) + 5) + 3)/(3(-2(-1|(-2cos(3\u03c0x - 2) - 1) - 3| - 2)^2 - 3(-1|(-2cos(3\u03c0x - 2) - 1) - 3| - 2) + 5) + 2) in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-10", "dataset": "MATH"} | |
| {"messages": [{"content": "How many local extrema (both minima and maxima) does the function f(x) = -2(2|(-2sin(2\u03c0((3x + 1)/(2x - 1)) - 2) - 2) + 2| - 1)^2 + 1(2|(-2sin(2\u03c0((3x + 1)/(2x - 1)) - 2) - 2) + 2| - 1) have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "58", "dataset": "MATH"} | |
| {"messages": [{"content": "Find the average of all x-coordinates of local minima of the function f(x) = 5(1sin(3\u03c0(1|((-1x + 1)/(-1x - 1)) + 1| + 2) - 3) + 2)^2 - 3(1sin(3\u03c0(1|((-1x + 1)/(-1x - 1)) + 1| + 2) - 3) + 2) - 4 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-1", "dataset": "MATH"} | |
| {"messages": [{"content": "Find the x-coordinate of the local maximum with the largest y-value of the function f(x) = -1|((-3(5(1cos(3\u03c0x - 3) + 3)^2 + 3(1cos(3\u03c0x - 3) + 3) - 1) + 2)/(2(5(1cos(3\u03c0x - 3) + 3)^2 + 3(1cos(3\u03c0x - 3) + 3) - 1) + 1))| - 3 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-9", "dataset": "MATH"} | |
| {"messages": [{"content": "Find the x-coordinate of the local maximum with the largest y-value of the function f(x) = -1cos(3\u03c0(2|((-1(1x^2 + 4x - 3) + 1)/(-1(1x^2 + 4x - 3) + 2)) - 2| + 2) - 3) + 1 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-5", "dataset": "MATH"} | |
| {"messages": [{"content": "Find the x-coordinate of the rightmost local minimum of the function f(x) = 1sin(3\u03c0(1|(5((-2x + 2)/(3x - 2))^2 - 3((-2x + 2)/(3x - 2)) - 3) + 3| + 3) - 1) - 1 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"} | |
| {"messages": [{"content": "How many local maxima does the function f(x) = (-1(-5(2|(-3cos(2\u03c0x + 1) - 1) + 2| + 1)^2 - 4(2|(-3cos(2\u03c0x + 1) - 1) + 2| + 1) + 1) - 1)/(-2(-5(2|(-3cos(2\u03c0x + 1) - 1) + 2| + 1)^2 - 4(2|(-3cos(2\u03c0x + 1) - 1) + 2| + 1) + 1) - 3) have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"} | |
| {"messages": [{"content": "Find the x-coordinate of the local minimum of the function f(x) = (2(-3|(-2cos(1\u03c0(-5x^2 - 2x + 4) + 1)) - 1| - 3) + 2)/(1(-3|(-2cos(1\u03c0(-5x^2 - 2x + 4) + 1)) - 1| - 3)) in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"} | |
| {"messages": [{"content": "Find the x-coordinate of the rightmost local minimum of the function f(x) = -4((3(2sin(2\u03c0(-3|x|) + 3) - 1) + 2)/(2(2sin(2\u03c0(-3|x|) + 3) - 1) + 2))^2 + 2((3(2sin(2\u03c0(-3|x|) + 3) - 1) + 2)/(2(2sin(2\u03c0(-3|x|) + 3) - 1) + 2)) + 3 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"} | |
| {"messages": [{"content": "Find the x-coordinate of the local maximum with the smallest y-value of the function f(x) = (-3(4(3cos(2\u03c0(-1|x - 3| - 1) - 3) - 1)^2 + 1(3cos(2\u03c0(-1|x - 3| - 1) - 3) - 1) + 2) - 2)/(1(4(3cos(2\u03c0(-1|x - 3| - 1) - 3) - 1)^2 + 1(3cos(2\u03c0(-1|x - 3| - 1) - 3) - 1) + 2) + 1) in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-10", "dataset": "MATH"} | |
| {"messages": [{"content": "Find the x-coordinate of the leftmost local minimum of the function f(x) = 2((3(1sin(1\u03c0(2|x - 2| + 2) + 1) + 1) + 1)/(1(1sin(1\u03c0(2|x - 2| + 2) + 1) + 1) - 2))^2 + 3((3(1sin(1\u03c0(2|x - 2| + 2) + 1) + 1) + 1)/(1(1sin(1\u03c0(2|x - 2| + 2) + 1) + 1) - 2)) + 2 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-10", "dataset": "MATH"} | |
| {"messages": [{"content": "Find the x-coordinate of the local maximum with the largest y-value of the function f(x) = 1|(-3cos(2\u03c0((2(3x^2 - 2x - 2) + 1)/(-2(3x^2 - 2x - 2) + 1)) + 3) + 2)| - 2 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-1", "dataset": "MATH"} | |
| {"messages": [{"content": "Find the x-coordinate of the rightmost local minimum of the function f(x) = 2sin(2\u03c0(4((3(2|x - 1| - 1) + 3)/(3(2|x - 1| - 1) - 2))^2 + 2((3(2|x - 1| - 1) + 3)/(3(2|x - 1| - 1) - 2)) + 2) + 2) in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8", "dataset": "MATH"} | |
| {"messages": [{"content": "Find the x-coordinate of the leftmost local extremum of the function f(x) = -3sin(1\u03c0(-1|(1((3x + 2)/(-2x - 3))^2 - 2((3x + 2)/(-2x - 3)) - 3) - 1| + 3) - 1) - 1 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-8", "dataset": "MATH"} | |
| {"messages": [{"content": "Find the average of all x-coordinates of local minima of the function f(x) = -2sin(2\u03c0(3(-1|((-1x + 3)/(-3x - 1)) + 3| - 2)^2 - 3(-1|((-1x + 3)/(-3x - 1)) + 3| - 2) + 3) + 1) + 3 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"} | |
| {"messages": [{"content": "How many local extrema (both minima and maxima) does the function f(x) = -1((-1(-2cos(3\u03c0(-1|x + 1| + 1) + 1) + 2) + 2)/(-1(-2cos(3\u03c0(-1|x + 1| + 1) + 1) + 2)))^2 + 4((-1(-2cos(3\u03c0(-1|x + 1| + 1) + 1) + 2) + 2)/(-1(-2cos(3\u03c0(-1|x + 1| + 1) + 1) + 2))) - 5 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "58", "dataset": "MATH"} | |
| {"messages": [{"content": "Find the x-coordinate of the local minimum with the smallest y-value of the function f(x) = 2sin(1\u03c0((2(-1|(5x^2 - 5x - 2) + 1| - 3) + 3)/(2(-1|(5x^2 - 5x - 2) + 1| - 3) - 1)) + 1) - 1 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"} | |
| {"messages": [{"content": "How many local extrema (both minima and maxima) does the function f(x) = (2(2|(-5(3sin(1\u03c0x - 1) - 1)^2 + 5(3sin(1\u03c0x - 1) - 1) - 3) + 3|) - 1)/(-2(2|(-5(3sin(1\u03c0x - 1) - 1)^2 + 5(3sin(1\u03c0x - 1) - 1) - 3) + 3|) - 3) have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "80", "dataset": "MATH"} | |
| {"messages": [{"content": "Find the x-coordinate of the local minimum with the largest y-value of the function f(x) = 5(2cos(2\u03c0((-3(-1|x - 1|) - 1)/(-1(-1|x - 1|)))) - 3)^2 - 2(2cos(2\u03c0((-3(-1|x - 1|) - 1)/(-1(-1|x - 1|)))) - 3) + 2 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"} | |
| {"messages": [{"content": "Find the x-coordinate of the local minimum with the smallest y-value of the function f(x) = 1|(2sin(2\u03c0((3(-5x^2 - 4x + 2) + 2)/(2(-5x^2 - 4x + 2) + 3)) - 1) + 1) + 1| - 2 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-2", "dataset": "MATH"} | |
| {"messages": [{"content": "Find the x-coordinate of the local maximum with the smallest y-value of the function f(x) = -2|(-2sin(2\u03c0(1((2x - 1)/(-2x))^2 - 4((2x - 1)/(-2x)) + 1)) - 2) - 3| + 2 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"} | |
| {"messages": [{"content": "Find the x-coordinate of the local extremum with the smallest y-value of the function f(x) = (2(3|(-2(3cos(3\u03c0x - 1) - 1)^2 - 5(3cos(3\u03c0x - 1) - 1) + 5)| + 1) - 3)/(1(3|(-2(3cos(3\u03c0x - 1) - 1)^2 - 5(3cos(3\u03c0x - 1) - 1) + 5)| + 1) + 1) in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-10", "dataset": "MATH"} | |
| {"messages": [{"content": "Find the x-coordinate of the leftmost local maximum of the function f(x) = (2(3|(3(-1sin(3\u03c0x) - 3)^2 - 5(-1sin(3\u03c0x) - 3) + 4) + 1| + 3) - 2)/(-1(3|(3(-1sin(3\u03c0x) - 3)^2 - 5(-1sin(3\u03c0x) - 3) + 4) + 1| + 3) + 2) in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-10", "dataset": "MATH"} | |
| {"messages": [{"content": "Find the x-coordinate of the local minimum with the smallest y-value of the function f(x) = 2sin(2\u03c0((-1(-2|(-1x^2 - 5x - 4) + 3| + 3) - 2)/(3(-2|(-1x^2 - 5x - 4) + 3| + 3) - 2)) - 1) + 2 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-5", "dataset": "MATH"} | |
| {"messages": [{"content": "Find the x-coordinate of the rightmost local minimum of the function f(x) = -1((1(-3sin(3\u03c0(3|x + 2|) + 2) + 2) - 2)/(-2(-3sin(3\u03c0(3|x + 2|) + 2) + 2) + 3))^2 - 2((1(-3sin(3\u03c0(3|x + 2|) + 2) + 2) - 2)/(-2(-3sin(3\u03c0(3|x + 2|) + 2) + 2) + 3)) - 5 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"} | |
| {"messages": [{"content": "How many local minima does the function f(x) = 4((2(3|(2cos(1\u03c0x - 2) - 1)| + 2) - 1)/(-2(3|(2cos(1\u03c0x - 2) - 1)| + 2)))^2 - 5((2(3|(2cos(1\u03c0x - 2) - 1)| + 2) - 1)/(-2(3|(2cos(1\u03c0x - 2) - 1)| + 2))) + 1 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"} | |
| {"messages": [{"content": "Find the average of all x-coordinates of local extrema of the function f(x) = 3sin(1\u03c0((-2(1|(-4x^2 - 2x - 1) - 1| - 2) - 2)/(2(1|(-4x^2 - 2x - 1) - 1| - 2) - 3)) + 1) + 1 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"} | |
| {"messages": [{"content": "Find the x-coordinate of the local minimum with the smallest y-value of the function f(x) = -5((-3(-3cos(3\u03c0(-3|x - 3| + 2) - 1) - 1) - 3)/(-1(-3cos(3\u03c0(-3|x - 3| + 2) - 1) - 1) + 2))^2 + 4((-3(-3cos(3\u03c0(-3|x - 3| + 2) - 1) - 1) - 3)/(-1(-3cos(3\u03c0(-3|x - 3| + 2) - 1) - 1) + 2)) - 5 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-10", "dataset": "MATH"} | |
| {"messages": [{"content": "Find the x-coordinate of the rightmost local minimum of the function f(x) = (1(2sin(2\u03c0(2(2|x - 2| + 2)^2 + 5(2|x - 2| + 2) - 4) - 1) + 2))/(-2(2sin(2\u03c0(2(2|x - 2| + 2)^2 + 5(2|x - 2| + 2) - 4) - 1) + 2) + 3) in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "9", "dataset": "MATH"} | |
| {"messages": [{"content": "Find the x-coordinate of the leftmost local extremum of the function f(x) = -1|(5(3cos(2\u03c0((2x + 3)/(-1x - 3)) - 1) - 1)^2 + 3(3cos(2\u03c0((2x + 3)/(-1x - 3)) - 1) - 1) + 2) - 3| + 2 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-8", "dataset": "MATH"} | |
| {"messages": [{"content": "How many local maxima does the function f(x) = 3|(-4((-2(3cos(3\u03c0x + 2) + 3) - 2)/(-3(3cos(3\u03c0x + 2) + 3) + 1))^2 - 1((-2(3cos(3\u03c0x + 2) + 3) - 2)/(-3(3cos(3\u03c0x + 2) + 3) + 1)) + 5) - 3| have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"} | |
| {"messages": [{"content": "Find the average of all x-coordinates of local extrema of the function f(x) = (-1(-2sin(2\u03c0(-3|(-5x^2 + 3x + 1) + 1| + 1)) + 1) - 2)/(2(-2sin(2\u03c0(-3|(-5x^2 + 3x + 1) + 1| + 1)) + 1) - 1) in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"} | |
| {"messages": [{"content": "Find the x-coordinate of the leftmost local maximum of the function f(x) = 2(2sin(1\u03c0((2(-3|x + 2| + 3) + 3)/(-1(-3|x + 2| + 3) + 2)) - 3) + 2)^2 - 3(2sin(1\u03c0((2(-3|x + 2| + 3) + 3)/(-1(-3|x + 2| + 3) + 2)) - 3) + 2) + 5 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-7", "dataset": "MATH"} | |
| {"messages": [{"content": "Find the x-coordinate of the rightmost local minimum of the function f(x) = 3cos(1\u03c0(-1|(-5((-3x + 3)/(-3x - 3))^2 + 2((-3x + 3)/(-3x - 3)) + 5) - 1| + 2) + 3) - 3 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"} | |
| {"messages": [{"content": "How many local extrema (both minima and maxima) does the function f(x) = (1(1cos(3\u03c0(-3(-3|x + 2| + 3)^2 + 1(-3|x + 2| + 3) - 4)) + 3))/(2(1cos(3\u03c0(-3(-3|x + 2| + 3)^2 + 1(-3|x + 2| + 3) - 4)) + 3) - 1) have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "505", "dataset": "MATH"} | |
| {"messages": [{"content": "Find the x-coordinate of the local maximum of the function f(x) = -2|((2(3cos(1\u03c0(-4x^2 - 2x + 1) - 2) + 3) + 2)/(-2(3cos(1\u03c0(-4x^2 - 2x + 1) - 2) + 3))) + 2| - 2 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"} | |
| {"messages": [{"content": "Find the x-coordinate of the local maximum with the smallest y-value of the function f(x) = 1(-2|(3sin(3\u03c0((-2x + 3)/(-3x - 2)) - 3) - 2) - 1| + 1)^2 - 3 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-4", "dataset": "MATH"} | |
| {"messages": [{"content": "Find the x-coordinate of the rightmost local maximum of the function f(x) = -3sin(3\u03c0((3(-3|(-3x^2 + 4x + 1) - 2| + 2) + 3)/(2(-3|(-3x^2 + 4x + 1) - 2| + 2) - 1)) - 1) - 3 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"} | |
| {"messages": [{"content": "Find the average of all x-coordinates of local maxima of the function f(x) = -2((3(1cos(1\u03c0(1|x + 2| + 2)) + 2) - 3)/(3(1cos(1\u03c0(1|x + 2| + 2)) + 2) + 1))^2 + 5((3(1cos(1\u03c0(1|x + 2| + 2)) + 2) - 3)/(3(1cos(1\u03c0(1|x + 2| + 2)) + 2) + 1)) + 3 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-1", "dataset": "MATH"} | |
