{"messages": [{"content": "Find the x-coordinate of the rightmost local extremum of the function f(x) = 3(-3|(1sin(2\u03c0(3((2x - 3)/(2x + 2)) - 4) - 3) - 3) + 2| - 2)^2 + 4(-3|(1sin(2\u03c0(3((2x - 3)/(2x + 2)) - 4) - 3) - 3) + 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": "9", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local maximum with the largest y-value of the function f(x) = -4((-2(-1(-3(3|x - 3| - 3)^2 + 1(3|x - 3| - 3)) - 3) + 3)/(-1(-1(-3(3|x - 3| - 3)^2 + 1(3|x - 3| - 3)) - 3) - 3))^2 + 1((-2(-1(-3(3|x - 3| - 3)^2 + 1(3|x - 3| - 3)) - 3) + 3)/(-1(-1(-3(3|x - 3| - 3)^2 + 1(3|x - 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": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the leftmost local minimum of the function f(x) = -1(-5(-1((3(-2|x - 1| - 1) + 2)/(1(-2|x - 1| - 1) + 3)) - 4)^2 + 5(-1((3(-2|x - 1| - 1) + 2)/(1(-2|x - 1| - 1) + 3)) - 4) - 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": "How many local minima does the function f(x) = -2|((2(-1(-2(-3x^2) + 5) + 5) - 3)/(1(-1(-2(-3x^2) + 5) + 5) + 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 x-coordinate of the local extremum with the smallest y-value of the function f(x) = 2|((1(-5(3cos(1\u03c0(2|x + 1| + 3) - 2) + 3)) - 3)/(-2(-5(3cos(1\u03c0(2|x + 1| + 3) - 2) + 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": "-1", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local minimum of the function f(x) = -4(3((2(3(-2x + 3)^2 - 1(-2x + 3) + 4) - 1)/(-2(3(-2x + 3)^2 - 1(-2x + 3) + 4) - 2)) + 2)^2 - 5(3((2(3(-2x + 3)^2 - 1(-2x + 3) + 4) - 1)/(-2(3(-2x + 3)^2 - 1(-2x + 3) + 4) - 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": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local maximum of the function f(x) = 3(2e^(-2(-5(-1|(4x^2 + 2x + 3) - 1| + 3) + 5)) + 2)^2 - 1(2e^(-2(-5(-1|(4x^2 + 2x + 3) - 1| + 3) + 5)) + 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": "0", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local minimum with the largest y-value of the function f(x) = 4(5((3(3cos(1\u03c0(-1x + 3) + 1) - 3) + 2)/(-1(3cos(1\u03c0(-1x + 3) + 1) - 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 x-coordinate of the rightmost local extremum of the function f(x) = (2(1e^(-2(-2|(3|(-2|x + 3| - 1) - 3| - 1) + 3| - 2)) - 3))/(3(1e^(-2(-2|(3|(-2|x + 3| - 1) - 3| - 1) + 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": "-2", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local minimum of the function f(x) = 2|(5(-1(2|(-2e^(2x) + 3) - 2| - 2) + 1)^2 + 5(-1(2|(-2e^(2x) + 3) - 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": "0", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the rightmost local extremum of the function f(x) = -1cos(3\u03c0(-4(-4(5(-3|x + 3| + 2)^2 - 5(-3|x + 3| + 2) - 2)^2 - 5(5(-3|x + 3| + 2)^2 - 5(-3|x + 3| + 2) - 2))^2 + 3(-4(5(-3|x + 3| + 2)^2 - 5(-3|x + 3| + 2) - 2)^2 - 5(5(-3|x + 3| + 2)^2 - 5(-3|x + 3| + 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": "How many local minima does the function f(x) = 3(-3cos(2\u03c0((-1(-3(-2|x - 1|)^2 + 1(-2|x - 1|) - 3))/(-2(-3(-2|x - 1|)^2 + 1(-2|x - 1|) - 3) + 3)) + 3) + 3) - 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 maximum of the function f(x) = (3((-1((1(1(-1sin(2\u03c0x - 3) - 2) - 5) + 3)/(3(1(-1sin(2\u03c0x - 3) - 2) - 5))))/(2((1(1(-1sin(2\u03c0x - 3) - 2) - 5) + 3)/(3(1(-1sin(2\u03c0x - 3) - 2) - 5))) + 2)) + 1)/(2((-1((1(1(-1sin(2\u03c0x - 3) - 2) - 5) + 3)/(3(1(-1sin(2\u03c0x - 3) - 2) - 5))))/(2((1(1(-1sin(2\u03c0x - 3) - 2) - 5) + 3)/(3(1(-1sin(2\u03c0x - 3) - 2) - 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": "9", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the leftmost local maximum of the function f(x) = 2cos(3\u03c0(-1(5(1|(4x - 4) + 1| - 2)^2 - 2)^2 + 1(5(1|(4x - 4) + 1| - 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": "-1", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the leftmost local extremum of the function f(x) = 4(3cos(3\u03c0(1(-1(1|x + 1| - 2) - 2)^2 - 3(-1(1|x + 1| - 2) - 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": "-10", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the leftmost local maximum of the function f(x) = -1(2|((-2(-1|(-4x^2 + 3x - 3) + 1| + 1) + 2)/(-1(-1|(-4x^2 + 3x - 3) + 1| + 1) - 2)) - 2| + 3)^2 + 3(2|((-2(-1|(-4x^2 + 3x - 3) + 1| + 1) + 2)/(-1(-1|(-4x^2 + 3x - 3) + 1| + 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 x-coordinate of the rightmost local extremum of the function f(x) = 3(2e^(-2(-2|(-1(-1|x + 3| - 1)) - 2| - 2)) - 1)^2 + 1(2e^(-2(-2|(-1(-1|x + 3| - 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": "Find the x-coordinate of the local maximum with the largest y-value of the function f(x) = -2(-5(3sin(3\u03c0(-1|(2|x + 1| + 3) + 1| - 2) - 3)) + 2)^2 - 2(-5(3sin(3\u03c0(-1|(2|x + 1| + 3) + 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": "-10", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the leftmost local maximum of the function f(x) = -3sin(2\u03c0((3(1|((3(-1|x - 3| - 3) - 1)/(-1(-1|x - 3| - 3) + 2))| + 2) + 1)/(-1(1|((3(-1|x - 3| - 3) - 1)/(-1(-1|x - 3| - 3) + 2))| + 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 minimum with the smallest y-value of the function f(x) = 1|(-1cos(3\u03c0(2|(5(4x) - 4) + 1| + 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": "-10", "dataset": "MATH"}
{"messages": [{"content": "How many local minima does the function f(x) = 1|(3((-2(-4((2x + 2)/(-3x + 4)) + 1) - 2)/(3(-4((2x + 2)/(-3x + 4)) + 1) + 2))^2 + 2((-2(-4((2x + 2)/(-3x + 4)) + 1) - 2)/(3(-4((2x + 2)/(-3x + 4)) + 1) + 2)) - 5) + 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 local extremum with the smallest y-value of the function f(x) = -2((2(3((3(2x + 4) + 2)/(1(2x + 4)))^2 + 2((3(2x + 4) + 2)/(1(2x + 4))) - 3) + 3)/(2(3((3(2x + 4) + 2)/(1(2x + 4)))^2 + 2((3(2x + 4) + 2)/(1(2x + 4))) - 3) - 1))^2 + 5((2(3((3(2x + 4) + 2)/(1(2x + 4)))^2 + 2((3(2x + 4) + 2)/(1(2x + 4))) - 3) + 3)/(2(3((3(2x + 4) + 2)/(1(2x + 4)))^2 + 2((3(2x + 4) + 2)/(1(2x + 4))) - 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": "-2", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local extremum of the function f(x) = (-3(-1|((2((-3(-1|x|))/(-1(-1|x|) + 2)) + 3)/(-1((-3(-1|x|))/(-1(-1|x|) + 2)) + 3)) - 1| + 1))/(1(-1|((2((-3(-1|x|))/(-1(-1|x|) + 2)) + 3)/(-1((-3(-1|x|))/(-1(-1|x|) + 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": "0", "dataset": "MATH"}
{"messages": [{"content": "Find the average of all x-coordinates of local minima of the function f(x) = -4(1((-1(-1sin(1\u03c0(-3|x + 1|)) - 1) + 3)/(1(-1sin(1\u03c0(-3|x + 1|)) - 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 average of all x-coordinates of local extrema of the function f(x) = (1(2cos(1\u03c0(-2(-5(-5x^2 - 2x - 2)^2 + 4(-5x^2 - 2x - 2) - 3)^2 - 3(-5(-5x^2 - 2x - 2)^2 + 4(-5x^2 - 2x - 2) - 3) + 2) + 1) - 2) + 3)/(-1(2cos(1\u03c0(-2(-5(-5x^2 - 2x - 2)^2 + 4(-5x^2 - 2x - 2) - 3)^2 - 3(-5(-5x^2 - 2x - 2)^2 + 4(-5x^2 - 2x - 2) - 3) + 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": "Find the x-coordinate of the leftmost local extremum of the function f(x) = 5(-3sin(3\u03c0(4((2(-1x^2 + 4x + 5) + 2)/(-2(-1x^2 + 4x + 5) - 3))^2 + 5((2(-1x^2 + 4x + 5) + 2)/(-2(-1x^2 + 4x + 5) - 3)) - 2) + 3) - 1)^2 + 4(-3sin(3\u03c0(4((2(-1x^2 + 4x + 5) + 2)/(-2(-1x^2 + 4x + 5) - 3))^2 + 5((2(-1x^2 + 4x + 5) + 2)/(-2(-1x^2 + 4x + 5) - 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": "-2", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local maximum with the largest y-value of the function f(x) = (1(-2(-4(3|(4x^2 - 1x) + 2| + 3)^2 - 1(3|(4x^2 - 1x) + 2| + 3) + 2)^2 + 2(-4(3|(4x^2 - 1x) + 2| + 3)^2 - 1(3|(4x^2 - 1x) + 2| + 3) + 2) + 4) + 2)/(1(-2(-4(3|(4x^2 - 1x) + 2| + 3)^2 - 1(3|(4x^2 - 1x) + 2| + 3) + 2)^2 + 2(-4(3|(4x^2 - 1x) + 2| + 3)^2 - 1(3|(4x^2 - 1x) + 2| + 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 extremum with the smallest y-value of the function f(x) = -2(1((-2(3(-1cos(3\u03c0x + 2) - 1)^2 - 5(-1cos(3\u03c0x + 2) - 1) + 3) - 3)/(-2(3(-1cos(3\u03c0x + 2) - 1)^2 - 5(-1cos(3\u03c0x + 2) - 1) + 3) + 3))^2 + 2((-2(3(-1cos(3\u03c0x + 2) - 1)^2 - 5(-1cos(3\u03c0x + 2) - 1) + 3) - 3)/(-2(3(-1cos(3\u03c0x + 2) - 1)^2 - 5(-1cos(3\u03c0x + 2) - 1) + 3) + 3)) + 3)^2 + 2(1((-2(3(-1cos(3\u03c0x + 2) - 1)^2 - 5(-1cos(3\u03c0x + 2) - 1) + 3) - 3)/(-2(3(-1cos(3\u03c0x + 2) - 1)^2 - 5(-1cos(3\u03c0x + 2) - 1) + 3) + 3))^2 + 2((-2(3(-1cos(3\u03c0x + 2) - 1)^2 - 5(-1cos(3\u03c0x + 2) - 1) + 3) - 3)/(-2(3(-1cos(3\u03c0x + 2) - 1)^2 - 5(-1cos(3\u03c0x + 2) - 1) + 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": "-10", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the rightmost local maximum of the function f(x) = (-1(1(2(5(1x^2 - 2x - 1)^2 + 4(1x^2 - 2x - 1))^2 + 3(5(1x^2 - 2x - 1)^2 + 4(1x^2 - 2x - 1)) + 3)^2 + 3(2(5(1x^2 - 2x - 1)^2 + 4(1x^2 - 2x - 1))^2 + 3(5(1x^2 - 2x - 1)^2 + 4(1x^2 - 2x - 1)) + 3)) + 2)/(1(1(2(5(1x^2 - 2x - 1)^2 + 4(1x^2 - 2x - 1))^2 + 3(5(1x^2 - 2x - 1)^2 + 4(1x^2 - 2x - 1)) + 3)^2 + 3(2(5(1x^2 - 2x - 1)^2 + 4(1x^2 - 2x - 1))^2 + 3(5(1x^2 - 2x - 1)^2 + 4(1x^2 - 2x - 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) = 3|(-1(3e^(2(2(-2|x + 2| + 2)^2 - 1(-2|x + 2| + 2) + 4)) + 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": "-3", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local minimum with the largest y-value of the function f(x) = 2cos(2\u03c0((3(2((-2((-3x + 1)/(-1x + 2)) + 2)/(3((-3x + 1)/(-1x + 2)) + 3)) - 4) - 3)/(1(2((-2((-3x + 1)/(-1x + 2)) + 2)/(3((-3x + 1)/(-1x + 2)) + 3)) - 4))) - 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": "-6", "dataset": "MATH"}
{"messages": [{"content": "Find the average of all x-coordinates of local extrema of the function f(x) = 1(-2|(4((2(-3|x - 1| + 2) - 3)/(-2(-3|x - 1| + 2) - 2))^2 - 1((2(-3|x - 1| + 2) - 3)/(-2(-3|x - 1| + 2) - 2)) - 4) + 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": "How many local minima does the function f(x) = (-2(3|(1|((-1(3e^(2x)) + 1)/(1(3e^(2x)) - 3)) - 2| - 3) + 2| + 2) - 1)/(2(3|(1|((-1(3e^(2x)) + 1)/(1(3e^(2x)) - 3)) - 2| - 3) + 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 rightmost local minimum of the function f(x) = 2|(-2sin(2\u03c0(-1(4(1x + 2) + 2) - 5) + 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 local minimum with the smallest y-value of the function f(x) = 4((-1((-3(-1((1x - 2)/(2x - 1)) - 3) - 3)/(-2(-1((1x - 2)/(2x - 1)) - 3) + 3)) + 1)/(2((-3(-1((1x - 2)/(2x - 1)) - 3) - 3)/(-2(-1((1x - 2)/(2x - 1)) - 3) + 3)) + 3))^2 - 1((-1((-3(-1((1x - 2)/(2x - 1)) - 3) - 3)/(-2(-1((1x - 2)/(2x - 1)) - 3) + 3)) + 1)/(2((-3(-1((1x - 2)/(2x - 1)) - 3) - 3)/(-2(-1((1x - 2)/(2x - 1)) - 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": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local extremum of the function f(x) = 1|(-2((1((-3(2x^2 - 4x + 4))/(2(2x^2 - 4x + 4) - 1)) - 1)/(-3((-3(2x^2 - 4x + 4))/(2(2x^2 - 4x + 4) - 1)) - 3))^2 + 5((1((-3(2x^2 - 4x + 4))/(2(2x^2 - 4x + 4) - 1)) - 1)/(-3((-3(2x^2 - 4x + 4))/(2(2x^2 - 4x + 4) - 1)) - 3)) + 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": "Find the average of all x-coordinates of local extrema of the function f(x) = (3(-3|((-2(3|(-1sin(3\u03c0x) + 3) - 1| - 3) - 1)/(-1(3|(-1sin(3\u03c0x) + 3) - 1| - 3) - 1)) - 3|) + 1)/(3(-3|((-2(3|(-1sin(3\u03c0x) + 3) - 1| - 3) - 1)/(-1(3|(-1sin(3\u03c0x) + 3) - 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": "0", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local extremum of the function f(x) = -5((-2(-2|(5(4x + 2)^2 + 2(4x + 2) - 5) + 1| + 1) - 1)/(2(-2|(5(4x + 2)^2 + 2(4x + 2) - 5) + 1| + 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": "-1", "dataset": "MATH"}
{"messages": [{"content": "How many local extrema (both minima and maxima) does the function f(x) = (2(1(-4(4(-1|x| - 2)^2 + 3(-1|x| - 2) - 3)^2 - 1(4(-1|x| - 2)^2 + 3(-1|x| - 2) - 3) + 1)^2 - 5(-4(4(-1|x| - 2)^2 + 3(-1|x| - 2) - 3)^2 - 1(4(-1|x| - 2)^2 + 3(-1|x| - 2) - 3) + 1) - 1) - 1)/(3(1(-4(4(-1|x| - 2)^2 + 3(-1|x| - 2) - 3)^2 - 1(4(-1|x| - 2)^2 + 3(-1|x| - 2) - 3) + 1)^2 - 5(-4(4(-1|x| - 2)^2 + 3(-1|x| - 2) - 3)^2 - 1(4(-1|x| - 2)^2 + 3(-1|x| - 2) - 3) + 1) - 1) + 1) have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "77", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local minimum of the function f(x) = -2(-2((-1(3(-1|x + 1| + 1)^2 + 1(-1|x + 1| + 1) + 2) + 3)/(-2(3(-1|x + 1| + 1)^2 + 1(-1|x + 1| + 1) + 2) + 3))^2 + 4((-1(3(-1|x + 1| + 1)^2 + 1(-1|x + 1| + 1) + 2) + 3)/(-2(3(-1|x + 1| + 1)^2 + 1(-1|x + 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": "-1", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the rightmost local extremum of the function f(x) = (-3(-4(3|((1(-2|x + 2| + 1) - 1)/(3(-2|x + 2| + 1) - 2)) - 3|)^2 + 3(3|((1(-2|x + 2| + 1) - 1)/(3(-2|x + 2| + 1) - 2)) - 3|) + 2) + 2)/(-2(-4(3|((1(-2|x + 2| + 1) - 1)/(3(-2|x + 2| + 1) - 2)) - 3|)^2 + 3(3|((1(-2|x + 2| + 1) - 1)/(3(-2|x + 2| + 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": "-2", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local minimum with the largest y-value of the function f(x) = 4(2(-1|(5(2cos(1\u03c0x + 3) - 1)^2 + 3(2cos(1\u03c0x + 3) - 1) + 1) - 2| + 2)^2 + 3(-1|(5(2cos(1\u03c0x + 3) - 1)^2 + 3(2cos(1\u03c0x + 3) - 1) + 1) - 2| + 2) - 5) - 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 maxima of the function f(x) = -1e^(-1(-1|(-1|((2(2x - 3) - 1)/(-3(2x - 3) - 3)) - 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 average of all x-coordinates of local maxima of the function f(x) = -3|(1sin(2\u03c0(-3(-2|(4x + 5)| + 1) - 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 local maximum with the largest y-value of the function f(x) = -1(-1|(-2|((1(2sin(2\u03c0x + 2) - 1) - 2)/(2(2sin(2\u03c0x + 2) - 1) - 3))| + 1) - 1| - 1)^2 - 5(-1|(-2|((1(2sin(2\u03c0x + 2) - 1) - 2)/(2(2sin(2\u03c0x + 2) - 1) - 3))| + 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": "-10", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local minimum of the function f(x) = 3e^(-1(5(1|(-2|(1|x - 3| - 1) - 2| - 2) + 1| + 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": "7", "dataset": "MATH"}
{"messages": [{"content": "How many local minima does the function f(x) = 1|(3cos(3\u03c0(-2|((-1(2|x + 2| - 3) - 1)/(2(2|x + 2| - 3))) + 2| - 2) - 1) + 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": "How many local minima does the function f(x) = -2|(-1|(5(-3(-4x^2 + 2x - 4)^2 - 2(-4x^2 + 2x - 4) + 5)^2 + 1(-3(-4x^2 + 2x - 4)^2 - 2(-4x^2 + 2x - 4) + 5) + 3) + 3| + 3) + 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": "Find the x-coordinate of the local maximum with the largest y-value of the function f(x) = 1cos(3\u03c0(-4(-1|((2(-1x - 5) - 1)/(-2(-1x - 5))) - 3| - 1)^2 + 5(-1|((2(-1x - 5) - 1)/(-2(-1x - 5))) - 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 average of all x-coordinates of local minima of the function f(x) = 3|(3sin(3\u03c0(-1|((1(5x + 5) - 3)/(-3(5x + 5) + 4)) + 2| - 2) - 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 x-coordinate of the leftmost local maximum of the function f(x) = 3|((-2(-4(1sin(2\u03c0((-1x + 3)/(-2x - 2)) + 3) - 2)^2 + 5(1sin(2\u03c0((-1x + 3)/(-2x - 2)) + 3) - 2) - 5) - 3)/(-1(-4(1sin(2\u03c0((-1x + 3)/(-2x - 2)) + 3) - 2)^2 + 5(1sin(2\u03c0((-1x + 3)/(-2x - 2)) + 3) - 2) - 5) + 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": "-4", "dataset": "MATH"}
{"messages": [{"content": "Find the average of all x-coordinates of local extrema of the function f(x) = 1cos(1\u03c0(3(4((2(3x^2 - 4x - 4) + 3)/(-1(3x^2 - 4x - 4) + 2))^2 - 4((2(3x^2 - 4x - 4) + 3)/(-1(3x^2 - 4x - 4) + 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": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local extremum of the function f(x) = (-1(-1((2(2|(3|x|) + 3|))/(-3(2|(3|x|) + 3|) - 3))^2 - 4((2(2|(3|x|) + 3|))/(-3(2|(3|x|) + 3|) - 3)) - 3) + 1)/(2(-1((2(2|(3|x|) + 3|))/(-3(2|(3|x|) + 3|) - 3))^2 - 4((2(2|(3|x|) + 3|))/(-3(2|(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": "0", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local maximum with the smallest y-value of the function f(x) = (-1(3|((2(-4(-3|x - 3| + 2) + 5) + 3)/(1(-4(-3|x - 3| + 2) + 5) + 2)) + 2|))/(-1(3|((2(-4(-3|x - 3| + 2) + 5) + 3)/(1(-4(-3|x - 3| + 2) + 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": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the leftmost local extremum of the function f(x) = -4(-4(-3|(5((2x - 1)/(-1x - 2)) + 2) + 3| + 3)^2 - 4(-3|(5((2x - 1)/(-1x - 2)) + 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": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local maximum with the largest y-value of the function f(x) = (-3(4(2cos(3\u03c0(3(4x^2 - 2x + 1)^2 + 4(4x^2 - 2x + 1) + 4) + 1) - 3)^2 + 5(2cos(3\u03c0(3(4x^2 - 2x + 1)^2 + 4(4x^2 - 2x + 1) + 4) + 1) - 3) - 1) - 2)/(-1(4(2cos(3\u03c0(3(4x^2 - 2x + 1)^2 + 4(4x^2 - 2x + 1) + 4) + 1) - 3)^2 + 5(2cos(3\u03c0(3(4x^2 - 2x + 1)^2 + 4(4x^2 - 2x + 1) + 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": "0", "dataset": "MATH"}