| {"messages": [{"content": "Find the x-coordinate of the rightmost local extremum of the function f(x) = (2(2|(-4(-2sin(2\u03c0x + 1) - 2)^2 + 1(-2sin(2\u03c0x + 1) - 2) - 1) - 2| + 3) + 1)/(-2(2|(-4(-2sin(2\u03c0x + 1) - 2)^2 + 1(-2sin(2\u03c0x + 1) - 2) - 1) - 2| + 3) + 3) in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"} | |
| {"messages": [{"content": "Find the x-coordinate of the local minimum with the largest y-value of the function f(x) = (-2(2|(-1(-3cos(1\u03c0x + 3))^2 - 1(-3cos(1\u03c0x + 3)) + 2) + 2| + 2) + 3)/(2(2|(-1(-3cos(1\u03c0x + 3))^2 - 1(-3cos(1\u03c0x + 3)) + 2) + 2| + 2) - 1) in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-9", "dataset": "MATH"} | |
| {"messages": [{"content": "Find the x-coordinate of the local minimum with the smallest y-value of the function f(x) = -5(-2|(-2sin(1\u03c0((-1x + 1)/(1x - 2)) + 3) - 2) + 3| - 1)^2 - 2(-2|(-2sin(1\u03c0((-1x + 1)/(1x - 2)) + 3) - 2) + 3| - 1) + 4 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"} | |
| {"messages": [{"content": "Find the x-coordinate of the local maximum with the smallest y-value of the function f(x) = -1sin(1\u03c0(-1((-3(3|x - 3| - 3) - 1)/(2(3|x - 3| - 3) + 2))^2 - 2((-3(3|x - 3| - 3) - 1)/(2(3|x - 3| - 3) + 2)) + 2) + 3) - 2 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"} | |
| {"messages": [{"content": "Find the average of all x-coordinates of local extrema of the function f(x) = -3|(-3cos(3\u03c0((-1(-1x^2 + 1x - 4) - 1)/(1(-1x^2 + 1x - 4) - 3)) + 1) + 1) - 2| - 1 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"} | |
| {"messages": [{"content": "Find the x-coordinate of the rightmost local extremum of the function f(x) = 1((-1(-2|(-2sin(1\u03c0x + 3))| + 3) + 2)/(-2(-2|(-2sin(1\u03c0x + 3))| + 3) - 1))^2 - 3((-1(-2|(-2sin(1\u03c0x + 3))| + 3) + 2)/(-2(-2|(-2sin(1\u03c0x + 3))| + 3) - 1)) - 1 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"} | |
| {"messages": [{"content": "Find the average of all x-coordinates of local extrema of the function f(x) = -2|(-1sin(2\u03c0(4((-2x - 2)/(-1x + 2))^2 - 1((-2x - 2)/(-1x + 2)) - 2) + 3) + 1) + 3| + 1 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"} | |
| {"messages": [{"content": "Find the x-coordinate of the local minimum with the smallest y-value of the function f(x) = -3|(-2cos(3\u03c0((2(2x^2 + 2x + 4) + 2)/(1(2x^2 + 2x + 4) - 2))) - 1) + 1| + 3 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-3", "dataset": "MATH"} | |
| {"messages": [{"content": "Find the x-coordinate of the local maximum with the smallest y-value of the function f(x) = (2(1cos(2\u03c0(2(-3|x - 3|)^2 + 3(-3|x - 3|) - 3) + 3)) + 3)/(2(1cos(2\u03c0(2(-3|x - 3|)^2 + 3(-3|x - 3|) - 3) + 3)) - 1) in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"} | |
| {"messages": [{"content": "Find the average of all x-coordinates of local minima of the function f(x) = -4(-2|(2cos(2\u03c0((2x + 2)/(-2x)))) - 1| - 1)^2 - 1(-2|(2cos(2\u03c0((2x + 2)/(-2x)))) - 1| - 1) - 4 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"} | |
| {"messages": [{"content": "Find the x-coordinate of the leftmost local maximum of the function f(x) = (-3(2|(-1cos(1\u03c0(-1x^2 - 5x - 1) - 2) + 2) - 2| + 2) - 3)/(2(2|(-1cos(1\u03c0(-1x^2 - 5x - 1) - 2) + 2) - 2| + 2) - 1) in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-10", "dataset": "MATH"} | |
| {"messages": [{"content": "Find the x-coordinate of the rightmost local extremum of the function f(x) = 3|(-3sin(2\u03c0(5((-1x + 3)/(-2x))^2 + 2((-1x + 3)/(-2x)) - 5) + 3) + 3) + 3| + 3 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"} | |
| {"messages": [{"content": "Find the x-coordinate of the rightmost local maximum of the function f(x) = (2(2|(-3cos(2\u03c0(-4x^2 + 3x + 3) + 1) - 1) - 1| - 2) + 3)/(-1(2|(-3cos(2\u03c0(-4x^2 + 3x + 3) + 1) - 1) - 1| - 2) + 2) in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"} | |
| {"messages": [{"content": "Find the x-coordinate of the rightmost local maximum of the function f(x) = (-3(-1(-1cos(3\u03c0(1|x + 2| - 1) - 3) + 2)^2 - 5(-1cos(3\u03c0(1|x + 2| - 1) - 3) + 2) + 4) + 2)/(-3(-1(-1cos(3\u03c0(1|x + 2| - 1) - 3) + 2)^2 - 5(-1cos(3\u03c0(1|x + 2| - 1) - 3) + 2) + 4) - 3) in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"} | |
| {"messages": [{"content": "Find the x-coordinate of the local maximum with the largest y-value of the function f(x) = 1sin(2\u03c0(-4(-2|((-2x - 2)/(-1x)) + 2| - 2)^2 + 3(-2|((-2x - 2)/(-1x)) + 2| - 2) - 5) - 1) - 2 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-10", "dataset": "MATH"} | |
| {"messages": [{"content": "Find the x-coordinate of the local minimum with the smallest y-value of the function f(x) = -2|(2sin(1\u03c0((3(1x^2 + 5x - 4) - 3)/(1(1x^2 + 5x - 4) - 3)) + 1) + 2)| in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-7", "dataset": "MATH"} | |
| {"messages": [{"content": "Find the x-coordinate of the leftmost local minimum of the function f(x) = 1sin(2\u03c0(-3|(-3((-2x + 2)/(2x + 2))^2 - 5((-2x + 2)/(2x + 2)) - 4) - 1| - 1) - 2) - 1 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-7", "dataset": "MATH"} | |
| {"messages": [{"content": "Find the x-coordinate of the leftmost local extremum of the function f(x) = -2|(4(1cos(3\u03c0((2x - 3)/(-3x - 2)) + 2) + 1)^2 - 1(1cos(3\u03c0((2x - 3)/(-3x - 2)) + 2) + 1) + 5) + 1| in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-7", "dataset": "MATH"} | |
| {"messages": [{"content": "Find the average of all x-coordinates of local minima of the function f(x) = 2sin(1\u03c0(-1|(4((2x - 1)/(3x - 2))^2 - 2) + 3| + 1)) + 2 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"} | |
| {"messages": [{"content": "Find the x-coordinate of the leftmost local minimum of the function f(x) = (-2(5(-1sin(1\u03c0(2|x - 2| - 1) + 2) - 1)^2 - 4(-1sin(1\u03c0(2|x - 2| - 1) + 2) - 1) - 4) + 2)/(1(5(-1sin(1\u03c0(2|x - 2| - 1) + 2) - 1)^2 - 4(-1sin(1\u03c0(2|x - 2| - 1) + 2) - 1) - 4) - 3) in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-10", "dataset": "MATH"} | |
| {"messages": [{"content": "Find the x-coordinate of the rightmost local extremum of the function f(x) = 3sin(2\u03c0(3|((-2(1x^2 + 2x + 5))/(-1(1x^2 + 2x + 5) - 1)) - 1| + 2) - 2) + 1 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"} | |
| {"messages": [{"content": "Find the x-coordinate of the rightmost local minimum of the function f(x) = 2((2(-1|(-2sin(3\u03c0x - 1))| - 2) + 2)/(-3(-1|(-2sin(3\u03c0x - 1))| - 2) + 1))^2 - 5((2(-1|(-2sin(3\u03c0x - 1))| - 2) + 2)/(-3(-1|(-2sin(3\u03c0x - 1))| - 2) + 1)) - 1 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "6", "dataset": "MATH"} | |
| {"messages": [{"content": "Find the x-coordinate of the local minimum with the largest y-value of the function f(x) = (2(-2|(2(-2sin(2\u03c0x + 2) + 3)^2) + 3| + 1) - 1)/(2(-2|(2(-2sin(2\u03c0x + 2) + 3)^2) + 3| + 1) + 3) in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-10", "dataset": "MATH"} | |
| {"messages": [{"content": "Find the x-coordinate of the rightmost local maximum of the function f(x) = -3sin(1\u03c0((3(3|(5x^2 + 1x - 1) + 1| + 3) + 1)/(1(3|(5x^2 + 1x - 1) + 1| + 3) + 2)) + 3) + 3 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"} | |
| {"messages": [{"content": "Find the x-coordinate of the local minimum with the largest y-value of the function f(x) = 2|(1((2(-2sin(3\u03c0x - 2)) - 1)/(-2(-2sin(3\u03c0x - 2)) + 3))^2 - 1((2(-2sin(3\u03c0x - 2)) - 1)/(-2(-2sin(3\u03c0x - 2)) + 3))) + 2| + 2 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-10", "dataset": "MATH"} | |
| {"messages": [{"content": "Find the x-coordinate of the local extremum with the smallest y-value of the function f(x) = -1cos(2\u03c0(-1(2|((-1x + 3)/(-2x + 3)) + 1|)^2 + 2(2|((-1x + 3)/(-2x + 3)) + 1|) + 2) + 1) - 2 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-4", "dataset": "MATH"} | |
| {"messages": [{"content": "Find the x-coordinate of the leftmost local maximum of the function f(x) = -4(-3sin(2\u03c0(-1|((-2x + 3)/(-3x + 2)) + 2| - 2) + 1) + 2)^2 - 3 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-4", "dataset": "MATH"} | |
| {"messages": [{"content": "Find the x-coordinate of the local minimum with the largest y-value of the function f(x) = 4(-3|(-2cos(2\u03c0((-2x + 2)/(-1x + 3)) - 3) - 2) + 3| + 1)^2 - 2(-3|(-2cos(2\u03c0((-2x + 2)/(-1x + 3)) - 3) - 2) + 3| + 1) + 4 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-9", "dataset": "MATH"} | |
| {"messages": [{"content": "Find the x-coordinate of the rightmost local minimum of the function f(x) = -2sin(3\u03c0(1((2(-2|x + 2| - 3))/(1(-2|x + 2| - 3) - 3))^2 - 1((2(-2|x + 2| - 3))/(1(-2|x + 2| - 3) - 3)) + 4) + 2) + 2 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "7", "dataset": "MATH"} | |
| {"messages": [{"content": "Find the x-coordinate of the local minimum with the largest y-value of the function f(x) = (-1(4(-2sin(2\u03c0(2|x - 3| + 1) + 1))^2 - 2(-2sin(2\u03c0(2|x - 3| + 1) + 1))) - 2)/(-1(4(-2sin(2\u03c0(2|x - 3| + 1) + 1))^2 - 2(-2sin(2\u03c0(2|x - 3| + 1) + 1)))) in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-10", "dataset": "MATH"} | |
| {"messages": [{"content": "Find the average of all x-coordinates of local maxima of the function f(x) = -1|(1sin(1\u03c0(-1((3x)/(2x + 2))^2 - 5) + 1) - 2) + 3| + 1 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-1", "dataset": "MATH"} | |
| {"messages": [{"content": "Find the x-coordinate of the rightmost local minimum of the function f(x) = (2(-1(1|(-3sin(2\u03c0x - 1) + 1) + 1| + 3)^2 + 4(1|(-3sin(2\u03c0x - 1) + 1) + 1| + 3) + 2) - 3)/(1(-1(1|(-3sin(2\u03c0x - 1) + 1) + 1| + 3)^2 + 4(1|(-3sin(2\u03c0x - 1) + 1) + 1| + 3) + 2) + 3) in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"} | |
| {"messages": [{"content": "Find the average of all x-coordinates of local maxima of the function f(x) = -1|(-5((3(-3cos(2\u03c0x + 2) - 3) + 3)/(-2(-3cos(2\u03c0x + 2) - 3) + 1))^2 - 4((3(-3cos(2\u03c0x + 2) - 3) + 3)/(-2(-3cos(2\u03c0x + 2) - 3) + 1)) - 5)| - 2 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"} | |
| {"messages": [{"content": "Find the average of all x-coordinates of local extrema of the function f(x) = -3|((-3(3cos(1\u03c0(-1x^2 + 3x + 3) + 1) + 1) + 3)/(-2(3cos(1\u03c0(-1x^2 + 3x + 3) + 1) + 1) + 3)) + 3| - 3 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-1", "dataset": "MATH"} | |
| {"messages": [{"content": "Find the x-coordinate of the rightmost local minimum of the function f(x) = -2cos(3\u03c0((2(-5(-1|x - 2| + 2)^2 - 5(-1|x - 2| + 2) + 3) + 3)/(-2(-5(-1|x - 2| + 2)^2 - 5(-1|x - 2| + 2) + 3) + 1)) - 3) + 1 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "6", "dataset": "MATH"} | |
| {"messages": [{"content": "Find the x-coordinate of the local maximum with the largest y-value of the function f(x) = 2|(-3sin(2\u03c0(-2((-3x - 3)/(2x + 2))^2 + 5((-3x - 3)/(2x + 2)) - 2) - 2) - 2) - 2| - 2 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-2", "dataset": "MATH"} | |
| {"messages": [{"content": "Find the x-coordinate of the rightmost local extremum of the function f(x) = 2|(1((1(3sin(1\u03c0x - 3) + 1) - 2)/(1(3sin(1\u03c0x - 3) + 1) + 3))^2 + 1((1(3sin(1\u03c0x - 3) + 1) - 2)/(1(3sin(1\u03c0x - 3) + 1) + 3)) - 1) + 1| in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "9", "dataset": "MATH"} | |
| {"messages": [{"content": "Find the x-coordinate of the local extremum with the smallest y-value of the function f(x) = (2(3cos(3\u03c0(-2(-2|x| + 1)^2 + 3(-2|x| + 1) - 2) - 3) + 1) - 2)/(2(3cos(3\u03c0(-2(-2|x| + 1)^2 + 3(-2|x| + 1) - 2) - 3) + 1) + 1) in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"} | |
| {"messages": [{"content": "Find the x-coordinate of the leftmost local extremum of the function f(x) = (-1(-4(2sin(1\u03c0(-3|x| + 2) - 1) + 3)^2 - 3(2sin(1\u03c0(-3|x| + 2) - 1) + 3) + 1) - 2)/(2(-4(2sin(1\u03c0(-3|x| + 2) - 1) + 3)^2 - 3(2sin(1\u03c0(-3|x| + 2) - 1) + 3) + 1) - 3) in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-10", "dataset": "MATH"} | |
| {"messages": [{"content": "Find the average of all x-coordinates of local extrema of the function f(x) = -5(-2|((2(-3sin(3\u03c0x + 1)) + 1)/(-1(-3sin(3\u03c0x + 1)) - 1)) + 1| - 2)^2 - 4(-2|((2(-3sin(3\u03c0x + 1)) + 1)/(-1(-3sin(3\u03c0x + 1)) - 1)) + 1| - 2) - 1 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"} | |
| {"messages": [{"content": "Find the average of all x-coordinates of local extrema of the function f(x) = (-3(-3(2|(1cos(1\u03c0x + 1)) + 1| + 2)^2 + 1(2|(1cos(1\u03c0x + 1)) + 1| + 2) - 4))/(2(-3(2|(1cos(1\u03c0x + 1)) + 1| + 2)^2 + 1(2|(1cos(1\u03c0x + 1)) + 1| + 2) - 4) + 1) in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"} | |
| {"messages": [{"content": "Find the x-coordinate of the local maximum with the smallest y-value of the function f(x) = 1|(-1sin(2\u03c0(-1((-3x - 3)/(1x - 2))^2 + 4((-3x - 3)/(1x - 2)) + 2) - 1) - 2) + 3| in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-8", "dataset": "MATH"} | |
| {"messages": [{"content": "Find the x-coordinate of the leftmost local minimum of the function f(x) = 1|((-2(-3(2cos(3\u03c0x + 3) - 1)^2 + 1(2cos(3\u03c0x + 3) - 1) - 1) + 1)/(-2(-3(2cos(3\u03c0x + 3) - 1)^2 + 1(2cos(3\u03c0x + 3) - 1) - 1) - 2))| + 3 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-10", "dataset": "MATH"} | |
| {"messages": [{"content": "Find the x-coordinate of the local extremum with the smallest y-value of the function f(x) = 1|(-3((-1(3sin(1\u03c0x - 3) + 3))/(3(3sin(1\u03c0x - 3) + 3) + 2))^2 + 1((-1(3sin(1\u03c0x - 3) + 3))/(3(3sin(1\u03c0x - 3) + 3) + 2)) - 3) - 2| - 1 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-10", "dataset": "MATH"} | |
| {"messages": [{"content": "Find the x-coordinate of the local maximum with the largest y-value of the function f(x) = 1((-1(1|(-1sin(2\u03c0x - 2) - 2) - 2| - 1) - 2)/(-3(1|(-1sin(2\u03c0x - 2) - 2) - 2| - 1) - 2))^2 + 5((-1(1|(-1sin(2\u03c0x - 2) - 2) - 2| - 1) - 2)/(-3(1|(-1sin(2\u03c0x - 2) - 2) - 2| - 1) - 2)) + 3 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-10", "dataset": "MATH"} | |
| {"messages": [{"content": "Find the x-coordinate of the local maximum of the function f(x) = -1sin(1\u03c0(2|((1(2x^2 + 4x + 1) + 2)/(-1(2x^2 + 4x + 1) - 3)) - 3| + 3)) in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-1", "dataset": "MATH"} | |
| {"messages": [{"content": "Find the x-coordinate of the rightmost local minimum of the function f(x) = 4(3|((-2(2sin(1\u03c0x - 1) + 2) - 2)/(-2(2sin(1\u03c0x - 1) + 2) + 3)) - 2|)^2 + 4 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"} | |
| {"messages": [{"content": "Find the x-coordinate of the rightmost local maximum of the function f(x) = -5(1|(-2cos(3\u03c0((2x - 1)/(-1x + 2)) + 2) + 3) - 1| - 3)^2 - 1(1|(-2cos(3\u03c0((2x - 1)/(-1x + 2)) + 2) + 3) - 1| - 3) + 5 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "9", "dataset": "MATH"} | |
| {"messages": [{"content": "Find the x-coordinate of the local maximum with the smallest y-value of the function f(x) = -2(-2sin(1\u03c0(-2|((2x + 1)/(-1x + 3)) - 2| + 1) - 1) + 1)^2 + 3(-2sin(1\u03c0(-2|((2x + 1)/(-1x + 3)) - 2| + 1) - 1) + 1) + 2 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-7", "dataset": "MATH"} | |
| {"messages": [{"content": "Find the x-coordinate of the rightmost local minimum of the function f(x) = -1sin(1\u03c0(-2|((1(3x^2 + 3x + 4) + 3)/(-2(3x^2 + 3x + 4) + 3)) - 3| + 1) - 1) + 1 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"} | |
| {"messages": [{"content": "Find the x-coordinate of the rightmost local extremum of the function f(x) = -4(-3|(3cos(3\u03c0((1x + 3)/(-2x)) - 1) - 1) - 3| + 2)^2 - 2(-3|(3cos(3\u03c0((1x + 3)/(-2x)) - 1) - 1) - 3| + 2) - 3 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"} | |
| {"messages": [{"content": "Find the x-coordinate of the rightmost local extremum of the function f(x) = 1|((1(-5(-2cos(2\u03c0x - 3) - 1)^2 + 5(-2cos(2\u03c0x - 3) - 1) + 5) + 2)/(1(-5(-2cos(2\u03c0x - 3) - 1)^2 + 5(-2cos(2\u03c0x - 3) - 1) + 5) - 3)) - 3| - 3 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"} | |
| {"messages": [{"content": "Find the average of all x-coordinates of local minima of the function f(x) = -5(-2sin(3\u03c0((-1(2|x - 3| - 1) - 2)/(-2(2|x - 3| - 1) - 3)) + 2) + 1)^2 + 4(-2sin(3\u03c0((-1(2|x - 3| - 1) - 2)/(-2(2|x - 3| - 1) - 3)) + 2) + 1) - 5 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"} | |
| {"messages": [{"content": "How many local extrema (both minima and maxima) does the function f(x) = -3sin(1\u03c0(1((-3(-2|x + 2| + 3) - 1)/(-2(-2|x + 2| + 3) + 1))^2 + 5((-3(-2|x + 2| + 3) - 1)/(-2(-2|x + 2| + 3) + 1)) + 2) + 1) + 3 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "83", "dataset": "MATH"} | |
| {"messages": [{"content": "How many local extrema (both minima and maxima) does the function f(x) = 1|((2(-5(2cos(2\u03c0x + 1) + 3)^2 + 1(2cos(2\u03c0x + 1) + 3) - 4) + 3)/(1(-5(2cos(2\u03c0x + 1) + 3)^2 + 1(2cos(2\u03c0x + 1) + 3) - 4))) - 3| + 2 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "40", "dataset": "MATH"} | |
| {"messages": [{"content": "Find the x-coordinate of the local maximum with the largest y-value of the function f(x) = -3(-1cos(2\u03c0(-2|((-1x - 2)/(2x - 1)) - 2| + 3) + 1) + 3)^2 - 5(-1cos(2\u03c0(-2|((-1x - 2)/(2x - 1)) - 2| + 3) + 1) + 3) in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-2", "dataset": "MATH"} | |
| {"messages": [{"content": "Find the x-coordinate of the rightmost local extremum of the function f(x) = -1|(-3cos(3\u03c0((2(-3x^2 + 2x - 3) + 1)/(1(-3x^2 + 2x - 3) + 2)) + 3) + 3) + 3| - 2 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8", "dataset": "MATH"} | |
| {"messages": [{"content": "How many local extrema (both minima and maxima) does the function f(x) = (3(4(-1sin(3\u03c0(2|x - 1| - 2) - 2))^2 + 2(-1sin(3\u03c0(2|x - 1| - 2) - 2)) - 3) - 1)/(1(4(-1sin(3\u03c0(2|x - 1| - 2) - 2))^2 + 2(-1sin(3\u03c0(2|x - 1| - 2) - 2)) - 3) + 1) have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "241", "dataset": "MATH"} | |
| {"messages": [{"content": "Find the x-coordinate of the leftmost local maximum of the function f(x) = -5((1(3|(-2cos(1\u03c0x + 3) - 2) + 2| - 1) + 3)/(1(3|(-2cos(1\u03c0x + 3) - 2) + 2| - 1) + 2))^2 - 3((1(3|(-2cos(1\u03c0x + 3) - 2) + 2| - 1) + 3)/(1(3|(-2cos(1\u03c0x + 3) - 2) + 2| - 1) + 2)) + 2 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-10", "dataset": "MATH"} | |
| {"messages": [{"content": "Find the average of all x-coordinates of local maxima of the function f(x) = -1|(3cos(2\u03c0(1((2x - 2)/(-1x - 1))^2 - 5((2x - 2)/(-1x - 1)) + 4) - 1) + 1) - 1| + 1 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-2", "dataset": "MATH"} | |
| {"messages": [{"content": "Find the x-coordinate of the local maximum with the smallest y-value of the function f(x) = (1(3sin(2\u03c0(4(2|x| + 2)^2 - 1(2|x| + 2) + 1)) + 3) - 2)/(1(3sin(2\u03c0(4(2|x| + 2)^2 - 1(2|x| + 2) + 1)) + 3)) in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-10", "dataset": "MATH"} | |
| {"messages": [{"content": "Find the x-coordinate of the rightmost local maximum of the function f(x) = (3(-2|(-2cos(2\u03c0(-1x^2 + 3x + 5)))| - 1) + 2)/(-3(-2|(-2cos(2\u03c0(-1x^2 + 3x + 5)))| - 1) + 4) in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8", "dataset": "MATH"} | |
| {"messages": [{"content": "Find the x-coordinate of the local extremum with the smallest y-value of the function f(x) = (-1(1sin(3\u03c0(-1(-3|x + 1| + 3)^2 - 3(-3|x + 1| + 3) - 5) - 3) - 3) - 3)/(3(1sin(3\u03c0(-1(-3|x + 1| + 3)^2 - 3(-3|x + 1| + 3) - 5) - 3) - 3) - 2) in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-10", "dataset": "MATH"} | |
| {"messages": [{"content": "Find the x-coordinate of the local minimum with the largest y-value of the function f(x) = 3sin(1\u03c0(-2|((-2(1x^2 + 5x - 3) - 2)/(1(1x^2 + 5x - 3) - 3)) + 3| - 1) + 1) + 2 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-7", "dataset": "MATH"} | |
| {"messages": [{"content": "Find the x-coordinate of the local extremum with the largest y-value of the function f(x) = 3sin(3\u03c0(-3|((-2(-1x^2 - 4x + 1) + 3)/(3(-1x^2 - 4x + 1) - 2)) - 1| + 2) - 2) + 3 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-5", "dataset": "MATH"} | |
| {"messages": [{"content": "Find the x-coordinate of the rightmost local maximum of the function f(x) = -3(1|((2(-1sin(1\u03c0x + 1) + 2) - 2)/(1(-1sin(1\u03c0x + 1) + 2))) + 3| - 2)^2 + 1(1|((2(-1sin(1\u03c0x + 1) + 2) - 2)/(1(-1sin(1\u03c0x + 1) + 2))) + 3| - 2) - 2 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8", "dataset": "MATH"} | |
| {"messages": [{"content": "Find the x-coordinate of the local minimum with the largest y-value of the function f(x) = 4(-2cos(2\u03c0((-1(-2|x - 2|) + 1)/(-1(-2|x - 2|))) - 2) + 2)^2 - 5(-2cos(2\u03c0((-1(-2|x - 2|) + 1)/(-1(-2|x - 2|))) - 2) + 2) + 3 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-1", "dataset": "MATH"} | |
| {"messages": [{"content": "Find the x-coordinate of the local extremum with the smallest y-value of the function f(x) = (3(-3cos(3\u03c0(-3(2|x - 2| - 2)^2 - 1) - 2)) - 3)/(-3(-3cos(3\u03c0(-3(2|x - 2| - 2)^2 - 1) - 2)) - 1) in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"} | |
| {"messages": [{"content": "Find the x-coordinate of the rightmost local minimum of the function f(x) = (1(-1cos(1\u03c0(-4(-3|x - 3| + 3)^2 - 3(-3|x - 3| + 3) - 5) - 1)) + 2)/(2(-1cos(1\u03c0(-4(-3|x - 3| + 3)^2 - 3(-3|x - 3| + 3) - 5) - 1)) - 1) in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"} | |
| {"messages": [{"content": "Find the x-coordinate of the local minimum with the largest y-value of the function f(x) = 2|(1(2sin(1\u03c0((-2x + 2)/(3x + 1))) + 3)^2 + 5) - 1| + 2 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-1", "dataset": "MATH"} | |
| {"messages": [{"content": "How many local minima does the function f(x) = -1(3|((-1(-1cos(3\u03c0x + 3) + 2) - 1)/(-1(-1cos(3\u03c0x + 3) + 2) + 3))| + 1)^2 + 1(3|((-1(-1cos(3\u03c0x + 3) + 2) - 1)/(-1(-1cos(3\u03c0x + 3) + 2) + 3))| + 1) + 4 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"} | |
| {"messages": [{"content": "Find the x-coordinate of the rightmost local extremum of the function f(x) = -1|(5(1cos(1\u03c0((1x + 1)/(-3x + 1)) - 3) - 1)^2 + 3(1cos(1\u03c0((1x + 1)/(-3x + 1)) - 3) - 1) + 2) + 1| - 1 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"} | |
| {"messages": [{"content": "How many local extrema (both minima and maxima) does the function f(x) = 2|(1(2cos(2\u03c0((-2x - 2)/(-1x - 2)) - 1) + 2)^2 - 4(2cos(2\u03c0((-2x - 2)/(-1x - 2)) - 1) + 2) - 1) - 2| + 3 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "57", "dataset": "MATH"} | |
| {"messages": [{"content": "Find the x-coordinate of the leftmost local extremum of the function f(x) = 2sin(1\u03c0(1((-3(-2|x - 2| + 3) - 2)/(2(-2|x - 2| + 3) - 1))^2 - 2) + 1) - 2 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-1", "dataset": "MATH"} | |
| {"messages": [{"content": "Find the x-coordinate of the local extremum with the largest y-value of the function f(x) = -1((-2(2|(1sin(2\u03c0x + 2) - 2) + 1| - 3) - 1)/(3(2|(1sin(2\u03c0x + 2) - 2) + 1| - 3) + 3))^2 - 1((-2(2|(1sin(2\u03c0x + 2) - 2) + 1| - 3) - 1)/(3(2|(1sin(2\u03c0x + 2) - 2) + 1| - 3) + 3)) - 4 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-10", "dataset": "MATH"} | |
| {"messages": [{"content": "Find the x-coordinate of the local minimum with the largest y-value of the function f(x) = 1sin(2\u03c0((2(-2|(-2x^2 + 1x + 1) - 1| - 3) - 3)/(-1(-2|(-2x^2 + 1x + 1) - 1| - 3) + 2)) - 2) in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"} | |
| {"messages": [{"content": "How many local extrema (both minima and maxima) does the function f(x) = -2|(-1sin(2\u03c0(1((-2x)/(1x + 3))^2 + 2) + 2) - 1) - 1| - 2 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "125", "dataset": "MATH"} | |