{"messages": [{"content": "Find the average of all x-coordinates of local extrema of the function f(x) = 1((2(2|((2(-4x - 3) + 2)/(-3(-4x - 3) - 3)) - 1| - 2))/(-1(2|((2(-4x - 3) + 2)/(-3(-4x - 3) - 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": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local minimum with the largest y-value of the function f(x) = -4(-2|(1(2sin(2\u03c0(2|x + 3| - 1) + 1)) - 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 local minimum of the function f(x) = (-3(-1(-2((-3(1x + 4) - 3)/(-2(1x + 4) - 1))^2 - 3((-3(1x + 4) - 3)/(-2(1x + 4) - 1)) - 1)) - 3)/(2(-1(-2((-3(1x + 4) - 3)/(-2(1x + 4) - 1))^2 - 3((-3(1x + 4) - 3)/(-2(1x + 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": "-5", "dataset": "MATH"}
{"messages": [{"content": "How many local minima does the function f(x) = -1|(5(1((-2(-4x^2 + 1x - 5))/(-3(-4x^2 + 1x - 5) + 4))^2 + 4((-2(-4x^2 + 1x - 5))/(-3(-4x^2 + 1x - 5) + 4)) + 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 leftmost local extremum of the function f(x) = -3(-2|(-2(1(3x^2 + 3x - 2)^2 + 5(3x^2 + 3x - 2) - 3) - 4) + 1| - 2)^2 + 4(-2|(-2(1(3x^2 + 3x - 2)^2 + 5(3x^2 + 3x - 2) - 3) - 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": "-2", "dataset": "MATH"}
{"messages": [{"content": "Find the average of all x-coordinates of local maxima of the function f(x) = (2(-1(-1|(5(2e^(2x) + 2) + 4) - 3| + 2)^2 + 2(-1|(5(2e^(2x) + 2) + 4) - 3| + 2) - 4) + 2)/(-1(-1(-1|(5(2e^(2x) + 2) + 4) - 3| + 2)^2 + 2(-1|(5(2e^(2x) + 2) + 4) - 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": "6", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the leftmost local extremum of the function f(x) = 1|(1cos(3\u03c0(-4((-1((-2x - 3)/(-1x + 3)) - 3)/(2((-2x - 3)/(-1x + 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": "-4", "dataset": "MATH"}
{"messages": [{"content": "Find the average of all x-coordinates of local extrema of the function f(x) = (-2(-3(-4((-2(3x^2 - 3x - 5) + 3)/(3(3x^2 - 3x - 5) - 1))^2 + 3((-2(3x^2 - 3x - 5) + 3)/(3(3x^2 - 3x - 5) - 1)) + 5) - 5) + 2)/(2(-3(-4((-2(3x^2 - 3x - 5) + 3)/(3(3x^2 - 3x - 5) - 1))^2 + 3((-2(3x^2 - 3x - 5) + 3)/(3(3x^2 - 3x - 5) - 1)) + 5) - 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": "0", "dataset": "MATH"}
{"messages": [{"content": "Find the average of all x-coordinates of local maxima of the function f(x) = 2|(-1(2|(-5(3cos(2\u03c0x + 2) + 1) + 5) + 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": "How many local extrema (both minima and maxima) does the function f(x) = 2cos(2\u03c0(3(2|(-3(5x^2 + 5x + 1) + 4) + 3| - 1) + 1) + 3) - 2 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "406", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local extremum of the function f(x) = -3|((-3(-2e^(-1(3|((-1x - 2)/(-2x - 1))| - 2)) - 2) - 1)/(3(-2e^(-1(3|((-1x - 2)/(-2x - 1))| - 2)) - 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": "How many local minima does the function f(x) = -3(1|(-1((2(-2x) + 1)/(2(-2x) + 3)) + 1) - 1|)^2 - 2(1|(-1((2(-2x) + 1)/(2(-2x) + 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": "How many local minima does the function f(x) = -2(3|((-1(-1(3x - 4)^2 - 4(3x - 4) - 3))/(1(-1(3x - 4)^2 - 4(3x - 4) - 3) - 2))| - 3)^2 + 2(3|((-1(-1(3x - 4)^2 - 4(3x - 4) - 3))/(1(-1(3x - 4)^2 - 4(3x - 4) - 3) - 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": "How many local minima does the function f(x) = -1((-2(4((-2(-2cos(1\u03c0x - 3) - 1) + 3)/(-2(-2cos(1\u03c0x - 3) - 1) + 1)) + 3) + 3)/(-1(4((-2(-2cos(1\u03c0x - 3) - 1) + 3)/(-2(-2cos(1\u03c0x - 3) - 1) + 1)) + 3) - 2))^2 - 4((-2(4((-2(-2cos(1\u03c0x - 3) - 1) + 3)/(-2(-2cos(1\u03c0x - 3) - 1) + 1)) + 3) + 3)/(-1(4((-2(-2cos(1\u03c0x - 3) - 1) + 3)/(-2(-2cos(1\u03c0x - 3) - 1) + 1)) + 3) - 2)) - 5 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) = (-3(-3(3(-5((3x)/(1x + 1)) + 5)^2 + 4(-5((3x)/(1x + 1)) + 5) - 2)^2 - 1(3(-5((3x)/(1x + 1)) + 5)^2 + 4(-5((3x)/(1x + 1)) + 5) - 2) + 1) + 1)/(-1(-3(3(-5((3x)/(1x + 1)) + 5)^2 + 4(-5((3x)/(1x + 1)) + 5) - 2)^2 - 1(3(-5((3x)/(1x + 1)) + 5)^2 + 4(-5((3x)/(1x + 1)) + 5) - 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 rightmost local maximum of the function f(x) = -3e^(2(2|(-1(1((2x - 3)/(2x)) - 5)^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": "0", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the leftmost local minimum of the function f(x) = (-1(2(3|(2cos(2\u03c0((3x + 3)/(2x)) + 2) - 2) + 2| - 3) - 5) - 2)/(-3(2(3|(2cos(2\u03c0((3x + 3)/(2x)) + 2) - 2) + 2| - 3) - 5) + 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": "-5", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local minimum with the smallest y-value of the function f(x) = -1(-1|(-3|(2(1sin(3\u03c0x) - 2)^2 + 2) - 2| + 3) - 1|)^2 + 5(-1|(-3|(2(1sin(3\u03c0x) - 2)^2 + 2) - 2| + 3) - 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": "-10", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local maximum of the function f(x) = 2((-2(5((-2((3x + 1)/(2x + 3)) - 2)/(-3((3x + 1)/(2x + 3)) - 2))^2) + 1)/(-2(5((-2((3x + 1)/(2x + 3)) - 2)/(-3((3x + 1)/(2x + 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 local extremum of the function f(x) = (-3(1|(2|((-1(1x^2 + 5) - 2)/(-3(1x^2 + 5) - 3)) + 2|)| + 1) - 1)/(3(1|(2|((-1(1x^2 + 5) - 2)/(-3(1x^2 + 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": "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((2(-4((-2x - 3)/(-2x + 3))^2 + 2((-2x - 3)/(-2x + 3)) - 3))/(-3(-4((-2x - 3)/(-2x + 3))^2 + 2((-2x - 3)/(-2x + 3)) - 3) + 4)) + 3)/(-1((2(-4((-2x - 3)/(-2x + 3))^2 + 2((-2x - 3)/(-2x + 3)) - 3))/(-3(-4((-2x - 3)/(-2x + 3))^2 + 2((-2x - 3)/(-2x + 3)) - 3) + 4)) + 2)) + 2)/(-3((2((2(-4((-2x - 3)/(-2x + 3))^2 + 2((-2x - 3)/(-2x + 3)) - 3))/(-3(-4((-2x - 3)/(-2x + 3))^2 + 2((-2x - 3)/(-2x + 3)) - 3) + 4)) + 3)/(-1((2(-4((-2x - 3)/(-2x + 3))^2 + 2((-2x - 3)/(-2x + 3)) - 3))/(-3(-4((-2x - 3)/(-2x + 3))^2 + 2((-2x - 3)/(-2x + 3)) - 3) + 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": "-2", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the rightmost local extremum of the function f(x) = -1(2(-1(4(1sin(2\u03c0x + 3))^2 - 4(1sin(2\u03c0x + 3)) - 3) + 2)^2 + 5(-1(4(1sin(2\u03c0x + 3))^2 - 4(1sin(2\u03c0x + 3)) - 3) + 2) + 3)^2 + 3(2(-1(4(1sin(2\u03c0x + 3))^2 - 4(1sin(2\u03c0x + 3)) - 3) + 2)^2 + 5(-1(4(1sin(2\u03c0x + 3))^2 - 4(1sin(2\u03c0x + 3)) - 3) + 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) = 5(3cos(1\u03c0(-1|(-1|(-1|x + 2| - 2) - 2| - 2) - 1| - 1) - 1) - 2)^2 + 3(3cos(1\u03c0(-1|(-1|(-1|x + 2| - 2) - 2| - 2) - 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": "-2", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local maximum of the function f(x) = (2((1((2(-5(-1|x| - 3) - 3))/(-1(-5(-1|x| - 3) - 3) - 1)) - 2)/(-1((2(-5(-1|x| - 3) - 3))/(-1(-5(-1|x| - 3) - 3) - 1)) + 3)) - 1)/(2((1((2(-5(-1|x| - 3) - 3))/(-1(-5(-1|x| - 3) - 3) - 1)) - 2)/(-1((2(-5(-1|x| - 3) - 3))/(-1(-5(-1|x| - 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": "0", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local minimum with the largest y-value of the function f(x) = 4(-5(-2|(-3|(-1x + 2) + 1|) + 2| - 3)^2 - 1(-2|(-3|(-1x + 2) + 1|) + 2| - 3) + 1)^2 + 1(-5(-2|(-3|(-1x + 2) + 1|) + 2| - 3)^2 - 1(-2|(-3|(-1x + 2) + 1|) + 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": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local minimum with the smallest y-value of the function f(x) = (2(-5((-1(-3|(1|x| - 3)| + 1) - 2)/(1(-3|(1|x| - 3)| + 1)))^2 - 5((-1(-3|(1|x| - 3)| + 1) - 2)/(1(-3|(1|x| - 3)| + 1))) - 1) - 1)/(1(-5((-1(-3|(1|x| - 3)| + 1) - 2)/(1(-3|(1|x| - 3)| + 1)))^2 - 5((-1(-3|(1|x| - 3)| + 1) - 2)/(1(-3|(1|x| - 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": "-5", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the leftmost local extremum of the function f(x) = 3|(2(-4(-2cos(2\u03c0(-2|x - 1| + 1) + 1) - 1)^2 + 1(-2cos(2\u03c0(-2|x - 1| + 1) + 1) - 1) + 3)^2 + 