| {"messages": [{"content": "Find the x-coordinate of the local minimum with the smallest y-value of the function f(x) = -3sin(2\u03c0(3|(4((2x)/(-2x + 3))^2 - 3((2x)/(-2x + 3)) + 3)| - 1) - 1) + 3 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-9", "dataset": "MATH"} | |
| {"messages": [{"content": "Find the x-coordinate of the rightmost local maximum of the function f(x) = 2|((1(2sin(2\u03c0(3x^2 - 3x + 2) + 3)))/(-1(2sin(2\u03c0(3x^2 - 3x + 2) + 3)) + 3)) - 3| + 1 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"} | |
| {"messages": [{"content": "Find the x-coordinate of the rightmost local minimum of the function f(x) = 1(2|((-1(2sin(2\u03c0x - 1) + 3) + 1)/(-1(2sin(2\u03c0x - 1) + 3) - 2)) - 2| + 1)^2 - 1(2|((-1(2sin(2\u03c0x - 1) + 3) + 1)/(-1(2sin(2\u03c0x - 1) + 3) - 2)) - 2| + 1) + 3 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "9", "dataset": "MATH"} | |
| {"messages": [{"content": "Find the x-coordinate of the rightmost local minimum of the function f(x) = -5(-1cos(3\u03c0(1|((-2x + 3)/(1x)) - 3| - 1) - 2) + 1)^2 + 3(-1cos(3\u03c0(1|((-2x + 3)/(1x)) - 3| - 1) - 2) + 1) + 3 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "7", "dataset": "MATH"} | |
| {"messages": [{"content": "Find the x-coordinate of the local extremum with the largest y-value of the function f(x) = -3|((3(1(3sin(2\u03c0x - 1))^2 + 4(3sin(2\u03c0x - 1)) - 2) + 1)/(-2(1(3sin(2\u03c0x - 1))^2 + 4(3sin(2\u03c0x - 1)) - 2) + 1)) - 1| + 3 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-9", "dataset": "MATH"} | |
| {"messages": [{"content": "Find the x-coordinate of the local minimum of the function f(x) = -1cos(3\u03c0((-2(-2|(-5x^2 + 4x - 3) - 1| + 3))/(-3(-2|(-5x^2 + 4x - 3) - 1| + 3) + 2)) - 3) in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"} | |
| {"messages": [{"content": "Find the x-coordinate of the local maximum with the smallest y-value of the function f(x) = (-2(-1cos(1\u03c0(-5(-2|x - 2| + 3)^2 - 3(-2|x - 2| + 3) + 2) - 1) - 2) - 3)/(3(-1cos(1\u03c0(-5(-2|x - 2| + 3)^2 - 3(-2|x - 2| + 3) + 2) - 1) - 2) - 1) in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"} | |
| {"messages": [{"content": "Find the x-coordinate of the local minimum with the largest y-value of the function f(x) = 2(-2|(-2sin(1\u03c0((-3x + 3)/(1x + 3))) - 3) + 2| - 1)^2 + 4 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-10", "dataset": "MATH"} | |
| {"messages": [{"content": "Find the x-coordinate of the rightmost local extremum of the function f(x) = 3(2cos(2\u03c0((3(-2|x - 2| + 1) + 2)/(2(-2|x - 2| + 1))) - 1) + 3)^2 + 3(2cos(2\u03c0((3(-2|x - 2| + 1) + 2)/(2(-2|x - 2| + 1))) - 1) + 3) + 4 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"} | |
| {"messages": [{"content": "Find the average of all x-coordinates of local minima of the function f(x) = (-3(-3(3cos(1\u03c0(-2|x + 1| - 1) + 1) + 3)^2 - 4(3cos(1\u03c0(-2|x + 1| - 1) + 1) + 3) + 2) + 3)/(1(-3(3cos(1\u03c0(-2|x + 1| - 1) + 1) + 3)^2 - 4(3cos(1\u03c0(-2|x + 1| - 1) + 1) + 3) + 2)) in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"} | |
| {"messages": [{"content": "Find the x-coordinate of the local maximum with the smallest y-value of the function f(x) = (2(-3cos(2\u03c0(-5(2|x - 2| + 3)^2 + 5(2|x - 2| + 3) - 3) + 3) + 3) - 2)/(3(-3cos(2\u03c0(-5(2|x - 2| + 3)^2 + 5(2|x - 2| + 3) - 3) + 3) + 3) - 2) in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-10", "dataset": "MATH"} | |
| {"messages": [{"content": "Find the average of all x-coordinates of local minima of the function f(x) = -3((2(2sin(2\u03c0(-3|x + 3| - 3) - 2) + 3) - 3)/(-1(2sin(2\u03c0(-3|x + 3| - 3) - 2) + 3)))^2 - 5((2(2sin(2\u03c0(-3|x + 3| - 3) - 2) + 3) - 3)/(-1(2sin(2\u03c0(-3|x + 3| - 3) - 2) + 3))) + 3 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"} | |
| {"messages": [{"content": "Find the x-coordinate of the local minimum with the smallest y-value of the function f(x) = 2|(4(3cos(2\u03c0((1x - 2)/(3x - 2)) + 2) + 3)^2 - 1(3cos(2\u03c0((1x - 2)/(3x - 2)) + 2) + 3) + 2) + 1| - 2 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"} | |
| {"messages": [{"content": "Find the x-coordinate of the local minimum with the largest y-value of the function f(x) = (-2(1(2cos(2\u03c0(3|x| + 3) - 1) - 3)^2 + 3(2cos(2\u03c0(3|x| + 3) - 1) - 3) - 5) + 1)/(-1(1(2cos(2\u03c0(3|x| + 3) - 1) - 3)^2 + 3(2cos(2\u03c0(3|x| + 3) - 1) - 3) - 5) - 1) in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-10", "dataset": "MATH"} | |
| {"messages": [{"content": "Find the x-coordinate of the leftmost local extremum of the function f(x) = 3(3cos(3\u03c0((2(2|x + 3| - 1) - 2)/(1(2|x + 3| - 1) - 2)) + 2) + 3)^2 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-7", "dataset": "MATH"} | |
| {"messages": [{"content": "Find the x-coordinate of the local minimum with the largest y-value of the function f(x) = 1cos(3\u03c0((3(-1|(2x^2 + 2x - 3) + 2|) - 3)/(-2(-1|(2x^2 + 2x - 3) + 2|))) + 3) in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-2", "dataset": "MATH"} | |
| {"messages": [{"content": "Find the average of all x-coordinates of local extrema of the function f(x) = 1|(-3(-3sin(3\u03c0((1x)/(1x - 3))) + 1)^2 - 4(-3sin(3\u03c0((1x)/(1x - 3))) + 1) + 5) - 2| + 1 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"} | |
| {"messages": [{"content": "Find the average of all x-coordinates of local minima of the function f(x) = 1|(-4(3sin(3\u03c0((3x + 3)/(1x - 3)) - 2) - 2)^2 - 1(3sin(3\u03c0((3x + 3)/(1x - 3)) - 2) - 2) - 4)| + 2 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"} | |
| {"messages": [{"content": "Find the x-coordinate of the leftmost local maximum of the function f(x) = -4((1(1|(1cos(3\u03c0x + 3) + 1) - 1| - 1) - 2)/(-1(1|(1cos(3\u03c0x + 3) + 1) - 1| - 1) + 3))^2 - 4((1(1|(1cos(3\u03c0x + 3) + 1) - 1| - 1) - 2)/(-1(1|(1cos(3\u03c0x + 3) + 1) - 1| - 1) + 3)) + 4 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-10", "dataset": "MATH"} | |
| {"messages": [{"content": "Find the x-coordinate of the local maximum with the smallest y-value of the function f(x) = (-2(2|(-2(1cos(2\u03c0x + 1))^2 - 1(1cos(2\u03c0x + 1)) - 2)| + 2) + 1)/(3(2|(-2(1cos(2\u03c0x + 1))^2 - 1(1cos(2\u03c0x + 1)) - 2)| + 2) + 1) in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-10", "dataset": "MATH"} | |
| {"messages": [{"content": "Find the x-coordinate of the leftmost local minimum of the function f(x) = -4(-1|((2(1sin(3\u03c0x + 3) - 2) + 2)/(3(1sin(3\u03c0x + 3) - 2))) + 3| - 3)^2 - 4(-1|((2(1sin(3\u03c0x + 3) - 2) + 2)/(3(1sin(3\u03c0x + 3) - 2))) + 3| - 3) - 5 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-10", "dataset": "MATH"} | |
| {"messages": [{"content": "Find the x-coordinate of the rightmost local maximum of the function f(x) = -3(-2sin(3\u03c0(1|((3x + 1)/(1x)) - 1| - 1) + 1) - 2)^2 - 2(-2sin(3\u03c0(1|((3x + 1)/(1x)) - 1| - 1) + 1) - 2) - 1 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8", "dataset": "MATH"} | |
| {"messages": [{"content": "Find the x-coordinate of the rightmost local maximum of the function f(x) = (-2(-1|(-4(2sin(2\u03c0x + 2))^2 + 3(2sin(2\u03c0x + 2)) - 3) + 2| - 1) + 1)/(-2(-1|(-4(2sin(2\u03c0x + 2))^2 + 3(2sin(2\u03c0x + 2)) - 3) + 2| - 1) + 3) in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"} | |
| {"messages": [{"content": "Find the x-coordinate of the leftmost local minimum of the function f(x) = (3(-2cos(2\u03c0(1|(-4x^2 + 3x - 1) - 2| - 2) - 3) + 1) + 3)/(2(-2cos(2\u03c0(1|(-4x^2 + 3x - 1) - 2| - 2) - 3) + 1) - 1) in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-10", "dataset": "MATH"} | |
| {"messages": [{"content": "Find the average of all x-coordinates of local minima of the function f(x) = (2(1(-1sin(3\u03c0(2|x + 2|) - 3))^2 + 4(-1sin(3\u03c0(2|x + 2|) - 3))) - 2)/(-2(1(-1sin(3\u03c0(2|x + 2|) - 3))^2 + 4(-1sin(3\u03c0(2|x + 2|) - 3))) + 3) in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"} | |
| {"messages": [{"content": "Find the x-coordinate of the rightmost local minimum of the function f(x) = 5(-2|((3(1cos(3\u03c0x - 1) - 1))/(-3(1cos(3\u03c0x - 1) - 1) + 2)) + 1|)^2 - 1(-2|((3(1cos(3\u03c0x - 1) - 1))/(-3(1cos(3\u03c0x - 1) - 1) + 2)) + 1|) - 4 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"} | |
| {"messages": [{"content": "Find the x-coordinate of the local extremum with the largest y-value of the function f(x) = 1|(-2cos(2\u03c0((-3(-5x^2 - 4x - 3) + 2)/(-1(-5x^2 - 4x - 3) - 3)) - 2) - 1) - 2| - 3 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-3", "dataset": "MATH"} | |
| {"messages": [{"content": "Find the average of all x-coordinates of local extrema of the function f(x) = 2|((-1(4(2cos(3\u03c0x - 3) + 3)^2 - 4(2cos(3\u03c0x - 3) + 3) + 4) + 3)/(2(4(2cos(3\u03c0x - 3) + 3)^2 - 4(2cos(3\u03c0x - 3) + 3) + 4) + 1))| - 3 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"} | |
| {"messages": [{"content": "Find the x-coordinate of the leftmost local minimum of the function f(x) = 3cos(1\u03c0(-3|(1((-1x + 3)/(-3x - 3))^2 - 1((-1x + 3)/(-3x - 3)) + 1)| - 3) + 3) + 2 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-3", "dataset": "MATH"} | |
| {"messages": [{"content": "Find the x-coordinate of the local maximum with the smallest y-value of the function f(x) = (-3(-1(2|(-1sin(2\u03c0x + 1) + 1) + 1| + 2)^2 - 3(2|(-1sin(2\u03c0x + 1) + 1) + 1| + 2) + 2) + 1)/(3(-1(2|(-1sin(2\u03c0x + 1) + 1) + 1| + 2)^2 - 3(2|(-1sin(2\u03c0x + 1) + 1) + 1| + 2) + 2) + 1) in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-9", "dataset": "MATH"} | |
| {"messages": [{"content": "Find the average of all x-coordinates of local extrema of the function f(x) = 1|((-1(1cos(3\u03c0(1x^2 - 5x + 3) + 3)) + 2)/(3(1cos(3\u03c0(1x^2 - 5x + 3) + 3)) + 1)) + 2| in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"} | |
| {"messages": [{"content": "Find the x-coordinate of the local maximum with the smallest y-value of the function f(x) = (-2(-1cos(3\u03c0(-2|(-2x^2 + 3x - 5) - 2|) - 2) - 1) + 3)/(1(-1cos(3\u03c0(-2|(-2x^2 + 3x - 5) - 2|) - 2) - 1) + 1) in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-10", "dataset": "MATH"} | |
| {"messages": [{"content": "Find the x-coordinate of the rightmost local maximum of the function f(x) = 4((2(2|(2cos(3\u03c0x + 3) - 3)| - 1) + 3)/(-3(2|(2cos(3\u03c0x + 3) - 3)| - 1) + 2))^2 - 2((2(2|(2cos(3\u03c0x + 3) - 3)| - 1) + 3)/(-3(2|(2cos(3\u03c0x + 3) - 3)| - 1) + 2)) - 3 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"} | |
| {"messages": [{"content": "Find the x-coordinate of the local maximum with the largest y-value of the function f(x) = -1|(-1sin(1\u03c0(-1((3x - 1)/(3x - 2))^2 + 2((3x - 1)/(3x - 2))) + 1) - 3) + 2| in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"} | |
| {"messages": [{"content": "Find the x-coordinate of the local maximum with the largest y-value of the function f(x) = -2|(2(-3sin(3\u03c0((1x + 2)/(3x + 3)) + 2) - 3)^2 + 1(-3sin(3\u03c0((1x + 2)/(3x + 3)) + 2) - 3) - 4)| + 3 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-8", "dataset": "MATH"} | |
| {"messages": [{"content": "Find the x-coordinate of the local extremum with the largest y-value of the function f(x) = (3(2(-2cos(2\u03c0(-1|x - 1| + 1) - 1) + 1)^2 + 2(-2cos(2\u03c0(-1|x - 1| + 1) - 1) + 1) + 3) - 1)/(-3(2(-2cos(2\u03c0(-1|x - 1| + 1) - 1) + 1)^2 + 2(-2cos(2\u03c0(-1|x - 1| + 1) - 1) + 1) + 3)) in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-10", "dataset": "MATH"} | |
| {"messages": [{"content": "Find the x-coordinate of the local maximum with the largest y-value of the function f(x) = (-3(5(3cos(3\u03c0(-2|x + 2| - 1) + 2) + 1)^2 + 2(3cos(3\u03c0(-2|x + 2| - 1) + 2) + 1) + 2) + 1)/(1(5(3cos(3\u03c0(-2|x + 2| - 1) + 2) + 1)^2 + 2(3cos(3\u03c0(-2|x + 2| - 1) + 2) + 1) + 2)) in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-10", "dataset": "MATH"} | |
| {"messages": [{"content": "Find the x-coordinate of the local extremum with the smallest y-value of the function f(x) = (1(-2|(-1(2cos(3\u03c0x + 3) + 1)^2 + 4(2cos(3\u03c0x + 3) + 1) - 3)| - 1))/(-1(-2|(-1(2cos(3\u03c0x + 3) + 1)^2 + 4(2cos(3\u03c0x + 3) + 1) - 3)| - 1) + 3) in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-10", "dataset": "MATH"} | |
| {"messages": [{"content": "How many local minima does the function f(x) = 2sin(1\u03c0((2(-3|(5x^2 - 1x - 4) + 3| - 3) + 2)/(2(-3|(5x^2 - 1x - 4) + 3| - 3) - 1)) - 1) + 3 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"} | |
| {"messages": [{"content": "Find the x-coordinate of the local minimum with the largest y-value of the function f(x) = -1|((2(-1cos(3\u03c0(2x^2 - 3x + 2) + 2) - 3) + 1)/(3(-1cos(3\u03c0(2x^2 - 3x + 2) + 2) - 3) - 2)) + 2| - 1 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-10", "dataset": "MATH"} | |
| {"messages": [{"content": "Find the x-coordinate of the rightmost local minimum of the function f(x) = -1(3sin(2\u03c0(-2|((-2x - 1)/(1x - 2)) - 1| - 1) + 3) - 1)^2 - 2 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8", "dataset": "MATH"} | |
| {"messages": [{"content": "How many local extrema (both minima and maxima) does the function f(x) = 2|(2cos(3\u03c0((2(-2x^2 + 2x + 2))/(1(-2x^2 + 2x + 2) + 2)) - 1) + 2)| have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "53", "dataset": "MATH"} | |
| {"messages": [{"content": "Find the x-coordinate of the leftmost local minimum of the function f(x) = (-1(3(-1|(-2sin(1\u03c0x - 3)) + 2| + 3)^2 - 5(-1|(-2sin(1\u03c0x - 3)) + 2| + 3) + 2) - 1)/(-2(3(-1|(-2sin(1\u03c0x - 3)) + 2| + 3)^2 - 5(-1|(-2sin(1\u03c0x - 3)) + 2| + 3) + 2) - 1) in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-10", "dataset": "MATH"} | |
| {"messages": [{"content": "Find the x-coordinate of the local minimum with the smallest y-value of the function f(x) = 3|(-1((1(-3cos(3\u03c0x + 2) + 3) - 2)/(2(-3cos(3\u03c0x + 2) + 3) + 2))^2 - 3((1(-3cos(3\u03c0x + 2) + 3) - 2)/(2(-3cos(3\u03c0x + 2) + 3) + 2)) - 1) - 3| - 1 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-10", "dataset": "MATH"} | |
| {"messages": [{"content": "Find the x-coordinate of the local extremum with the largest y-value of the function f(x) = (3(3(2sin(1\u03c0(2|x - 3| - 2) + 1) - 1)^2 - 1(2sin(1\u03c0(2|x - 3| - 2) + 1) - 1) - 5) - 1)/(-2(3(2sin(1\u03c0(2|x - 3| - 2) + 1) - 1)^2 - 1(2sin(1\u03c0(2|x - 3| - 2) + 1) - 1) - 5) - 1) in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-10", "dataset": "MATH"} | |
| {"messages": [{"content": "Find the average of all x-coordinates of local maxima of the function f(x) = -1(-3|((-2(2cos(1\u03c0x + 2) - 2) - 1)/(1(2cos(1\u03c0x + 2) - 2))) + 2| - 1)^2 - 1(-3|((-2(2cos(1\u03c0x + 2) - 2) - 1)/(1(2cos(1\u03c0x + 2) - 2))) + 2| - 1) - 5 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-1", "dataset": "MATH"} | |
| {"messages": [{"content": "Find the x-coordinate of the rightmost local minimum of the function f(x) = 1sin(1\u03c0(1|(1((2x)/(1x - 3))^2 + 4((2x)/(1x - 3)) + 3) - 2| + 2) - 1) + 2 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "9", "dataset": "MATH"} | |
| {"messages": [{"content": "How many local extrema (both minima and maxima) does the function f(x) = -3|(-3cos(2\u03c0((3(-5x^2 + 5x + 2) - 3)/(2(-5x^2 + 5x + 2) - 1)) + 3) + 1) + 3| + 3 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "21", "dataset": "MATH"} | |
| {"messages": [{"content": "Find the x-coordinate of the rightmost local extremum of the function f(x) = -2sin(2\u03c0(-1|(1((2x)/(-1x - 1))^2 - 2((2x)/(-1x - 1)) - 5) - 3| - 2) + 3) - 2 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8", "dataset": "MATH"} | |
| {"messages": [{"content": "Find the x-coordinate of the local maximum with the smallest y-value of the function f(x) = (-2(-1sin(2\u03c0(-3|(5x^2 + 5x + 3) + 2| - 3) + 1) - 1) - 2)/(-1(-1sin(2\u03c0(-3|(5x^2 + 5x + 3) + 2| - 3) + 1) - 1) + 3) in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"} | |
| {"messages": [{"content": "Find the x-coordinate of the rightmost local extremum of the function f(x) = (1(3(-2sin(2\u03c0(2|x + 3|)) + 2)^2 + 5(-2sin(2\u03c0(2|x + 3|)) + 2) + 5) + 2)/(3(3(-2sin(2\u03c0(2|x + 3|)) + 2)^2 + 5(-2sin(2\u03c0(2|x + 3|)) + 2) + 5) - 2) in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"} | |
| {"messages": [{"content": "Find the x-coordinate of the rightmost local maximum of the function f(x) = -3|(-2sin(3\u03c0((2(-5x^2 - 1x + 5) + 3)/(1(-5x^2 - 1x + 5) - 2)) + 2)) + 2| - 2 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "6", "dataset": "MATH"} | |
| {"messages": [{"content": "Find the x-coordinate of the local extremum with the largest y-value of the function f(x) = 5(-3sin(2\u03c0((-3(-2|x - 3| + 1) - 3)/(-2(-2|x - 3| + 1) - 1)) + 3))^2 - 1(-3sin(2\u03c0((-3(-2|x - 3| + 1) - 3)/(-2(-2|x - 3| + 1) - 1)) + 3)) - 1 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"} | |
| {"messages": [{"content": "Find the x-coordinate of the local extremum with the largest y-value of the function f(x) = 3|(-2sin(1\u03c0((3(-1x^2 + 1x + 4) - 2)/(1(-1x^2 + 1x + 4) + 1)) + 2)) + 1| - 3 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-2", "dataset": "MATH"} | |
| {"messages": [{"content": "How many local extrema (both minima and maxima) does the function f(x) = 2|(-3sin(3\u03c0(-2((3x - 2)/(-2x - 3))^2 - 4)) + 1) + 2| + 1 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "133", "dataset": "MATH"} | |
| {"messages": [{"content": "Find the x-coordinate of the leftmost local maximum of the function f(x) = (2(-2|(1sin(3\u03c0(1x^2 + 5x - 3) - 1) + 3) - 1| - 1) + 3)/(-2(-2|(1sin(3\u03c0(1x^2 + 5x - 3) - 1) + 3) - 1| - 1) - 2) in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-10", "dataset": "MATH"} | |
| {"messages": [{"content": "Find the x-coordinate of the leftmost local maximum of the function f(x) = 1cos(2\u03c0(1|(4((2x + 1)/(-2x - 3))^2 - 5((2x + 1)/(-2x - 3)) + 5) - 3| + 2) - 1) + 1 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-8", "dataset": "MATH"} | |
| {"messages": [{"content": "Find the average of all x-coordinates of local extrema of the function f(x) = -1|((-2(1(2cos(2\u03c0x + 1) - 2)^2 - 3(2cos(2\u03c0x + 1) - 2) - 1))/(-1(1(2cos(2\u03c0x + 1) - 2)^2 - 3(2cos(2\u03c0x + 1) - 2) - 1) - 2)) + 2| - 3 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"} | |
| {"messages": [{"content": "Find the average of all x-coordinates of local maxima of the function f(x) = -3cos(1\u03c0((1(1(1|x + 3|)^2 + 4(1|x + 3|)) + 2)/(-2(1(1|x + 3|)^2 + 4(1|x + 3|)) + 3)) - 1) + 2 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-3", "dataset": "MATH"} | |
| {"messages": [{"content": "Find the x-coordinate of the rightmost local maximum of the function f(x) = 2((2(-2|(-1cos(3\u03c0x) - 2) - 3| + 3) - 3)/(1(-2|(-1cos(3\u03c0x) - 2) - 3| + 3) + 3))^2 - 2 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"} | |
| {"messages": [{"content": "Find the x-coordinate of the local extremum with the smallest y-value of the function f(x) = (-3(4(1|(-2sin(2\u03c0x - 2)) + 2| + 2)^2 - 2) + 2)/(2(4(1|(-2sin(2\u03c0x - 2)) + 2| + 2)^2 - 2) - 1) in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-10", "dataset": "MATH"} | |
| {"messages": [{"content": "Find the x-coordinate of the local minimum of the function f(x) = 3cos(2\u03c0(5((1(3|x| + 2) + 1)/(2(3|x| + 2) + 3))^2 + 1((1(3|x| + 2) + 1)/(2(3|x| + 2) + 3)) - 1) + 3) in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"} | |
| {"messages": [{"content": "Find the x-coordinate of the local minimum with the smallest y-value of the function f(x) = -1|(2cos(3\u03c0((1(-1x^2 + 4x))/(1(-1x^2 + 4x) - 2)) - 3)) - 3| + 1 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-1", "dataset": "MATH"} | |
| {"messages": [{"content": "Find the average of all x-coordinates of local minima of the function f(x) = (3(-2cos(2\u03c0(-1|(-5x^2 + 5x + 4) - 1| + 1)) - 3) - 1)/(-3(-2cos(2\u03c0(-1|(-5x^2 + 5x + 4) - 1| + 1)) - 3) + 4) in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"} | |
| {"messages": [{"content": "Find the x-coordinate of the leftmost local extremum of the function f(x) = -2cos(2\u03c0(3((-3(-2|x + 1| - 1) + 1)/(-1(-2|x + 1| - 1) - 2))^2 + 3((-3(-2|x + 1| - 1) + 1)/(-1(-2|x + 1| - 1) - 2))) + 1) + 1 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-10", "dataset": "MATH"} | |
| {"messages": [{"content": "Find the x-coordinate of the leftmost local maximum of the function f(x) = 1|(2cos(2\u03c0(1((-3x + 2)/(-2x - 1))^2 - 2((-3x + 2)/(-2x - 1)) + 2) + 1) + 2) + 2| + 1 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-5", "dataset": "MATH"} | |
| {"messages": [{"content": "Find the x-coordinate of the local minimum with the largest y-value of the function f(x) = (3(3cos(1\u03c0(-1|(5x^2 + 5x + 2) - 1| + 3) - 1)))/(-3(3cos(1\u03c0(-1|(5x^2 + 5x + 2) - 1| + 3) - 1)) - 1) in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"} | |
| {"messages": [{"content": "Find the x-coordinate of the rightmost local maximum of the function f(x) = (1(-3(-2sin(3\u03c0(1|x - 3| + 1) - 3) + 2)^2 - 2(-2sin(3\u03c0(1|x - 3| + 1) - 3) + 2) + 4) - 3)/(-1(-3(-2sin(3\u03c0(1|x - 3| + 1) - 3) + 2)^2 - 2(-2sin(3\u03c0(1|x - 3| + 1) - 3) + 2) + 4) - 3) in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "9", "dataset": "MATH"} | |
| {"messages": [{"content": "Find the x-coordinate of the local minimum with the largest y-value of the function f(x) = -1(-2sin(3\u03c0((-2(-2|x + 2|) - 1)/(-1(-2|x + 2|) - 2)) - 2) + 1)^2 + 1 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-7", "dataset": "MATH"} | |
| {"messages": [{"content": "Find the x-coordinate of the leftmost local extremum of the function f(x) = -5(-1|(3sin(2\u03c0((-1x - 1)/(2x - 1)) + 2)) - 2| + 1)^2 - 3(-1|(3sin(2\u03c0((-1x - 1)/(2x - 1)) + 2)) - 2| + 1) in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-3", "dataset": "MATH"} | |
| {"messages": [{"content": "Find the x-coordinate of the local extremum with the smallest y-value of the function f(x) = 1(-1|(-3cos(3\u03c0((1x + 3)/(2x + 3)) + 1)) - 3| - 3)^2 + 1(-1|(-3cos(3\u03c0((1x + 3)/(2x + 3)) + 1)) - 3| - 3) + 5 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-4", "dataset": "MATH"} | |
| {"messages": [{"content": "How many local extrema (both minima and maxima) does the function f(x) = 2sin(3\u03c0((3(4(-2|x + 2| - 1)^2 - 4(-2|x + 2| - 1)) + 2)/(1(4(-2|x + 2| - 1)^2 - 4(-2|x + 2| - 1))))) - 2 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"} | |
| {"messages": [{"content": "Find the x-coordinate of the leftmost local minimum of the function f(x) = -5(3cos(3\u03c0(-2|((3x - 3)/(-3x + 2))| - 2) + 2) + 2)^2 - 3(3cos(3\u03c0(-2|((3x - 3)/(-3x + 2))| - 2) + 2) + 2) + 3 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-2", "dataset": "MATH"} | |
| {"messages": [{"content": "Find the average of all x-coordinates of local maxima of the function f(x) = 2sin(1\u03c0((1(2(-2|x - 3|)^2 + 5(-2|x - 3|) - 4) + 3)/(-1(2(-2|x - 3|)^2 + 5(-2|x - 3|) - 4) - 1)) - 2) + 1 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"} | |
| {"messages": [{"content": "Find the x-coordinate of the rightmost local extremum of the function f(x) = 3|(2sin(3\u03c0((1(-2x^2 - 4x + 3))/(2(-2x^2 - 4x + 3) - 1)) + 2) - 3) - 1| - 3 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"} | |
| {"messages": [{"content": "Find the x-coordinate of the leftmost local minimum of the function f(x) = 2|((-2(-3cos(3\u03c0(-4x^2 - 5x + 1) - 1) + 3))/(1(-3cos(3\u03c0(-4x^2 - 5x + 1) - 1) + 3) + 3))| + 1 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-10", "dataset": "MATH"} | |
| {"messages": [{"content": "Find the x-coordinate of the local maximum of the function f(x) = 1|(3cos(3\u03c0((3(3x^2 - 4x + 4) + 3)/(-3(3x^2 - 4x + 4))) - 1) - 3)| - 3 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"} | |
| {"messages": [{"content": "Find the x-coordinate of the leftmost local minimum of the function f(x) = (-3(-3|(4(-2cos(1\u03c0x - 3) - 1)^2 - 5(-2cos(1\u03c0x - 3) - 1) - 5) - 3| - 3))/(2(-3|(4(-2cos(1\u03c0x - 3) - 1)^2 - 5(-2cos(1\u03c0x - 3) - 1) - 5) - 3| - 3)) in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-10", "dataset": "MATH"} | |