3(-4(-2cos(2\u03c0(-2|x - 1| + 1) + 1) - 1)^2 + 1(-2cos(2\u03c0(-2|x - 1| + 1) + 1) - 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 average of all x-coordinates of local extrema of the function f(x) = 3(-3(-5(1|(3sin(1\u03c0x - 2) + 1)| + 1)^2 - 5(1|(3sin(1\u03c0x - 2) + 1)| + 1) - 5)^2 + 2)^2 + 2(-3(-5(1|(3sin(1\u03c0x - 2) + 1)| + 1)^2 - 5(1|(3sin(1\u03c0x - 2) + 1)| + 1) - 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": "0", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the leftmost local maximum of the function f(x) = 2(4(3cos(3\u03c0(1|(4x - 1) + 1| + 1) + 1)) - 1)^2 - 5(4(3cos(3\u03c0(1|(4x - 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": "-10", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local minimum of the function f(x) = 4((-2((2(4((1x)/(-1x + 2))^2 + 4((1x)/(-1x + 2)) - 2) - 3)/(1(4((1x)/(-1x + 2))^2 + 4((1x)/(-1x + 2)) - 2))) + 1)/(2((2(4((1x)/(-1x + 2))^2 + 4((1x)/(-1x + 2)) - 2) - 3)/(1(4((1x)/(-1x + 2))^2 + 4((1x)/(-1x + 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": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the average of all x-coordinates of local minima of the function f(x) = -3(2sin(3\u03c0(2|(-3(2x^2 + 1)^2 + 1(2x^2 + 1) - 2) - 3| + 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": "0", "dataset": "MATH"}
{"messages": [{"content": "How many local minima does the function f(x) = 4(3|(5(1|(2x^2 + 3x) + 1| + 2) + 5) - 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 x-coordinate of the local minimum with the largest y-value of the function f(x) = 2|((-3(3cos(3\u03c0(1(-1x^2 - 2x + 2)^2 + 3) - 1) - 1) + 1)/(2(3cos(3\u03c0(1(-1x^2 - 2x + 2)^2 + 3) - 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": "-10", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the rightmost local extremum of the function f(x) = -2cos(1\u03c0((-3(2|((3((2x)/(-2x - 2)) + 1)/(-1((2x)/(-2x - 2)) + 2)) + 1| - 2) + 1)/(2(2|((3((2x)/(-2x - 2)) + 1)/(-1((2x)/(-2x - 2)) + 2)) + 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": "4", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local maximum with the largest y-value of the function f(x) = 4(-5(2(-3e^(1((-2x)/(3x - 2))) + 3)^2 - 3(-3e^(1((-2x)/(3x - 2))) + 3) - 1)^2 - 5(2(-3e^(1((-2x)/(3x - 2))) + 3)^2 - 3(-3e^(1((-2x)/(3x - 2))) + 3) - 1) - 1)^2 + 4(-5(2(-3e^(1((-2x)/(3x - 2))) + 3)^2 - 3(-3e^(1((-2x)/(3x - 2))) + 3) - 1)^2 - 5(2(-3e^(1((-2x)/(3x - 2))) + 3)^2 - 3(-3e^(1((-2x)/(3x - 2))) + 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": "-1", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local maximum of the function f(x) = (-1((1((2(-4(1x^2 + 3x) + 1) - 3)/(-2(-4(1x^2 + 3x) + 1) - 2)) - 2)/(-3((2(-4(1x^2 + 3x) + 1) - 3)/(-2(-4(1x^2 + 3x) + 1) - 2)) - 1)))/(3((1((2(-4(1x^2 + 3x) + 1) - 3)/(-2(-4(1x^2 + 3x) + 1) - 2)) - 2)/(-3((2(-4(1x^2 + 3x) + 1) - 3)/(-2(-4(1x^2 + 3x) + 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": "-2", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local maximum of the function f(x) = (1(-1((1((-3(-2x^2 - 5x + 5))/(-1(-2x^2 - 5x + 5) - 2)) + 2)/(-3((-3(-2x^2 - 5x + 5))/(-1(-2x^2 - 5x + 5) - 2)) + 2))) - 2)/(-2(-1((1((-3(-2x^2 - 5x + 5))/(-1(-2x^2 - 5x + 5) - 2)) + 2)/(-3((-3(-2x^2 - 5x + 5))/(-1(-2x^2 - 5x + 5) - 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 leftmost local extremum of the function f(x) = -3|(-2(-1(-1cos(3\u03c0((1x)/(2x + 3)) - 3)) - 5)^2 + 4(-1(-1cos(3\u03c0((1x)/(2x + 3)) - 3)) - 5) - 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": "-6", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local extremum with the largest y-value of the function f(x) = 3(-2sin(3\u03c0(1(5(-3x^2 - 3x + 5) + 1)^2 + 2(5(-3x^2 - 3x + 5) + 1) + 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": "-3", "dataset": "MATH"}
{"messages": [{"content": "How many local maxima does the function f(x) = -1|(1(2|(3sin(1\u03c0(-2x - 5) - 1)) - 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": "How many local minima does the function f(x) = -2(2cos(1\u03c0((1(-2|((1x + 3)/(-3x - 2)) + 3| - 3) - 3)/(-2(-2|((1x + 3)/(-3x - 2)) + 3| - 3) - 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": "How many local extrema (both minima and maxima) does the function f(x) = 4((-1(2sin(3\u03c0(-1(4x^2 + 4x + 5)^2 - 1(4x^2 + 4x + 5) - 3) - 2)) - 1)/(-3(2sin(3\u03c0(-1(4x^2 + 4x + 5)^2 - 1(4x^2 + 4x + 5) - 3) - 2)) + 1)) - 3 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "159", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the rightmost local extremum of the function f(x) = -2(3((-1(3(5x^2 + 5x + 1)^2 + 1) - 1)/(-1(3(5x^2 + 5x + 1)^2 + 1) + 3)) + 2)^2 - 2(3((-1(3(5x^2 + 5x + 1)^2 + 1) - 1)/(-1(3(5x^2 + 5x + 1)^2 + 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": "0", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local extremum of the function f(x) = (-1(-2((1((-2(1x^2 - 2x - 1) - 1)/(2(1x^2 - 2x - 1) - 3)) - 3)/(1((-2(1x^2 - 2x - 1) - 1)/(2(1x^2 - 2x - 1) - 3)) + 2)) - 5))/(2(-2((1((-2(1x^2 - 2x - 1) - 1)/(2(1x^2 - 2x - 1) - 3)) - 3)/(1((-2(1x^2 - 2x - 1) - 1)/(2(1x^2 - 2x - 1) - 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": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local maximum with the smallest y-value of the function f(x) = (-1(4(2(-2sin(1\u03c0(1x - 5) + 2) - 3) - 2) - 2) + 1)/(-1(4(2(-2sin(1\u03c0(1x - 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": "-9", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local maximum of the function f(x) = (2(1(5(-2(-2x^2 + 1x + 4)^2 + 2(-2x^2 + 1x + 4) + 3) + 5) + 2) + 2)/(2(1(5(-2(-2x^2 + 1x + 4)^2 + 2(-2x^2 + 1x + 4) + 3) + 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 x-coordinate of the rightmost local extremum of the function f(x) = 1((2(3e^(-2((-3(-2|x - 1| + 2) + 1)/(-3(-2|x - 1| + 2) + 4))) + 3) - 3)/(3(3e^(-2((-3(-2|x - 1| + 2) + 1)/(-3(-2|x - 1| + 2) + 4))) + 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": "1", "dataset": "MATH"}
{"messages": [{"content": "How many local minima does the function f(x) = 1|(-3e^(-2(5(2|((-1x - 3)/(1x + 2)) - 1|) + 2)) + 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 leftmost local minimum of the function f(x) = 1(-4(5(3cos(1\u03c0(-2x^2 - 1x + 5) + 2) + 3) - 5)^2 + 1(5(3cos(1\u03c0(-2x^2 - 1x + 5) + 2) + 3) - 5) + 1)^2 + 3(-4(5(3cos(1\u03c0(-2x^2 - 1x + 5) + 2) + 3) - 5)^2 + 1(5(3cos(1\u03c0(-2x^2 - 1x + 5) + 2) + 3) - 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": "-7", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local minimum with the largest y-value of the function f(x) = 5((2(1|(-2(1sin(1\u03c0x + 1) - 3)^2 - 2(1sin(1\u03c0x + 1) - 3) + 4) + 3| - 3) - 1)/(1(1|(-2(1sin(1\u03c0x + 1) - 3)^2 - 2(1sin(1\u03c0x + 1) - 3) + 4) + 3| - 3) + 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": "-10", "dataset": "MATH"}
{"messages": [{"content": "How many local extrema (both minima and maxima) does the function f(x) = 2|(-1|(5(-2(-3sin(2\u03c0x - 2) + 1)^2 + 4(-3sin(2\u03c0x - 2) + 1) + 1) + 3)| + 3) + 2| + 3 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "180", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the rightmost local maximum of the function f(x) = (-2(-3e^(1(1((1(-2x^2 - 4x) + 3)/(1(-2x^2 - 4x) + 1))))) - 1)/(1(-3e^(1(1((1(-2x^2 - 4x) + 3)/(1(-2x^2 - 4x) + 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 maxima does the function f(x) = 1|(3((-2(3(1x^2 + 2x + 3) + 3) - 3)/(-3(3(1x^2 + 2x + 3) + 3) - 1))^2 - 4((-2(3(1x^2 + 2x + 3) + 3) - 3)/(-3(3(1x^2 + 2x + 3) + 3) - 1)) + 4) - 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 local maximum with the smallest y-value of the function f(x) = -3|(-1|(-2cos(1\u03c0(-2|(4x + 3) - 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": "-4", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local extremum with the smallest y-value of the function f(x) = (-3(-4(-2(4(-2x^2 + 5x + 2) + 4) + 2)^2 - 3(-2(4(-2x^2 + 5x + 2) + 4) + 2) - 1))/(-1(-4(-2(4(-2x^2 + 5x + 2) + 4) + 2)^2 - 3(-2(4(-2x^2 + 5x + 2) + 4) + 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": "How many local maxima does the function f(x) = 4(1(1|(1|(-1x) - 2| - 2) + 2|)^2 + 5(1|(1|(-1x) - 2| - 2) + 2|) + 2)^2 - 2(1(1|(1|(-1x) - 2| - 2) + 2|)^2 + 5(1|(1|(-1x) - 2| - 2) + 2|) + 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) = -4(3|(2((2(4x^2 + 3x - 3) + 3)/(1(4x^2 + 3x - 3) - 3))^2 - 2((2(4x^2 + 3x - 3) + 3)/(1(4x^2 + 3x - 3) - 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": "0", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the leftmost local extremum of the function f(x) = 3((1(3(2e^(2(1x^2 + 1x - 4)))^2 + 3(2e^(2(1x^2 + 1x - 4))) + 1) - 3)/(3(3(2e^(2(1x^2 + 1x - 4)))^2 + 3(2e^(2(1x^2 + 1x - 4))) + 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": "-4", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local minimum with the smallest y-value of the function f(x) = (1(1|(-3|(1sin(2\u03c0((1x + 2)/(2x + 2)) - 3) - 3) + 1| - 2) - 2| + 1) + 1)/(2(1|(-3|(1sin(2\u03c0((1x + 2)/(2x + 2)) - 3) - 3) + 1| - 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": "-3", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local extremum with the smallest y-value of the function f(x) = (-1(-3(-4(-3|(-1x + 2) + 1|) - 4)^2 - 1))/(3(-3(-4(-3|(-1x + 2) + 1|) - 4)^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": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the average of all x-coordinates of local maxima of the function f(x) = (3(-1(2(-2e^(1(4x^2 - 4x + 3)) - 2) - 4) + 5))/(1(-1(2(-2e^(1(4x^2 - 4x + 3)) - 2) - 4) + 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": "How many local maxima does the function f(x) = 1|(2|((-1((1(3x^2 + 1x + 1) - 2)/(1(3x^2 + 1x + 1))))/(2((1(3x^2 + 1x + 1) - 2)/(1(3x^2 + 1x + 1))) + 1)) - 2| - 2) + 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 minima of the function f(x) = 2|(2|(3(-2sin(1\u03c0(-1x + 2) + 3))^2 + 3(-2sin(1\u03c0(-1x + 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": "-1", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local minimum of the function f(x) = 3|(-3sin(2\u03c0((1(2((1x - 1)/(-2x + 3))^2 + 4((1x - 1)/(-2x + 3)) + 2) + 1)/(-3(2((1x - 1)/(-2x + 3))^2 + 4((1x - 1)/(-2x + 3)) + 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": "2", "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|(-3|(-3x + 1) + 1| + 3) + 2| + 2)^2 - 2(2|(-3|(-3x + 1) + 1| + 3) + 2| + 2) - 3) - 1)/(3(-3(2|(-3|(-3x + 1) + 1| + 3) + 2| + 2)^2 - 2(2|(-3|(-3x + 1) + 1| + 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": "1", "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(5(1x^2 + 2x - 4) - 4) + 2)/(-1(5(1x^2 + 2x - 4) - 4))) - 1| - 3) + 3)/(3(1|((1(5(1x^2 + 2x - 4) - 4) + 2)/(-1(5(1x^2 + 2x - 4) - 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": "-1", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the rightmost local maximum of the function f(x) = 2sin(2\u03c0(-3(5(1((3x - 2)/(2x - 3))^2 - 2((3x - 2)/(2x - 3)) - 3) - 1)^2 - 1(5(1((3x - 2)/(2x - 3))^2 - 2((3x - 2)/(2x - 3)) - 3) - 1) - 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": "10", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local extremum with the largest y-value of the function f(x) = -5(5(1|(-2cos(2\u03c0(2|x + 3| - 3) - 3) - 2) + 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": "-3", "dataset": "MATH"}
{"messages": [{"content": "Find the average of all x-coordinates of local minima of the function f(x) = (-2(3|(-1cos(1\u03c0(-3|((-2x + 2)/(3x - 2)) + 1| - 1)) + 3) - 3| + 3) + 2)/(2(3|(-1cos(1\u03c0(-3|((-2x + 2)/(3x - 2)) + 1| - 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": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the rightmost local minimum of the function f(x) = (1((3((-2(1e^(1(5x^2 - 3x + 1)) + 3) - 3)/(-3(1e^(1(5x^2 - 3x + 1)) + 3) - 2)) - 3)/(1((-2(1e^(1(5x^2 - 3x + 1)) + 3) - 3)/(-3(1e^(1(5x^2 - 3x + 1)) + 3) - 2)) + 2)))/(-1((3((-2(1e^(1(5x^2 - 3x + 1)) + 3) - 3)/(-3(1e^(1(5x^2 - 3x + 1)) + 3) - 2)) - 3)/(1((-2(1e^(1(5x^2 - 3x + 1)) + 3) - 3)/(-3(1e^(1(5x^2 - 3x + 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": "5", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local maximum with the smallest y-value of the function f(x) = -5((2(4(-1(-5x + 5)^2 - 2(-5x + 5) + 3)^2 + 3(-1(-5x + 5)^2 - 2(-5x + 5) + 3) - 2))/(-1(4(-1(-5x + 5)^2 - 2(-5x + 5) + 3)^2 + 3(-1(-5x + 5)^2 - 2(-5x + 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": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the leftmost local minimum of the function f(x) = -3|(3sin(1\u03c0(-1(4((-1x - 1)/(-2x)) + 1) + 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": "-4", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local extremum with the largest y-value of the function f(x) = -2(-1|(-3(3(2cos(1\u03c0x + 2) + 1) + 4)^2 - 1(3(2cos(1\u03c0x + 2) + 1) + 4) - 4) + 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 local maximum with the smallest y-value of the function f(x) = (2(-1sin(3\u03c0(-5(-1(1x - 3)^2 - 1(1x - 3) - 4)^2 + 1) - 3) - 1) + 1)/(2(-1sin(3\u03c0(-5(-1(1x - 3)^2 - 1(1x - 3) - 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": "-7", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local minimum of the function f(x) = 3|((2(2|(-4(-1|x + 2| - 1)^2 + 4(-1|x + 2| - 1) + 5) + 3| - 2) + 1)/(-3(2|(-4(-1|x + 2| - 1)^2 + 4(-1|x + 2| - 1) + 5) + 3| - 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 maximum of the function f(x) = (-1(-2(2cos(2\u03c0(3|(3|x + 3| + 1) - 2| + 2) - 2) - 1)^2 + 1(2cos(2\u03c0(3|(3|x + 3| + 1) - 2| + 2) - 2) - 1)) + 3)/(-3(-2(2cos(2\u03c0(3|(3|x + 3| + 1) - 2| + 2) - 2) - 1)^2 + 1(2cos(2\u03c0(3|(3|x + 3| + 1) - 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 x-coordinate of the rightmost local extremum of the function f(x) = -1(5(-5(3((-2x - 3)/(-2x - 2))^2 + 5)^2 - 5) + 1)^2 - 4(5(-5(3((-2x - 3)/(-2x - 2))^2 + 5)^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": "-2", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the leftmost local extremum of the function f(x) = 1((-3(1(3((-3x - 3)/(-2x + 3)) + 1)^2 - 4(3((-3x - 3)/(-2x + 3)) + 1) + 4) + 1)/(-2(1(3((-3x - 3)/(-2x + 3)) + 1)^2 - 4(3((-3x - 3)/(-2x + 3)) + 1) + 4) + 3))^2 - 4((-3(1(3((-3x - 3)/(-2x + 3)) + 1)^2 - 4(3((-3x - 3)/(-2x + 3)) + 1) + 4) + 1)/(-2(1(3((-3x - 3)/(-2x + 3)) + 1)^2 - 4(3((-3x - 3)/(-2x + 3)) + 1) + 4) + 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": "-7", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local maximum with the smallest y-value of the function f(x) = -4(4((-3(2(1x^2)^2 - 1(1x^2) - 2) - 2)/(-2(2(1x^2)^2 - 1(1x^2) - 2) + 3))^2 - 4((-3(2(1x^2)^2 - 1(1x^2) - 2) - 2)/(-2(2(1x^2)^2 - 1(1x^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": "0", "dataset": "MATH"}
{"messages": [{"content": "How many local maxima does the function f(x) = 4((2((-3((-1(3|x + 2|))/(-1(3|x + 2|) + 3)) - 3)/(-2((-1(3|x + 2|))/(-1(3|x + 2|) + 3)) + 3)) - 1)/(3((-3((-1(3|x + 2|))/(-1(3|x + 2|) + 3)) - 3)/(-2((-1(3|x + 2|))/(-1(3|x + 2|) + 3)) + 3)) + 2))^2 - 5((2((-3((-1(3|x + 2|))/(-1(3|x + 2|) + 3)) - 3)/(-2((-1(3|x + 2|))/(-1(3|x + 2|) + 3)) + 3)) - 1)/(3((-3((-1(3|x + 2|))/(-1(3|x + 2|) + 3)) - 3)/(-2((-1(3|x + 2|))/(-1(3|x + 2|) + 3)) + 3)) + 2)) - 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) = 2(-2(2(-2sin(1\u03c0((2x - 1)/(-1x + 3))) + 3)^2 + 3(-2sin(1\u03c0((2x - 1)/(-1x + 3))) + 3) + 3) - 4) - 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 of the function f(x) = 1sin(2\u03c0(-3((-1(-2(-1x^2 + 3x - 5)^2 + 4(-1x^2 + 3x - 5) + 1) + 3)/(3(-2(-1x^2 + 3x - 5)^2 + 4(-1x^2 + 3x - 5) + 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": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the rightmost local extremum of the function f(x) = -4(2(3(4(1|x - 1| - 2)^2 - 2(1|x - 1| - 2) + 2)^2 - 1(4(1|x - 1| - 2)^2 - 2(1|x - 1| - 2) + 2) - 3) - 5)^2 - 5(2(3(4(1|x - 1| - 2)^2 - 2(1|x - 1| - 2) + 2)^2 - 1(4(1|x - 1| - 2)^2 - 2(1|x - 1| - 2) + 2) - 3) - 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": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the leftmost local maximum of the function f(x) = -3(-2e^(2(-1((-2((3x - 2)/(-1x + 2)) + 3)/(3((3x - 2)/(-1x + 2)) + 3)) - 5)) + 2)^2 - 4(-2e^(2(-1((-2((3x - 2)/(-1x + 2)) + 3)/(3((3x - 2)/(-1x + 2)) + 3)) - 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": "0", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the rightmost local extremum of the function f(x) = (3(3(5(3|(-1x^2 - 3x + 1) - 2|)^2 - 3) + 4) - 1)/(-2(3(5(3|(-1x^2 - 3x + 1) - 2|)^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": "0", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local extremum of the function f(x) = 2(4((3((-2((2x - 3)/(2x + 1)) - 2)/(1((2x - 3)/(2x + 1)))) + 1)/(-2((-2((2x - 3)/(2x + 1)) - 2)/(1((2x - 3)/(2x + 1)))) + 3)) - 4)^2 - 3(4((3((-2((2x - 3)/(2x + 1)) - 2)/(1((2x - 3)/(2x + 1)))) + 1)/(-2((-2((2x - 3)/(2x + 1)) - 2)/(1((2x - 3)/(2x + 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 minimum of the function f(x) = (-1(-4(-2sin(2\u03c0(5(3|x - 2| + 2)) - 2) - 2)) + 3)/(-3(-4(-2sin(2\u03c0(5(3|x - 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": "-10", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local minimum of the function f(x) = (-2((2(3|(-4((2x - 1)/(1x)) + 2) - 3| + 1) + 3)/(2(3|(-4((2x - 1)/(1x)) + 2) - 3| + 1) - 1)))/(-3((2(3|(-4((2x - 1)/(1x)) + 2) - 3| + 1) + 3)/(2(3|(-4((2x - 1)/(1x)) + 2) - 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": "0", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local minimum of the function f(x) = 1|(-3|(2|(-3(-4x)^2 + 1(-4x) - 3) + 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": "0", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local extremum of the function f(x) = -3|(-1(3(1((-3x - 1)/(-2x - 2)) + 3)^2 - 1(1((-3x - 1)/(-2x - 2)) + 3) + 5)^2 - 1(3(1((-3x - 1)/(-2x - 2)) + 3)^2 - 1(1((-3x - 1)/(-2x - 2)) + 3) + 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": "-1", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local maximum of the function f(x) = (-2(-2sin(2\u03c0((-3(2|(-1|x - 3|) - 2| - 1) + 2)/(1(2|(-1|x - 3|) - 2| - 1)))) - 1))/(-3(-2sin(2\u03c0((-3(2|(-1|x - 3|) - 2| - 1) + 2)/(1(2|(-1|x - 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": "3", "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(-4(-3x + 5)^2 - 4(-3x + 5) + 5) + 3)/(1(-4(-3x + 5)^2 - 4(-3x + 5) + 5)))^2 - 2((-1(-4(-3x + 5)^2 - 4(-3x + 5) + 5) + 3)/(1(-4(-3x + 5)^2 - 4(-3x + 5) + 5))) + 3) + 3)/(2(4((-1(-4(-3x + 5)^2 - 4(-3x + 5) + 5) + 3)/(1(-4(-3x + 5)^2 - 4(-3x + 5) + 5)))^2 - 2((-1(-4(-3x + 5)^2 - 4(-3x + 5) + 5) + 3)/(1(-4(-3x + 5)^2 - 4(-3x + 5) + 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": "1", "dataset": "MATH"}
{"messages": [{"content": "How many local minima does the function f(x) = (-2(3cos(2\u03c0((2(1|(3x + 4) - 3| + 1) + 1)/(-2(1|(3x + 4) - 3| + 1) - 3)) - 2) - 2) + 3)/(-2(3cos(2\u03c0((2(1|(3x + 4) - 3| + 1) + 1)/(-2(1|(3x + 4) - 3| + 1) - 3)) - 2) - 2) - 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 of the function f(x) = 2(-1(2|((2(4x^2 - 1x) + 3)/(-3(4x^2 - 1x) - 3)) - 1| - 1) + 3)^2 - 5(-1(2|((2(4x^2 - 1x) + 3)/(-3(4x^2 - 1x) - 3)) - 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": "0", "dataset": "MATH"}
{"messages": [{"content": "How many local maxima does the function f(x) = 3(-3|(-3|(1|(4x + 4) - 3| - 3) - 1| + 3) - 3| - 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 x-coordinate of the local minimum with the largest y-value of the function f(x) = 2((1(2|((-2(-1x + 1) + 1)/(1(-1x + 1) + 2))| - 3) + 2)/(-2(2|((-2(-1x + 1) + 1)/(1(-1x + 1) + 2))| - 3) - 3))^2 - 1((1(2|((-2(-1x + 1) + 1)/(1(-1x + 1) + 2))| - 3) + 2)/(-2(2|((-2(-1x + 1) + 1)/(1(-1x + 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": "-1", "dataset": "MATH"}
{"messages": [{"content": "Find the average of all x-coordinates of local maxima of the function f(x) = 1cos(2\u03c0((-3(2|(3(-1x^2 + 2) + 1) + 3| + 2) - 2)/(-1(2|(3(-1x^2 + 2) + 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": "0", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local minimum of the function f(x) = 1((2(5(4((-1x - 3)/(-2x - 2))^2 - 2((-1x - 3)/(-2x - 2)) - 2) - 2) - 2)/(-1(5(4((-1x - 3)/(-2x - 2))^2 - 2((-1x - 3)/(-2x - 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": "-5", "dataset": "MATH"}
{"messages": [{"content": "Find the average of all x-coordinates of local extrema of the function f(x) = 2(1(-1(-1cos(3\u03c0((-2x - 1)/(1x + 3)) + 2) + 2)^2 + 1(-1cos(3\u03c0((-2x - 1)/(1x + 3)) + 2) + 2) + 1)^2 - 1(-1(-1cos(3\u03c0((-2x - 1)/(1x + 3)) + 2) + 2)^2 + 1(-1cos(3\u03c0((-2x - 1)/(1x + 3)) + 2) + 2) + 1) - 2)^2 - 1(1(-1(-1cos(3\u03c0((-2x - 1)/(1x + 3)) + 2) + 2)^2 + 1(-1cos(3\u03c0((-2x - 1)/(1x + 3)) + 2) + 2) + 1)^2 - 1(-1(-1cos(3\u03c0((-2x - 1)/(1x + 3)) + 2) + 2)^2 + 1(-1cos(3\u03c0((-2x - 1)/(1x + 3)) + 2) + 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": "-3", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local maximum with the largest y-value of the function f(x) = -1|(2(-1(1|(3x + 5) - 1| - 1)^2 + 5(1|(3x + 5) - 1| - 1) - 4)^2 - 4(-1(1|(3x + 5) - 1| - 1)^2 + 5(1|(3x + 5) - 1| - 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": "-2", "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|(4(-3|x - 3| + 3) + 1) + 1| + 2) - 2| - 3))/(-1(-2|(2|(4(-3|x - 3| + 3) + 1) + 1| + 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": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local extremum with the largest y-value of the function f(x) = -1|(-1|(-2|(2cos(1\u03c0(5x) - 2) - 1) - 2| + 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 extremum of the function f(x) = -1cos(3\u03c0((-2(-5(1(2|x|)^2 + 2(2|x|) + 1)^2 - 5(1(2|x|)^2 + 2(2|x|) + 1) + 3) + 2)/(-1(-5(1(2|x|)^2 + 2(2|x|) + 1)^2 - 5(1(2|x|)^2 + 2(2|x|) + 1) + 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": "0", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the rightmost local minimum of the function f(x) = -2((-1(1sin(2\u03c0((3(1|x + 2| - 3) - 3)/(-1(1|x + 2| - 3) - 1)) + 2) - 2))/(-1(1sin(2\u03c0((3(1|x + 2| - 3) - 3)/(-1(1|x + 2| - 3) - 1)) + 2) - 2) + 3))^2 - 3((-1(1sin(2\u03c0((3(1|x + 2| - 3) - 3)/(-1(1|x + 2| - 3) - 1)) + 2) - 2))/(-1(1sin(2\u03c0((3(1|x + 2| - 3) - 3)/(-1(1|x + 2| - 3) - 1)) + 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": "4", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local extremum of the function f(x) = -5(4(5(-3e^(-1(4x^2 + 3x - 3)))^2 - 1(-3e^(-1(4x^2 + 3x - 3))) + 3)^2 - 5(5(-3e^(-1(4x^2 + 3x - 3)))^2 - 1(-3e^(-1(4x^2 + 3x - 3))) + 3) + 4)^2 + 5(4(5(-3e^(-1(4x^2 + 3x - 3)))^2 - 1(-3e^(-1(4x^2 + 3x - 3))) + 3)^2 - 5(5(-3e^(-1(4x^2 + 3x - 3)))^2 - 1(-3e^(-1(4x^2 + 3x - 3))) + 3) + 4) - 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 smallest y-value of the function f(x) = 3(-2((3(-1((1x + 2)/(1x - 3)) - 4) - 3)/(-1(-1((1x + 2)/(1x - 3)) - 4) + 2)) - 1)^2 - 2(-2((3(-1((1x + 2)/(1x - 3)) - 4) - 3)/(-1(-1((1x + 2)/(1x - 3)) - 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": "2", "dataset": "MATH"}
{"messages": [{"content": "How many local extrema (both minima and maxima) does the function f(x) = 3|((2((-3(-5((-2x + 2)/(1x - 2))^2 - 5((-2x + 2)/(1x - 2)) + 5) - 3)/(3(-5((-2x + 2)/(1x - 2))^2 - 5((-2x + 2)/(1x - 2)) + 5) + 1)))/(-2((-3(-5((-2x + 2)/(1x - 2))^2 - 5((-2x + 2)/(1x - 2)) + 5) - 3)/(3(-5((-2x + 2)/(1x - 2))^2 - 5((-2x + 2)/(1x - 2)) + 5) + 1)) - 3)) - 1| - 3 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 rightmost local minimum of the function f(x) = 3|(1(5(-5(-2cos(1\u03c0x + 3) - 2)^2 - 1(-2cos(1\u03c0x + 3) - 2)))^2 - 4(5(-5(-2cos(1\u03c0x + 3) - 2)^2 - 1(-2cos(1\u03c0x + 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": "8", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the rightmost local minimum of the function f(x) = 1((-1(1((-1(2cos(1\u03c0x - 1) + 3) - 2)/(-3(2cos(1\u03c0x - 1) + 3))) + 2) + 3)/(2(1((-1(2cos(1\u03c0x - 1) + 3) - 2)/(-3(2cos(1\u03c0x - 1) + 3))) + 2) + 3))^2 + 5((-1(1((-1(2cos(1\u03c0x - 1) + 3) - 2)/(-3(2cos(1\u03c0x - 1) + 3))) + 2) + 3)/(2(1((-1(2cos(1\u03c0x - 1) + 3) - 2)/(-3(2cos(1\u03c0x - 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": "9", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the leftmost local minimum of the function f(x) = 2sin(1\u03c0(5((1(2(4x + 5)^2 - 3(4x + 5) + 4) + 1)/(-3(2(4x + 5)^2 - 3(4x + 5) + 4) + 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": "-1", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local extremum of the function f(x) = 4(1((1(1|(5x^2 + 3) - 2| + 2) - 3)/(-1(1|(5x^2 + 3) - 2| + 2)))^2 - 3((1(1|(5x^2 + 3) - 2| + 2) - 3)/(-1(1|(5x^2 + 3) - 2| + 2))) + 3)^2 - 5(1((1(1|(5x^2 + 3) - 2| + 2) - 3)/(-1(1|(5x^2 + 3) - 2| + 2)))^2 - 3((1(1|(5x^2 + 3) - 2| + 2) - 3)/(-1(1|(5x^2 + 3) - 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": "0", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the rightmost local extremum of the function f(x) = (-1(2(4(-1e^(2((3x - 2)/(3x))) + 3) + 4) + 5) + 2)/(-2(2(4(-1e^(2((3x - 2)/(3x))) + 3) + 4) + 5) - 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(-1(2|((-1(2cos(1\u03c0x - 3) - 2) + 3)/(2(2cos(1\u03c0x - 3) - 2) + 2))| - 3) + 4)^2 - 2(-1(2|((-1(2cos(1\u03c0x - 3) - 2) + 3)/(2(2cos(1\u03c0x - 3) - 2) + 2))| - 3) + 4) - 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) = -2|(1|(2((1(-5x^2 + 5x + 5) - 3)/(3(-5x^2 + 5x + 5))) + 5) - 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": "0", "dataset": "MATH"}