| {"messages": [{"content": "Find the x-coordinate of the leftmost local maximum of the function f(x) = 2(-1|(-3cos(3\u03c0((1x)/(2x - 1)) - 3) + 1) - 3|)^2 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-1", "dataset": "MATH"} | |
| {"messages": [{"content": "Find the x-coordinate of the leftmost local extremum of the function f(x) = -1|((1(-2cos(2\u03c0(-1x^2 - 4) - 3) + 2) - 3)/(-3(-2cos(2\u03c0(-1x^2 - 4) - 3) + 2)))| + 2 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-10", "dataset": "MATH"} | |
| {"messages": [{"content": "Find the x-coordinate of the local extremum with the smallest y-value of the function f(x) = -3|((-3(1(-1sin(1\u03c0x - 3) + 1)^2 - 1(-1sin(1\u03c0x - 3) + 1) - 5) + 2)/(1(1(-1sin(1\u03c0x - 3) + 1)^2 - 1(-1sin(1\u03c0x - 3) + 1) - 5) + 1)) - 3| - 2 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-10", "dataset": "MATH"} | |
| {"messages": [{"content": "Find the average of all x-coordinates of local minima of the function f(x) = -2|(3cos(3\u03c0((3(1x^2 - 1x - 2) + 2)/(2(1x^2 - 1x - 2))) - 2)) + 1| + 3 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"} | |
| {"messages": [{"content": "Find the x-coordinate of the local extremum with the smallest y-value of the function f(x) = 1(3|((1(-1cos(2\u03c0x + 1)) + 3)/(-3(-1cos(2\u03c0x + 1)) - 3)) - 1| - 3)^2 + 1 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-10", "dataset": "MATH"} | |
| {"messages": [{"content": "Find the x-coordinate of the local maximum with the smallest y-value of the function f(x) = (-3(-2(-2cos(3\u03c0(-2|x - 1| - 1) - 3) + 2)^2 - 2(-2cos(3\u03c0(-2|x - 1| - 1) - 3) + 2) + 1))/(-1(-2(-2cos(3\u03c0(-2|x - 1| - 1) - 3) + 2)^2 - 2(-2cos(3\u03c0(-2|x - 1| - 1) - 3) + 2) + 1) + 3) in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-10", "dataset": "MATH"} | |
| {"messages": [{"content": "Find the x-coordinate of the rightmost local maximum of the function f(x) = 1|(5((-3(3cos(2\u03c0x + 3) + 2))/(-1(3cos(2\u03c0x + 3) + 2) + 2))^2 - 1((-3(3cos(2\u03c0x + 3) + 2))/(-1(3cos(2\u03c0x + 3) + 2) + 2)) - 4) + 2| - 1 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"} | |
| {"messages": [{"content": "Find the x-coordinate of the local extremum with the smallest y-value of the function f(x) = 2sin(1\u03c0(-5(-3|((1x + 1)/(-2x - 3)) - 3| + 3)^2 - 5(-3|((1x + 1)/(-2x - 3)) - 3| + 3) + 3) - 3) + 1 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-9", "dataset": "MATH"} | |
| {"messages": [{"content": "Find the average of all x-coordinates of local maxima of the function f(x) = 2|((-1(3cos(2\u03c0(3x^2 - 2x - 2) - 1)) - 3)/(-2(3cos(2\u03c0(3x^2 - 2x - 2) - 1)) - 1)) - 1| + 2 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"} | |
| {"messages": [{"content": "Find the x-coordinate of the local extremum with the smallest y-value of the function f(x) = 4(1|((1(-1sin(2\u03c0x - 3) + 2) - 3)/(-2(-1sin(2\u03c0x - 3) + 2) + 1)) + 2| + 2)^2 - 4(1|((1(-1sin(2\u03c0x - 3) + 2) - 3)/(-2(-1sin(2\u03c0x - 3) + 2) + 1)) + 2| + 2) - 5 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-10", "dataset": "MATH"} | |
| {"messages": [{"content": "Find the x-coordinate of the rightmost local extremum of the function f(x) = -1cos(2\u03c0(-2|((1(-1x^2 - 3x + 4) + 2)/(1(-1x^2 - 3x + 4) + 1)) - 2|) - 2) + 3 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"} | |
| {"messages": [{"content": "Find the x-coordinate of the rightmost local maximum of the function f(x) = 1(-1sin(3\u03c0((-2(1|x - 1| + 2) - 2)/(-1(1|x - 1| + 2))) - 3) - 3)^2 + 2(-1sin(3\u03c0((-2(1|x - 1| + 2) - 2)/(-1(1|x - 1| + 2))) - 3) - 3) - 5 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"} | |
| {"messages": [{"content": "Find the x-coordinate of the local minimum with the smallest y-value of the function f(x) = (2(-2|(3sin(2\u03c0(1x^2 - 2x - 4) + 2) + 2) + 2|) + 1)/(2(-2|(3sin(2\u03c0(1x^2 - 2x - 4) + 2) + 2) + 2|)) in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-10", "dataset": "MATH"} | |
| {"messages": [{"content": "Find the x-coordinate of the leftmost local maximum of the function f(x) = (-2(-3sin(1\u03c0(-1(1|x + 3| - 1)^2 + 2(1|x + 3| - 1))) + 2) + 3)/(3(-3sin(1\u03c0(-1(1|x + 3| - 1)^2 + 2(1|x + 3| - 1))) + 2) + 1) in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-10", "dataset": "MATH"} | |
| {"messages": [{"content": "Find the x-coordinate of the local extremum with the largest y-value of the function f(x) = 1|(4((-1(1cos(1\u03c0x + 3)) - 1)/(1(1cos(1\u03c0x + 3))))^2 + 3((-1(1cos(1\u03c0x + 3)) - 1)/(1(1cos(1\u03c0x + 3)))) + 3) - 1| - 2 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-9", "dataset": "MATH"} | |
| {"messages": [{"content": "Find the x-coordinate of the local maximum of the function f(x) = -3|(-3sin(2\u03c0(-5((3x)/(2x - 1))^2 + 5) - 2) - 2) + 2| - 3 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"} | |
| {"messages": [{"content": "Find the average of all x-coordinates of local maxima of the function f(x) = 1|(5((-3(3sin(3\u03c0x - 3) - 1) - 2)/(1(3sin(3\u03c0x - 3) - 1) + 2))^2 + 1((-3(3sin(3\u03c0x - 3) - 1) - 2)/(1(3sin(3\u03c0x - 3) - 1) + 2)) - 4) - 2| + 3 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"} | |
| {"messages": [{"content": "Find the x-coordinate of the leftmost local maximum of the function f(x) = (-3(5(2sin(1\u03c0(2|x + 2| - 2) - 1) - 1)^2 + 1(2sin(1\u03c0(2|x + 2| - 2) - 1) - 1) + 3) - 1)/(-1(5(2sin(1\u03c0(2|x + 2| - 2) - 1) - 1)^2 + 1(2sin(1\u03c0(2|x + 2| - 2) - 1) - 1) + 3) - 3) in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-10", "dataset": "MATH"} | |
| {"messages": [{"content": "Find the x-coordinate of the local extremum with the smallest y-value of the function f(x) = (-3(3|(-1cos(1\u03c0(2x^2 + 3x - 3) - 3) + 1)| - 3) - 1)/(1(3|(-1cos(1\u03c0(2x^2 + 3x - 3) - 3) + 1)| - 3) - 3) in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-10", "dataset": "MATH"} | |
| {"messages": [{"content": "How many local maxima does the function f(x) = (2(2|(-4(-1sin(3\u03c0x - 3))^2 + 1(-1sin(3\u03c0x - 3)) + 2)| + 2) - 1)/(-2(2|(-4(-1sin(3\u03c0x - 3))^2 + 1(-1sin(3\u03c0x - 3)) + 2)| + 2) - 1) have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"} | |
| {"messages": [{"content": "Find the x-coordinate of the leftmost local minimum of the function f(x) = -2|(-2cos(1\u03c0((-2(5x^2 - 4x + 5) + 2)/(-1(5x^2 - 4x + 5) + 3)) + 2)) + 1| - 3 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-1", "dataset": "MATH"} | |
| {"messages": [{"content": "Find the average of all x-coordinates of local extrema of the function f(x) = -1(-2cos(1\u03c0((-3(-1|x + 3| - 2) - 3)/(-2(-1|x + 3| - 2))) - 3))^2 - 2(-2cos(1\u03c0((-3(-1|x + 3| - 2) - 3)/(-2(-1|x + 3| - 2))) - 3)) + 2 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-4", "dataset": "MATH"} | |
| {"messages": [{"content": "Find the x-coordinate of the local minimum with the largest y-value of the function f(x) = 1cos(1\u03c0((-1(2(-3|x - 3| - 2)^2 + 5(-3|x - 3| - 2) - 3) - 1)/(2(2(-3|x - 3| - 2)^2 + 5(-3|x - 3| - 2) - 3))) + 1) + 3 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"} | |
| {"messages": [{"content": "How many local extrema (both minima and maxima) does the function f(x) = 3sin(1\u03c0(-2|((1(-4x^2 - 2x - 3) - 3)/(-1(-4x^2 - 2x - 3))) - 2| - 1) + 1) + 2 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5", "dataset": "MATH"} | |
| {"messages": [{"content": "Find the x-coordinate of the local minimum with the largest y-value of the function f(x) = (-1(-1|(-3(-2sin(2\u03c0x - 1) - 3)^2 + 3(-2sin(2\u03c0x - 1) - 3) + 4)| - 3) + 1)/(2(-1|(-3(-2sin(2\u03c0x - 1) - 3)^2 + 3(-2sin(2\u03c0x - 1) - 3) + 4)| - 3) + 1) in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-9", "dataset": "MATH"} | |
| {"messages": [{"content": "Find the x-coordinate of the local minimum of the function f(x) = -1|((2(3cos(1\u03c0(-4x^2 - 4x + 5) - 3) - 2) + 2)/(-2(3cos(1\u03c0(-4x^2 - 4x + 5) - 3) - 2))) + 2| + 2 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"} | |
| {"messages": [{"content": "Find the x-coordinate of the leftmost local extremum of the function f(x) = 2((-1(-1cos(2\u03c0(3|x + 2| - 1) + 2) - 1) + 1)/(-1(-1cos(2\u03c0(3|x + 2| - 1) + 2) - 1) + 2))^2 - 2((-1(-1cos(2\u03c0(3|x + 2| - 1) + 2) - 1) + 1)/(-1(-1cos(2\u03c0(3|x + 2| - 1) + 2) - 1) + 2)) + 5 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-10", "dataset": "MATH"} | |
| {"messages": [{"content": "Find the x-coordinate of the local maximum with the largest y-value of the function f(x) = (3(5(3sin(1\u03c0(2|x|) + 1) - 2)^2 + 5(3sin(1\u03c0(2|x|) + 1) - 2) - 1) + 3)/(2(5(3sin(1\u03c0(2|x|) + 1) - 2)^2 + 5(3sin(1\u03c0(2|x|) + 1) - 2) - 1) - 1) in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"} | |
| {"messages": [{"content": "Find the x-coordinate of the leftmost local minimum of the function f(x) = (1(-4(-3cos(2\u03c0(-3|x + 1| - 1) + 3) + 1)^2 - 1(-3cos(2\u03c0(-3|x + 1| - 1) + 3) + 1)) - 2)/(2(-4(-3cos(2\u03c0(-3|x + 1| - 1) + 3) + 1)^2 - 1(-3cos(2\u03c0(-3|x + 1| - 1) + 3) + 1)) + 1) in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-10", "dataset": "MATH"} | |
| {"messages": [{"content": "Find the average of all x-coordinates of local minima of the function f(x) = 1|(-1cos(3\u03c0((-3(-1x^2 - 4x + 2))/(3(-1x^2 - 4x + 2) + 2)) - 3) - 2)| - 3 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-2", "dataset": "MATH"} | |
| {"messages": [{"content": "Find the x-coordinate of the local extremum with the largest y-value of the function f(x) = 4((-3(3cos(1\u03c0(1|x - 2|)) + 2) - 2)/(3(3cos(1\u03c0(1|x - 2|)) + 2) + 3))^2 + 1((-3(3cos(1\u03c0(1|x - 2|)) + 2) - 2)/(3(3cos(1\u03c0(1|x - 2|)) + 2) + 3)) + 5 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-10", "dataset": "MATH"} | |
| {"messages": [{"content": "Find the x-coordinate of the local extremum with the smallest y-value of the function f(x) = (1(2|(2cos(2\u03c0(-4x^2 - 3) + 2) - 1) + 1|))/(2(2|(2cos(2\u03c0(-4x^2 - 3) + 2) - 1) + 1|) - 1) in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-10", "dataset": "MATH"} | |
| {"messages": [{"content": "Find the average of all x-coordinates of local minima of the function f(x) = 2|((1(-1cos(2\u03c0(4x^2 - 3x + 3) + 2) + 3) - 1)/(-3(-1cos(2\u03c0(4x^2 - 3x + 3) + 2) + 3) - 3)) + 2| in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"} | |
| {"messages": [{"content": "How many local minima does the function f(x) = -2|((3(2sin(3\u03c0(1x^2 - 5x - 3) + 3) + 1) + 1)/(3(2sin(3\u03c0(1x^2 - 5x - 3) + 3) + 1) + 2)) - 1| + 1 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"} | |
| {"messages": [{"content": "How many local extrema (both minima and maxima) does the function f(x) = (-3(-2cos(3\u03c0(3|(2x^2 - 2x - 5) - 1|) + 1) + 1) - 1)/(2(-2cos(3\u03c0(3|(2x^2 - 2x - 5) - 1|) + 1) + 1) + 3) have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "499", "dataset": "MATH"} | |
| {"messages": [{"content": "Find the x-coordinate of the local extremum with the smallest y-value of the function f(x) = 3|(-3sin(3\u03c0(-1((2x + 1)/(-3x + 1))^2 - 4) + 2) - 2) + 3| + 3 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"} | |
| {"messages": [{"content": "Find the x-coordinate of the leftmost local maximum of the function f(x) = -1sin(1\u03c0(3(-2|((2x + 3)/(-3x - 1)) - 3| + 2)^2 - 1(-2|((2x + 3)/(-3x - 1)) - 3| + 2) + 3) - 1) + 3 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-9", "dataset": "MATH"} | |
| {"messages": [{"content": "Find the x-coordinate of the leftmost local maximum of the function f(x) = -5(2|(2cos(3\u03c0((3x - 1)/(-2x - 1)) + 2) - 1) + 3| - 1)^2 - 3(2|(2cos(3\u03c0((3x - 1)/(-2x - 1)) + 2) - 1) + 3| - 1) - 3 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-4", "dataset": "MATH"} | |
| {"messages": [{"content": "Find the x-coordinate of the local maximum of the function f(x) = -2|(2sin(2\u03c0(-2((3x - 2)/(1x - 3))^2 + 5((3x - 2)/(1x - 3)) - 2) + 1) - 2) + 1| + 1 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-1", "dataset": "MATH"} | |
| {"messages": [{"content": "Find the x-coordinate of the local maximum with the largest y-value of the function f(x) = 5(-1|((-2(2cos(2\u03c0x + 2) + 3) + 2)/(-2(2cos(2\u03c0x + 2) + 3))) + 1| - 3)^2 + 2(-1|((-2(2cos(2\u03c0x + 2) + 3) + 2)/(-2(2cos(2\u03c0x + 2) + 3))) + 1| - 3) + 3 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-9", "dataset": "MATH"} | |
| {"messages": [{"content": "Find the x-coordinate of the local minimum with the smallest y-value of the function f(x) = (-1(5(3|(3cos(1\u03c0x - 2) - 2) + 3|)^2 - 3(3|(3cos(1\u03c0x - 2) - 2) + 3|) - 5) - 3)/(1(5(3|(3cos(1\u03c0x - 2) - 2) + 3|)^2 - 3(3|(3cos(1\u03c0x - 2) - 2) + 3|) - 5)) in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-10", "dataset": "MATH"} | |
| {"messages": [{"content": "Find the x-coordinate of the local minimum with the largest y-value of the function f(x) = (-3(-1(-2|(-3sin(1\u03c0x + 3) + 1) + 2| + 2)^2 + 2(-2|(-3sin(1\u03c0x + 3) + 1) + 2| + 2) - 1) + 1)/(-2(-1(-2|(-3sin(1\u03c0x + 3) + 1) + 2| + 2)^2 + 2(-2|(-3sin(1\u03c0x + 3) + 1) + 2| + 2) - 1)) in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-8", "dataset": "MATH"} | |
| {"messages": [{"content": "Find the average of all x-coordinates of local minima of the function f(x) = 1|(1((3(2sin(3\u03c0x - 3)) + 2)/(2(2sin(3\u03c0x - 3)) + 1))^2 + 4((3(2sin(3\u03c0x - 3)) + 2)/(2(2sin(3\u03c0x - 3)) + 1)) + 5) + 3| - 1 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"} | |
| {"messages": [{"content": "Find the x-coordinate of the leftmost local maximum of the function f(x) = -3sin(3\u03c0(5((-3(2|x| - 2) + 3)/(-2(2|x| - 2) + 3))^2 + 3((-3(2|x| - 2) + 3)/(-2(2|x| - 2) + 3)) + 3) - 2) - 3 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-7", "dataset": "MATH"} | |
| {"messages": [{"content": "Find the x-coordinate of the local minimum with the largest y-value of the function f(x) = (2(-1|(2(-2sin(2\u03c0x - 2) - 1)^2 + 3(-2sin(2\u03c0x - 2) - 1) + 1) + 1| - 2) - 1)/(1(-1|(2(-2sin(2\u03c0x - 2) - 1)^2 + 3(-2sin(2\u03c0x - 2) - 1) + 1) + 1| - 2) + 2) in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-10", "dataset": "MATH"} | |
| {"messages": [{"content": "Find the x-coordinate of the leftmost local maximum of the function f(x) = -3((-3(-3|(1cos(1\u03c0x - 1) + 1) + 3| - 3) - 2)/(-3(-3|(1cos(1\u03c0x - 1) + 1) + 3| - 3)))^2 - 1((-3(-3|(1cos(1\u03c0x - 1) + 1) + 3| - 3) - 2)/(-3(-3|(1cos(1\u03c0x - 1) + 1) + 3| - 3))) + 2 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-9", "dataset": "MATH"} | |
| {"messages": [{"content": "How many local extrema (both minima and maxima) does the function f(x) = 1|((-2(5(1cos(1\u03c0x + 1))^2 - 1(1cos(1\u03c0x + 1)) - 4) - 3)/(-2(5(1cos(1\u03c0x + 1))^2 - 1(1cos(1\u03c0x + 1)) - 4) - 2)) + 3| + 1 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "71", "dataset": "MATH"} | |
| {"messages": [{"content": "Find the x-coordinate of the local extremum with the smallest y-value of the function f(x) = -2|(1sin(2\u03c0((-2(5x^2 - 3) - 1)/(-2(5x^2 - 3)))) - 3) - 2| - 2 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-1", "dataset": "MATH"} | |
| {"messages": [{"content": "Find the x-coordinate of the local minimum with the smallest y-value of the function f(x) = -3cos(1\u03c0(-2|((2(-2x^2 + 3x) + 2)/(1(-2x^2 + 3x) - 2)) + 2| + 2) - 3) in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-2", "dataset": "MATH"} | |
| {"messages": [{"content": "Find the x-coordinate of the local maximum with the smallest y-value of the function f(x) = -1sin(3\u03c0((-1(3|(1x^2 - 2) - 3| - 3) + 1)/(-1(3|(1x^2 - 2) - 3| - 3) - 2)) + 1) + 3 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"} | |
| {"messages": [{"content": "Find the x-coordinate of the rightmost local extremum of the function f(x) = -2cos(2\u03c0(-3((-2(1|x - 3| - 3))/(-2(1|x - 3| - 3) - 2))^2 + 1((-2(1|x - 3| - 3))/(-2(1|x - 3| - 3) - 2)) + 1) + 3) + 2 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "9", "dataset": "MATH"} | |
| {"messages": [{"content": "Find the x-coordinate of the local minimum with the smallest y-value of the function f(x) = 2sin(1\u03c0((-1(-1|(3x^2 - 2x - 4) + 2| + 2) + 3)/(-3(-1|(3x^2 - 2x - 4) + 2| + 2))) + 3) - 1 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-1", "dataset": "MATH"} | |
| {"messages": [{"content": "Find the x-coordinate of the leftmost local minimum of the function f(x) = -1cos(3\u03c0(5(-1|((2x + 3)/(-3x + 2)) + 3|)^2 - 4(-1|((2x + 3)/(-3x + 2)) + 3|) + 3) - 3) in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-9", "dataset": "MATH"} | |
| {"messages": [{"content": "Find the x-coordinate of the rightmost local maximum of the function f(x) = -2cos(1\u03c0(-4((-3(2|x + 1| + 1) - 1)/(-1(2|x + 1| + 1) - 2))^2 + 4((-3(2|x + 1| + 1) - 1)/(-1(2|x + 1| + 1) - 2)) - 3)) + 2 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "9", "dataset": "MATH"} | |
| {"messages": [{"content": "Find the x-coordinate of the rightmost local extremum of the function f(x) = (-3(-5(3|(-3sin(3\u03c0x - 3) + 3) - 1| - 1)^2 - 4(3|(-3sin(3\u03c0x - 3) + 3) - 1| - 1) + 2) - 2)/(2(-5(3|(-3sin(3\u03c0x - 3) + 3) - 1| - 1)^2 - 4(3|(-3sin(3\u03c0x - 3) + 3) - 1| - 1) + 2) + 2) in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"} | |
| {"messages": [{"content": "Find the x-coordinate of the local maximum with the smallest y-value of the function f(x) = 2cos(2\u03c0(3|((2(-1x^2 - 2x + 5) - 3)/(-1(-1x^2 - 2x + 5) - 3)) - 1| + 1) - 1) + 2 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-1", "dataset": "MATH"} | |
| {"messages": [{"content": "Find the average of all x-coordinates of local extrema of the function f(x) = -1|(-3cos(1\u03c0(-2((1x + 2)/(3x - 2))^2 + 2((1x + 2)/(3x - 2)) - 2) + 3)) + 1| - 1 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"} | |
| {"messages": [{"content": "Find the x-coordinate of the rightmost local maximum of the function f(x) = -3|((-1(4(1cos(2\u03c0x - 1) - 1)^2 + 3(1cos(2\u03c0x - 1) - 1) + 1) + 1)/(1(4(1cos(2\u03c0x - 1) - 1)^2 + 3(1cos(2\u03c0x - 1) - 1) + 1) + 1)) - 3| + 3 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "9", "dataset": "MATH"} | |
| {"messages": [{"content": "Find the x-coordinate of the local extremum with the smallest y-value of the function f(x) = 3|(4(-1sin(1\u03c0((-1x)/(-2x + 3)) + 2) - 2)^2 + 1(-1sin(1\u03c0((-1x)/(-2x + 3)) + 2) - 2) + 3) - 3| + 3 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"} | |
| {"messages": [{"content": "Find the x-coordinate of the local minimum with the smallest y-value of the function f(x) = 4(-1|(-1cos(1\u03c0((-3x - 1)/(-3x - 2)) - 3)) - 2|)^2 - 4(-1|(-1cos(1\u03c0((-3x - 1)/(-3x - 2)) - 3)) - 2|) + 5 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-1", "dataset": "MATH"} | |
| {"messages": [{"content": "Find the x-coordinate of the leftmost local maximum of the function f(x) = 1((1(-2|(2cos(3\u03c0x + 2) + 3) + 2|) + 1)/(2(-2|(2cos(3\u03c0x + 2) + 3) + 2|) + 1))^2 - 1((1(-2|(2cos(3\u03c0x + 2) + 3) + 2|) + 1)/(2(-2|(2cos(3\u03c0x + 2) + 3) + 2|) + 1)) in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-10", "dataset": "MATH"} | |
| {"messages": [{"content": "Find the average of all x-coordinates of local extrema of the function f(x) = 1sin(3\u03c0(-2(-2|((-1x + 3)/(2x - 1)) - 1| - 2)^2 + 1(-2|((-1x + 3)/(2x - 1)) - 1| - 2) + 2) + 1) + 2 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"} | |
| {"messages": [{"content": "Find the average of all x-coordinates of local extrema of the function f(x) = 2(1|((3(1sin(3\u03c0x + 3) + 2) - 3)/(-2(1sin(3\u03c0x + 3) + 2) - 3))| + 1)^2 - 5(1|((3(1sin(3\u03c0x + 3) + 2) - 3)/(-2(1sin(3\u03c0x + 3) + 2) - 3))| + 1) + 2 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"} | |
| {"messages": [{"content": "Find the x-coordinate of the local maximum with the smallest y-value of the function f(x) = -5(-3|(-1cos(3\u03c0((-2x - 3)/(1x - 3)) + 2) - 1) - 2| + 3)^2 + 3(-3|(-1cos(3\u03c0((-2x - 3)/(1x - 3)) + 2) - 1) - 2| + 3) in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-8", "dataset": "MATH"} | |
| {"messages": [{"content": "Find the x-coordinate of the local minimum with the largest y-value of the function f(x) = 1((2(1|(2cos(1\u03c0x - 2)) - 3| - 3) - 2)/(-1(1|(2cos(1\u03c0x - 2)) - 3| - 3) + 2))^2 + 3((2(1|(2cos(1\u03c0x - 2)) - 3| - 3) - 2)/(-1(1|(2cos(1\u03c0x - 2)) - 3| - 3) + 2)) + 3 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-9", "dataset": "MATH"} | |
| {"messages": [{"content": "Find the x-coordinate of the leftmost local extremum of the function f(x) = 3cos(1\u03c0((1(-3(1|x + 1|)^2 + 1(1|x + 1|) + 3) + 1)/(1(-3(1|x + 1|)^2 + 1(1|x + 1|) + 3) + 3)) - 3) - 1 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-3", "dataset": "MATH"} | |
| {"messages": [{"content": "Find the x-coordinate of the local extremum with the smallest y-value of the function f(x) = -2sin(2\u03c0((-1(-3(-1|x - 2| + 3)^2 + 1(-1|x - 2| + 3) + 3) + 3)/(-2(-3(-1|x - 2| + 3)^2 + 1(-1|x - 2| + 3) + 3) - 3)) + 2) - 2 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-3", "dataset": "MATH"} | |
| {"messages": [{"content": "Find the x-coordinate of the local maximum with the smallest y-value of the function f(x) = 1sin(2\u03c0(-3((1(1|x + 3| + 1) - 1)/(1(1|x + 3| + 1) + 3))^2 - 1((1(1|x + 3| + 1) - 1)/(1(1|x + 3| + 1) + 3))) - 1) + 2 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-9", "dataset": "MATH"} | |
| {"messages": [{"content": "Find the x-coordinate of the leftmost local maximum of the function f(x) = 2(-2|(-1cos(3\u03c0((3x - 1)/(1x + 2)) + 1) + 1) + 3| + 2)^2 + 1(-2|(-1cos(3\u03c0((3x - 1)/(1x + 2)) + 1) + 1) + 3| + 2) - 1 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-8", "dataset": "MATH"} | |
| {"messages": [{"content": "Find the x-coordinate of the leftmost local minimum of the function f(x) = (1(-2|(2cos(2\u03c0(-5x^2 + 5x + 3) + 2) + 1) - 1|) - 1)/(3(-2|(2cos(2\u03c0(-5x^2 + 5x + 3) + 2) + 1) - 1|) - 1) in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-10", "dataset": "MATH"} | |
| {"messages": [{"content": "Find the x-coordinate of the leftmost local extremum of the function f(x) = 2sin(1\u03c0((2(3|(-2x^2 + 4x - 3)| + 3) - 2)/(-1(3|(-2x^2 + 4x - 3)| + 3) - 2))) - 1 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"} | |
| {"messages": [{"content": "Find the x-coordinate of the local maximum with the smallest y-value of the function f(x) = 1sin(1\u03c0(-1|((-3(-4x^2 + 4x) - 2)/(-1(-4x^2 + 4x) + 2)) + 2| + 3) + 2) - 2 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"} | |
| {"messages": [{"content": "Find the x-coordinate of the leftmost local maximum of the function f(x) = 2|(4(2cos(3\u03c0((-2x + 2)/(1x)) - 1))^2 + 3(2cos(3\u03c0((-2x + 2)/(1x)) - 1)) - 1) + 3| + 2 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-9", "dataset": "MATH"} | |
| {"messages": [{"content": "Find the x-coordinate of the leftmost local minimum of the function f(x) = (2(2(-1cos(3\u03c0(-3|x + 2| + 2)) - 2)^2 - 5(-1cos(3\u03c0(-3|x + 2| + 2)) - 2) - 1) - 1)/(-2(2(-1cos(3\u03c0(-3|x + 2| + 2)) - 2)^2 - 5(-1cos(3\u03c0(-3|x + 2| + 2)) - 2) - 1) - 1) in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-10", "dataset": "MATH"} | |
| {"messages": [{"content": "Find the average of all x-coordinates of local minima of the function f(x) = 1cos(1\u03c0(-1|(-3((-3x - 3)/(1x))^2 + 4((-3x - 3)/(1x)) + 3) + 3| + 1) - 1) - 1 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"} | |
| {"messages": [{"content": "Find the x-coordinate of the leftmost local extremum of the function f(x) = -3(1sin(3\u03c0((3(3|x - 3| + 3) + 2)/(-3(3|x - 3| + 3) - 3)) - 1))^2 + 3(1sin(3\u03c0((3(3|x - 3| + 3) + 2)/(-3(3|x - 3| + 3) - 3)) - 1)) + 3 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"} | |
| {"messages": [{"content": "Find the x-coordinate of the rightmost local minimum of the function f(x) = -1sin(3\u03c0((-3(-4(-1|x + 3| - 1)^2 + 1(-1|x + 3| - 1)))/(-2(-4(-1|x + 3| - 1)^2 + 1(-1|x + 3| - 1)))) + 2) in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "9", "dataset": "MATH"} | |