{"messages": [{"content": "How many local extrema (both minima and maxima) does the function f(x) = -3((2(-1((-2(2sin(3\u03c0x + 1) + 2) - 2)/(-2(2sin(3\u03c0x + 1) + 2) + 1))^2 + 5((-2(2sin(3\u03c0x + 1) + 2) - 2)/(-2(2sin(3\u03c0x + 1) + 2) + 1))) - 2)/(2(-1((-2(2sin(3\u03c0x + 1) + 2) - 2)/(-2(2sin(3\u03c0x + 1) + 2) + 1))^2 + 5((-2(2sin(3\u03c0x + 1) + 2) - 2)/(-2(2sin(3\u03c0x + 1) + 2) + 1))) + 2))^2 + 3((2(-1((-2(2sin(3\u03c0x + 1) + 2) - 2)/(-2(2sin(3\u03c0x + 1) + 2) + 1))^2 + 5((-2(2sin(3\u03c0x + 1) + 2) - 2)/(-2(2sin(3\u03c0x + 1) + 2) + 1))) - 2)/(2(-1((-2(2sin(3\u03c0x + 1) + 2) - 2)/(-2(2sin(3\u03c0x + 1) + 2) + 1))^2 + 5((-2(2sin(3\u03c0x + 1) + 2) - 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": "216", "dataset": "MATH"}
{"messages": [{"content": "How many local maxima does the function f(x) = 1|(3cos(2\u03c0((-2(-1(-2x^2 - 1x - 3)^2 + 5(-2x^2 - 1x - 3) - 1) + 3)/(-3(-1(-2x^2 - 1x - 3)^2 + 5(-2x^2 - 1x - 3) - 1) + 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 rightmost local maximum of the function f(x) = (3(4(4(2|(3sin(1\u03c0x + 2) + 2) - 2| - 1) + 3) - 2) + 2)/(-2(4(4(2|(3sin(1\u03c0x + 2) + 2) - 2| - 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 average of all x-coordinates of local minima of the function f(x) = (-1(1(-2|(-1e^(2(-4x^2 + 5x)) + 1) + 3| + 2)^2 - 4(-2|(-1e^(2(-4x^2 + 5x)) + 1) + 3| + 2) + 1) + 1)/(2(1(-2|(-1e^(2(-4x^2 + 5x)) + 1) + 3| + 2)^2 - 4(-2|(-1e^(2(-4x^2 + 5x)) + 1) + 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": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the rightmost local maximum of the function f(x) = 1(-2cos(3\u03c0(2|((3(1|x + 3| - 1))/(2(1|x + 3| - 1) + 3)) + 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": "6", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local extremum of the function f(x) = (2(-2|((1(1|(-4x^2 - 5x - 5) - 1|) + 1)/(-3(1|(-4x^2 - 5x - 5) - 1|) - 1)) - 2| + 2) - 1)/(-2(-2|((1(1|(-4x^2 - 5x - 5) - 1|) + 1)/(-3(1|(-4x^2 - 5x - 5) - 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": "-1", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local maximum with the largest y-value of the function f(x) = -2(-1((-2(4(-2sin(1\u03c0x - 2) + 2)^2 - 5(-2sin(1\u03c0x - 2) + 2) + 3) - 1)/(2(4(-2sin(1\u03c0x - 2) + 2)^2 - 5(-2sin(1\u03c0x - 2) + 2) + 3) - 3)) - 4)^2 + 4(-1((-2(4(-2sin(1\u03c0x - 2) + 2)^2 - 5(-2sin(1\u03c0x - 2) + 2) + 3) - 1)/(2(4(-2sin(1\u03c0x - 2) + 2)^2 - 5(-2sin(1\u03c0x - 2) + 2) + 3) - 3)) - 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": "-9", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the rightmost local maximum of the function f(x) = -1|(-2e^(2((2(2(-2x^2 + 2)^2 + 4) - 1)/(2(2(-2x^2 + 2)^2 + 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": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local minimum with the largest y-value of the function f(x) = -3(2(-1|(1(-1cos(2\u03c0x - 2) + 2)^2 + 2(-1cos(2\u03c0x - 2) + 2) + 2) - 3| - 1)^2 + 3(-1|(1(-1cos(2\u03c0x - 2) + 2)^2 + 2(-1cos(2\u03c0x - 2) + 2) + 2) - 3| - 1) - 4)^2 + 5(2(-1|(1(-1cos(2\u03c0x - 2) + 2)^2 + 2(-1cos(2\u03c0x - 2) + 2) + 2) - 3| - 1)^2 + 3(-1|(1(-1cos(2\u03c0x - 2) + 2)^2 + 2(-1cos(2\u03c0x - 2) + 2) + 2) - 3| - 1) - 4) + 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": "How many local minima does the function f(x) = -1|(2(-3e^(-1(-3(4x^2 + 4x + 5)^2 + 2(4x^2 + 4x + 5))) + 3)^2 - 2(-3e^(-1(-3(4x^2 + 4x + 5)^2 + 2(4x^2 + 4x + 5))) + 3) - 4) + 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|(-1(3|(-1(-3e^(-2x) + 2)^2 + 3(-3e^(-2x) + 2) + 5) + 1| + 3)^2 + 4(3|(-1(-3e^(-2x) + 2)^2 + 3(-3e^(-2x) + 2) + 5) + 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": "0", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local extremum of the function f(x) = (-1(3(2|((-1(-1|x - 1|) + 3)/(3(-1|x - 1|) - 1)) - 1| - 3) - 3) - 2)/(-3(3(2|((-1(-1|x - 1|) + 3)/(3(-1|x - 1|) - 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": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local minimum with the smallest y-value of the function f(x) = -1(5(1sin(2\u03c0(-3(4x^2 - 3x - 5)^2 - 1(4x^2 - 3x - 5) - 3) + 1) + 1)^2 - 5(1sin(2\u03c0(-3(4x^2 - 3x - 5)^2 - 1(4x^2 - 3x - 5) - 3) + 1) + 1) + 5) - 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": "-2", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the leftmost local minimum of the function f(x) = 3((1(1cos(1\u03c0(5((-2x + 1)/(3x + 1))^2 + 1((-2x + 1)/(3x + 1)) - 3) - 2)) + 1)/(-3(1cos(1\u03c0(5((-2x + 1)/(3x + 1))^2 + 1((-2x + 1)/(3x + 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": "-4", "dataset": "MATH"}
{"messages": [{"content": "How many local minima does the function f(x) = 4((-2(3(3|(1|x| - 1) + 3| + 2) + 1) + 3)/(2(3(3|(1|x| - 1) + 3| + 2) + 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) = 5((3(-1|(3(-2|x + 1| + 1)^2 + 2(-2|x + 1| + 1) - 1) - 1| - 1) + 2)/(-1(-1|(3(-2|x + 1| + 1)^2 + 2(-2|x + 1| + 1) - 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": "0", "dataset": "MATH"}
{"messages": [{"content": "How many local maxima does the function f(x) = (-1(-3(-2|(5(4x - 3)^2 - 5(4x - 3)) - 2| - 3) - 4) + 3)/(1(-3(-2|(5(4x - 3)^2 - 5(4x - 3)) - 2| - 3) - 4) + 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": "How many local maxima does the function f(x) = 1|(1((2(3((2x + 2)/(-3x - 3)) - 1) + 3)/(1(3((2x + 2)/(-3x - 3)) - 1) + 1))^2 - 1((2(3((2x + 2)/(-3x - 3)) - 1) + 3)/(1(3((2x + 2)/(-3x - 3)) - 1) + 1)) - 2) + 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) = -1|(3|(1|(-1cos(2\u03c0(3x^2 - 4x + 3) - 3) + 3) + 1| + 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 average of all x-coordinates of local maxima of the function f(x) = -2(-2((-3(-4((1x + 3)/(-3x)) - 1))/(2(-4((1x + 3)/(-3x)) - 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": "-3", "dataset": "MATH"}
{"messages": [{"content": "Find the average of all x-coordinates of local extrema of the function f(x) = -1|(-2|((-3(-2(-1cos(3\u03c0x - 1))^2 + 4(-1cos(3\u03c0x - 1)) - 3) + 1)/(3(-2(-1cos(3\u03c0x - 1))^2 + 4(-1cos(3\u03c0x - 1)) - 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": "How many local maxima does the function f(x) = -1|(2(-1(-1((-2x - 1)/(-1x + 2))^2 - 3((-2x - 1)/(-1x + 2)) + 3)^2 - 2(-1((-2x - 1)/(-1x + 2))^2 - 3((-2x - 1)/(-1x + 2)) + 3) - 1) + 4) + 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 largest y-value of the function f(x) = 1(-3((1(3cos(2\u03c0(-3x + 5)) + 2) + 1)/(-2(3cos(2\u03c0(-3x + 5)) + 2) - 3))^2 - 2)^2 + 5(-3((1(3cos(2\u03c0(-3x + 5)) + 2) + 1)/(-2(3cos(2\u03c0(-3x + 5)) + 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 leftmost local minimum of the function f(x) = -2|(-4((-2((3(1x^2 - 3x - 3) - 3)/(-2(1x^2 - 3x - 3) + 3)) + 2)/(-1((3(1x^2 - 3x - 3) - 3)/(-2(1x^2 - 3x - 3) + 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": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local maximum with the smallest y-value of the function f(x) = -2|(1((1(-4(1|x - 3| - 3) - 1) - 2)/(-3(-4(1|x - 3| - 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": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the average of all x-coordinates of local extrema of the function f(x) = (1(3(-1sin(3\u03c0(2(5x^2)^2 + 2(5x^2) + 3)) - 2)^2 - 3(-1sin(3\u03c0(2(5x^2)^2 + 2(5x^2) + 3)) - 2) + 4))/(2(3(-1sin(3\u03c0(2(5x^2)^2 + 2(5x^2) + 3)) - 2)^2 - 3(-1sin(3\u03c0(2(5x^2)^2 + 2(5x^2) + 3)) - 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": "0", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the rightmost local minimum of the function f(x) = 1|((1(4(-3cos(2\u03c0(2x^2 + 2x - 1) + 3) - 1)^2 - 2(-3cos(2\u03c0(2x^2 + 2x - 1) + 3) - 1) - 5) - 1)/(-2(4(-3cos(2\u03c0(2x^2 + 2x - 1) + 3) - 1)^2 - 2(-3cos(2\u03c0(2x^2 + 2x - 1) + 3) - 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": "10", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the rightmost local minimum of the function f(x) = (3(-1(4(1|(1x^2 + 5x - 2) - 3| + 3)^2 + 5(1|(1x^2 + 5x - 2) - 3| + 3) - 