| {"messages": [{"content": "Find the average of all x-coordinates of local minima of the function f(x) = -1|((-2(-1sin(1\u03c0(5x^2 + 2x - 4) + 2) - 2) + 3)/(-2(-1sin(1\u03c0(5x^2 + 2x - 4) + 2) - 2) + 1)) - 1| + 1 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"} | |
| {"messages": [{"content": "Find the average of all x-coordinates of local maxima of the function f(x) = 2|(1sin(1\u03c0(-1((-2x - 1)/(1x - 3))^2 - 4((-2x - 1)/(1x - 3)) - 1) - 2) + 1) + 3| - 3 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"} | |
| {"messages": [{"content": "Find the x-coordinate of the local maximum with the smallest y-value of the function f(x) = 3(3|((1(-1cos(1\u03c0x + 3) + 3) - 1)/(3(-1cos(1\u03c0x + 3) + 3) + 2)) + 3| + 2)^2 + 4(3|((1(-1cos(1\u03c0x + 3) + 3) - 1)/(3(-1cos(1\u03c0x + 3) + 3) + 2)) + 3| + 2) + 4 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-10", "dataset": "MATH"} | |
| {"messages": [{"content": "Find the x-coordinate of the local maximum with the largest y-value of the function f(x) = -4(3|((3(2sin(3\u03c0x - 3) + 2) - 2)/(-1(2sin(3\u03c0x - 3) + 2) + 2)) - 1|)^2 - 1(3|((3(2sin(3\u03c0x - 3) + 2) - 2)/(-1(2sin(3\u03c0x - 3) + 2) + 2)) - 1|) + 2 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-10", "dataset": "MATH"} | |
| {"messages": [{"content": "Find the x-coordinate of the local extremum with the largest y-value of the function f(x) = -3cos(3\u03c0((2(-2|(-3x^2 - 4x + 3)| + 2) + 1)/(2(-2|(-3x^2 - 4x + 3)| + 2) + 3)) - 2) + 1 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-2", "dataset": "MATH"} | |
| {"messages": [{"content": "Find the x-coordinate of the local maximum with the smallest y-value of the function f(x) = -3|((2(-2sin(2\u03c0(-5x^2 - 2x + 4) + 2) + 3) + 1)/(-3(-2sin(2\u03c0(-5x^2 - 2x + 4) + 2) + 3) - 3)) - 1| - 2 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-10", "dataset": "MATH"} | |
| {"messages": [{"content": "Find the average of all x-coordinates of local minima of the function f(x) = -2(2sin(1\u03c0((1(-2|x + 2|) + 1)/(1(-2|x + 2|) + 3)) + 2) + 2)^2 + 1(2sin(1\u03c0((1(-2|x + 2|) + 1)/(1(-2|x + 2|) + 3)) + 2) + 2) in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-2", "dataset": "MATH"} | |
| {"messages": [{"content": "Find the x-coordinate of the local minimum with the smallest y-value of the function f(x) = (3(-5(-2|(-3sin(2\u03c0x - 1) + 2) + 1|)^2 - 3(-2|(-3sin(2\u03c0x - 1) + 2) + 1|)) - 3)/(1(-5(-2|(-3sin(2\u03c0x - 1) + 2) + 1|)^2 - 3(-2|(-3sin(2\u03c0x - 1) + 2) + 1|)) + 2) in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-10", "dataset": "MATH"} | |
| {"messages": [{"content": "Find the x-coordinate of the leftmost local minimum of the function f(x) = 2|(3(1cos(3\u03c0((-3x + 3)/(-1x)) + 1) + 2)^2 - 1) + 3| - 2 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-5", "dataset": "MATH"} | |
| {"messages": [{"content": "Find the x-coordinate of the local maximum with the largest y-value of the function f(x) = 2|(-1cos(2\u03c0((-3(1x^2 - 3x + 3) - 2)/(3(1x^2 - 3x + 3) + 3)) + 2) + 2) + 1| + 3 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"} | |
| {"messages": [{"content": "Find the x-coordinate of the leftmost local extremum of the function f(x) = (2(2|(-2sin(2\u03c0(1x^2 + 5x - 5)) + 1) - 2| + 3) - 1)/(-3(2|(-2sin(2\u03c0(1x^2 + 5x - 5)) + 1) - 2| + 3) + 2) in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-10", "dataset": "MATH"} | |
| {"messages": [{"content": "Find the average of all x-coordinates of local maxima of the function f(x) = -3|(4(-1sin(1\u03c0((-1x - 2)/(1x + 3)) + 1) - 1)^2 + 1(-1sin(1\u03c0((-1x - 2)/(1x + 3)) + 1) - 1) + 1) - 3| + 2 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-2", "dataset": "MATH"} | |
| {"messages": [{"content": "Find the x-coordinate of the local extremum with the smallest y-value of the function f(x) = 2cos(3\u03c0(1(-3|((1x + 2)/(-2x - 2)) - 2| - 1)^2 + 1(-3|((1x + 2)/(-2x - 2)) - 2| - 1) + 5) + 3) + 1 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-10", "dataset": "MATH"} | |
| {"messages": [{"content": "Find the x-coordinate of the local minimum with the smallest y-value of the function f(x) = -2|(-3sin(3\u03c0((2(2x^2 + 2x - 2) - 2)/(3(2x^2 + 2x - 2) - 2)) + 1))| - 3 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-2", "dataset": "MATH"} | |
| {"messages": [{"content": "Find the x-coordinate of the local extremum with the largest y-value of the function f(x) = (-3(1sin(2\u03c0(3|(3x^2 - 2x + 4) - 1|) - 1)) + 3)/(2(1sin(2\u03c0(3|(3x^2 - 2x + 4) - 1|) - 1)) - 1) in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-10", "dataset": "MATH"} | |
| {"messages": [{"content": "Find the average of all x-coordinates of local extrema of the function f(x) = (2(1sin(3\u03c0(3|(-1x^2 + 4x - 2)| - 1) + 3) - 2) + 2)/(1(1sin(3\u03c0(3|(-1x^2 + 4x - 2)| - 1) + 3) - 2) + 3) in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"} | |
| {"messages": [{"content": "Find the x-coordinate of the local extremum with the largest y-value of the function f(x) = 1|(1((1(2sin(1\u03c0x)) - 3)/(-1(2sin(1\u03c0x)) - 3))^2 + 1((1(2sin(1\u03c0x)) - 3)/(-1(2sin(1\u03c0x)) - 3)) + 3) - 2| + 2 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-8", "dataset": "MATH"} | |
| {"messages": [{"content": "Find the x-coordinate of the leftmost local maximum of the function f(x) = (-2(-2(3|(2cos(3\u03c0x + 3) - 3) - 2| - 2)^2 + 3(3|(2cos(3\u03c0x + 3) - 3) - 2| - 2) - 2) + 3)/(-1(-2(3|(2cos(3\u03c0x + 3) - 3) - 2| - 2)^2 + 3(3|(2cos(3\u03c0x + 3) - 3) - 2| - 2) - 2) - 3) in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-10", "dataset": "MATH"} | |
| {"messages": [{"content": "Find the x-coordinate of the local extremum with the largest y-value of the function f(x) = (-1(-3(1cos(3\u03c0(3|x + 2| - 2) - 3) + 1)^2 + 4(1cos(3\u03c0(3|x + 2| - 2) - 3) + 1) - 4))/(-3(-3(1cos(3\u03c0(3|x + 2| - 2) - 3) + 1)^2 + 4(1cos(3\u03c0(3|x + 2| - 2) - 3) + 1) - 4) + 1) in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-10", "dataset": "MATH"} | |
| {"messages": [{"content": "Find the x-coordinate of the leftmost local extremum of the function f(x) = 1(-1|(3cos(3\u03c0((-1x - 3)/(1x + 1))) + 1) + 3| - 2)^2 - 5(-1|(3cos(3\u03c0((-1x - 3)/(1x + 1))) + 1) + 3| - 2) + 3 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-7", "dataset": "MATH"} | |
| {"messages": [{"content": "Find the x-coordinate of the local minimum with the smallest y-value of the function f(x) = -2sin(2\u03c0(2|((-3(-3x^2 - 3x + 5) + 3)/(3(-3x^2 - 3x + 5) + 2)) - 3| - 2) - 2) - 3 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-3", "dataset": "MATH"} | |
| {"messages": [{"content": "Find the x-coordinate of the local maximum of the function f(x) = 3(1|((1(-2cos(2\u03c0x)))/(1(-2cos(2\u03c0x)) + 2)) + 2| - 3)^2 + 1(1|((1(-2cos(2\u03c0x)))/(1(-2cos(2\u03c0x)) + 2)) + 2| - 3) + 2 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"} | |
| {"messages": [{"content": "Find the average of all x-coordinates of local maxima of the function f(x) = 3|(5(2sin(2\u03c0((3x - 2)/(-2x + 1)) + 3) + 2)^2 + 2(2sin(2\u03c0((3x - 2)/(-2x + 1)) + 3) + 2) - 4) + 1| + 1 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"} | |
| {"messages": [{"content": "Find the x-coordinate of the leftmost local maximum of the function f(x) = 3sin(3\u03c0(1|((2(1x^2 + 5x - 3))/(-3(1x^2 + 5x - 3) - 2)) + 3| - 3) + 3) + 2 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-6", "dataset": "MATH"} | |
| {"messages": [{"content": "How many local maxima does the function f(x) = (3(-1sin(3\u03c0(-1(-2|x + 1|)^2 + 3(-2|x + 1|) - 2) - 2) + 1) + 2)/(-1(-1sin(3\u03c0(-1(-2|x + 1|)^2 + 3(-2|x + 1|) - 2) - 2) + 1) + 2) have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"} | |
| {"messages": [{"content": "Find the average of all x-coordinates of local maxima of the function f(x) = -3|((-3(3sin(3\u03c0(-4x^2 - 2x - 2) - 2) + 1) - 1)/(1(3sin(3\u03c0(-4x^2 - 2x - 2) - 2) + 1))) - 2| + 3 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"} | |
| {"messages": [{"content": "Find the x-coordinate of the leftmost local minimum of the function f(x) = (-1(3sin(1\u03c0(3|(-1x^2 - 3x - 3) + 3| + 3) - 1)) + 2)/(2(3sin(1\u03c0(3|(-1x^2 - 3x - 3) + 3| + 3) - 1)) - 1) in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-10", "dataset": "MATH"} | |
| {"messages": [{"content": "Find the x-coordinate of the leftmost local minimum of the function f(x) = -2|(1sin(3\u03c0((-1(-1x^2 + 4x + 3) + 1)/(-1(-1x^2 + 4x + 3) - 2)) + 2) - 3) + 3| + 3 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-2", "dataset": "MATH"} | |
| {"messages": [{"content": "Find the x-coordinate of the leftmost local extremum of the function f(x) = 2|(-3((-2(-2sin(3\u03c0x + 2)) + 3)/(3(-2sin(3\u03c0x + 2)) + 2))^2 + 5((-2(-2sin(3\u03c0x + 2)) + 3)/(3(-2sin(3\u03c0x + 2)) + 2)) + 3)| - 1 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-10", "dataset": "MATH"} | |
| {"messages": [{"content": "Find the x-coordinate of the leftmost local extremum of the function f(x) = -2cos(1\u03c0(-4(2|((-3x - 2)/(-3x + 4)) - 1| - 3)^2 - 2(2|((-3x - 2)/(-3x + 4)) - 1| - 3)) - 1) - 2 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-10", "dataset": "MATH"} | |
| {"messages": [{"content": "Find the x-coordinate of the leftmost local extremum of the function f(x) = 2sin(1\u03c0((-2(-3(-2|x - 1|)^2 + 1(-2|x - 1|) + 2) - 3)/(-3(-3(-2|x - 1|)^2 + 1(-2|x - 1|) + 2) - 1))) + 3 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"} | |
| {"messages": [{"content": "Find the x-coordinate of the local extremum with the largest y-value of the function f(x) = (2(1sin(2\u03c0(-1(-2|x - 3| - 1)^2 + 5(-2|x - 3| - 1) + 2) - 1) - 3) - 2)/(-3(1sin(2\u03c0(-1(-2|x - 3| - 1)^2 + 5(-2|x - 3| - 1) + 2) - 1) - 3) - 2) in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-10", "dataset": "MATH"} | |
| {"messages": [{"content": "Find the x-coordinate of the local minimum with the smallest y-value of the function f(x) = 3sin(2\u03c0((1(-3|(-4x^2 + 4) + 3| - 1) + 2)/(-3(-3|(-4x^2 + 4) + 3| - 1) + 2)) - 1) - 2 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-1", "dataset": "MATH"} | |
| {"messages": [{"content": "Find the average of all x-coordinates of local maxima of the function f(x) = 3cos(1\u03c0(4(1|((-1x - 1)/(-3x - 2)) + 1| - 1)^2 + 4(1|((-1x - 1)/(-3x - 2)) + 1| - 1) + 4) + 3) + 1 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-1", "dataset": "MATH"} | |
| {"messages": [{"content": "Find the x-coordinate of the leftmost local minimum of the function f(x) = (2(3(3cos(3\u03c0(3|x + 3| + 1) + 1) + 3)^2 + 3) - 2)/(2(3(3cos(3\u03c0(3|x + 3| + 1) + 1) + 3)^2 + 3) - 1) in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-10", "dataset": "MATH"} | |
| {"messages": [{"content": "Find the x-coordinate of the leftmost local maximum of the function f(x) = 1cos(1\u03c0((-3(-4(-2|x + 3| + 2)^2 - 4(-2|x + 3| + 2) - 3) + 3)/(-3(-4(-2|x + 3| + 2)^2 - 4(-2|x + 3| + 2) - 3) - 3)) - 1) - 3 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-4", "dataset": "MATH"} | |
| {"messages": [{"content": "Find the average of all x-coordinates of local maxima of the function f(x) = -2|(-1sin(3\u03c0(4((3x + 3)/(-3x))^2 + 5) + 1) + 2)| + 3 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"} | |
| {"messages": [{"content": "Find the average of all x-coordinates of local minima of the function f(x) = -1cos(3\u03c0((1(1(-2|x - 2| + 1)^2 + 2(-2|x - 2| + 1) - 4))/(2(1(-2|x - 2| + 1)^2 + 2(-2|x - 2| + 1) - 4) + 1)) - 1) - 1 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"} | |
| {"messages": [{"content": "Find the x-coordinate of the leftmost local extremum of the function f(x) = 1|(1sin(2\u03c0((-3(-3x^2 - 3x - 5))/(3(-3x^2 - 3x - 5) - 2)) + 1) + 3) - 3| + 1 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-1", "dataset": "MATH"} | |
| {"messages": [{"content": "How many local extrema (both minima and maxima) does the function f(x) = -3sin(1\u03c0(4(1|((3x - 3)/(-1x - 2)) - 2| - 2)^2 + 2) - 2) - 3 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "222", "dataset": "MATH"} | |