1)^2 + 5(4(1|(1x^2 + 5x - 2) - 3| + 3)^2 + 5(1|(1x^2 + 5x - 2) - 3| + 3) - 1) + 3) - 1)/(-1(-1(4(1|(1x^2 + 5x - 2) - 3| + 3)^2 + 5(1|(1x^2 + 5x - 2) - 3| + 3) - 1)^2 + 5(4(1|(1x^2 + 5x - 2) - 3| + 3)^2 + 5(1|(1x^2 + 5x - 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": "-2", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local extremum with the smallest y-value of the function f(x) = -3cos(2\u03c0(3(-5(-2((-1x + 2)/(1x)))^2 - 3(-2((-1x + 2)/(1x))) - 5)^2 - 5(-5(-2((-1x + 2)/(1x)))^2 - 3(-2((-1x + 2)/(1x))) - 5) - 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) = -3sin(2\u03c0(-4(-5(2((-2x - 1)/(1x + 3))^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": "-1", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local extremum of the function f(x) = (2(-3|((3(2|((3x - 3)/(-3x + 4)) + 2|))/(-2(2|((3x - 3)/(-3x + 4)) + 2|) + 3)) + 2|) + 3)/(-3(-3|((3(2|((3x - 3)/(-3x + 4)) + 2|))/(-2(2|((3x - 3)/(-3x + 4)) + 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 leftmost local minimum of the function f(x) = -1(2|(-1(2cos(3\u03c0(2|x - 2| - 3) + 1) - 3) + 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": "How many local minima does the function f(x) = -2|(2(-3e^(-2(1(-1x^2 + 4x - 4) - 2)) + 1) + 4) + 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 maximum with the smallest y-value of the function f(x) = -3((1(2(-3|((-1x + 2)/(-2x - 1))| + 2)^2 + 3(-3|((-1x + 2)/(-2x - 1))| + 2) - 1) + 2)/(-1(2(-3|((-1x + 2)/(-2x - 1))| + 2)^2 + 3(-3|((-1x + 2)/(-2x - 1))| + 2) - 1) + 2))^2 + 3((1(2(-3|((-1x + 2)/(-2x - 1))| + 2)^2 + 3(-3|((-1x + 2)/(-2x - 1))| + 2) - 1) + 2)/(-1(2(-3|((-1x + 2)/(-2x - 1))| + 2)^2 + 3(-3|((-1x + 2)/(-2x - 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": "0", "dataset": "MATH"}
{"messages": [{"content": "Find the average of all x-coordinates of local maxima of the function f(x) = -5(3(2((3(2x - 1) - 1)/(1(2x - 1)))^2 - 5((3(2x - 1) - 1)/(1(2x - 1))) + 5)^2 + 1(2((3(2x - 1) - 1)/(1(2x - 1)))^2 - 5((3(2x - 1) - 1)/(1(2x - 1))) + 5) - 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 rightmost local minimum of the function f(x) = -3cos(1\u03c0(3(1|(1|(3x - 3) + 1| - 1) + 3| - 3)^2 + 5(1|(1|(3x - 3) + 1| - 1) + 3| - 3) - 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": "10", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the leftmost local extremum of the function f(x) = (-2(1cos(3\u03c0(-3|(2|((2x)/(1x + 1)) - 1| - 1) + 1| - 2) - 3) - 3) + 2)/(-2(1cos(3\u03c0(-3|(2|((2x)/(1x + 1)) - 1| - 1) + 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": "How many local maxima does the function f(x) = -2((1((3(-5(4x^2 - 1x + 3) - 4) - 1)/(-3(-5(4x^2 - 1x + 3) - 4) - 2)) - 3)/(-3((3(-5(4x^2 - 1x + 3) - 4) - 1)/(-3(-5(4x^2 - 1x + 3) - 4) - 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 average of all x-coordinates of local maxima of the function f(x) = -3(5(5(-2sin(3\u03c0(1|x - 2| + 1) + 1) - 1) + 2)^2 + 1(5(-2sin(3\u03c0(1|x - 2| + 1) + 1) - 1) + 2) - 4)^2 - 3(5(5(-2sin(3\u03c0(1|x - 2| + 1) + 1) - 1) + 2)^2 + 1(5(-2sin(3\u03c0(1|x - 2| + 1) + 1) - 1) + 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": "0", "dataset": "MATH"}
{"messages": [{"content": "Find the average of all x-coordinates of local extrema of the function f(x) = -5(-2((-1(-3|((2x - 3)/(-1x + 2)) - 1| - 2) - 3)/(-1(-3|((2x - 3)/(-1x + 2)) - 1| - 2) - 2)))^2 - 1(-2((-1(-3|((2x - 3)/(-1x + 2)) - 1| - 2) - 3)/(-1(-3|((2x - 3)/(-1x + 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": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local extremum with the largest y-value of the function f(x) = 1sin(1\u03c0(-3|(-1|(4(-2|x + 1| - 1)^2 - 2(-2|x + 1| - 1) - 2) - 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 minimum of the function f(x) = 3|(1(-3|((2((1x + 2)/(-1x - 3)) + 3)/(1((1x + 2)/(-1x - 3)))) - 3| - 3)^2 + 1(-3|((2((1x + 2)/(-1x - 3)) + 3)/(1((1x + 2)/(-1x - 3)))) - 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": "-3", "dataset": "MATH"}
{"messages": [{"content": "How many local minima does the function f(x) = -1(-2e^(-1(-5(2|(-1x^2 + 3) + 2| - 2)^2 + 5(2|(-1x^2 + 3) + 2| - 2) + 1)))^2 + 1(-2e^(-1(-5(2|(-1x^2 + 3) + 2| - 2)^2 + 5(2|(-1x^2 + 3) + 2| - 2) + 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 extremum of the function f(x) = (2(2(-3(2|((1x)/(-1x - 3)) - 3| + 2) - 3)^2 + 3(-3(2|((1x)/(-1x - 3)) - 3| + 2) - 3) - 2) + 2)/(1(2(-3(2|((1x)/(-1x - 3)) - 3| + 2) - 3)^2 + 3(-3(2|((1x)/(-1x - 3)) - 3| + 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": "-3", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local extremum with the smallest y-value of the function f(x) = -3sin(2\u03c0(-1|(1(5((2x + 1)/(-3x - 3))^2 + 1((2x + 1)/(-3x - 3)) + 1)^2 - 2(5((2x + 1)/(-3x - 3))^2 + 1((2x + 1)/(-3x - 3)) + 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": "-8", "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(1|((-3(-3x - 4) + 2)/(-3(-3x - 4) - 2)) + 2| + 3) + 3)/(-1(1|((-3(-3x - 4) + 2)/(-3(-3x - 4) - 2)) + 2| + 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": "-1", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local minimum of the function f(x) = 1|((-3((-1(3|(-2|x - 1| + 1) + 1| + 1) + 2)/(2(3|(-2|x - 1| + 1) + 1| + 1) + 2)))/(1((-1(3|(-2|x - 1| + 1) + 1| + 1) + 2)/(2(3|(-2|x - 1| + 1) + 1| + 1) + 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": "0", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the rightmost local maximum of the function f(x) = -1(-4(2cos(3\u03c0(5((2x - 3)/(-3x)) - 1) - 1) + 3) - 5) + 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": "5", "dataset": "MATH"}
{"messages": [{"content": "How many local maxima does the function f(x) = -2(2|(1|(-3(4x^2 + 3x - 4) - 2)| + 1) + 3| - 3) + 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": "How many local maxima does the function f(x) = 5((1(2|(5(-5x)^2) + 1| - 2) - 1)/(3(2|(5(-5x)^2) + 1| - 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 local extremum with the largest y-value of the function f(x) = -3(-2(2e^(-1((1((-1x - 3)/(2x)) + 2)/(1((-1x - 3)/(2x)) + 3)))) + 4)^2 + 1(-2(2e^(-1((1((-1x - 3)/(2x)) + 2)/(1((-1x - 3)/(2x)) + 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": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the average of all x-coordinates of local extrema of the function f(x) = -3cos(1\u03c0(-1((2(2|(-3x^2 - 5x) + 1|) + 3)/(2(2|(-3x^2 - 5x) + 1|) + 2))^2 - 3((2(2|(-3x^2 - 5x) + 1|) + 3)/(2(2|(-3x^2 - 5x) + 1|) + 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 of the function f(x) = 4((-2(2|((-2(-2x^2 - 2x - 5) - 1)/(-1(-2x^2 - 2x - 5) + 2)) + 2| + 3) - 3)/(-2(2|((-2(-2x^2 - 2x - 5) - 1)/(-1(-2x^2 - 2x - 5) + 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 x-coordinate of the local maximum of the function f(x) = -2(2(-2|(1(3|x + 3| + 1)) - 1| - 3)^2 + 2(-2|(1(3|x + 3| + 1)) - 1| - 3) - 5)^2 + 3(2(-2|(1(3|x + 3| + 1)) - 1| - 3)^2 + 2(-2|(1(3|x + 3| + 1)) - 1| - 3) - 5) + 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) = (3((-1((2(2(-1sin(2\u03c0x - 3) - 2) + 4) - 2)/(-2(2(-1sin(2\u03c0x - 3) - 2) + 4) - 1)) + 2)/(2((2(2(-1sin(2\u03c0x - 3) - 2) + 4) - 2)/(-2(2(-1sin(2\u03c0x - 3) - 2) + 4) - 1)) + 2)) - 2)/(2((-1((2(2(-1sin(2\u03c0x - 3) - 2) + 4) - 2)/(-2(2(-1sin(2\u03c0x - 3) - 2) + 4) - 1)) + 2)/(2((2(2(-1sin(2\u03c0x - 3) - 2) + 4) - 2)/(-2(2(-1sin(2\u03c0x - 3) - 2) + 4) - 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": "-9", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local minimum of the function f(x) = (3((-1(-5(4(2|x| - 3) + 4)^2 - 2(4(2|x| - 3) + 4) + 3) + 1)/(2(-5(4(2|x| - 3) + 4)^2 - 2(4(2|x| - 3) + 4) + 3) + 1)) + 3)/(-2((-1(-5(4(2|x| - 3) + 4)^2 - 2(4(2|x| - 3) + 4) + 3) + 1)/(2(-5(4(2|x| - 3) + 4)^2 - 2(4(2|x| - 3) + 4) + 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 extremum with the smallest y-value of the function f(x) = -1((-1(3cos(3\u03c0(1(-1x^2)^2 - 4(-1x^2) + 1) - 3) - 1) - 3)/(2(3cos(3\u03c0(1(-1x^2)^2 - 4(-1x^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": "How many local extrema (both minima and maxima) does the function f(x) = 4(1e^(-1(1(1(2x^2 + 4x - 1) + 4)^2 + 3(1(2x^2 + 4x - 1) + 4) + 4)) + 1)^2 + 2(1e^(-1(1(1(2x^2 + 4x - 1) + 4)^2 + 3(1(2x^2 + 4x - 1) + 4) + 4)) + 1) + 3 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "How many local minima does the function f(x) = 4((2(2(-5(-1x - 2)^2 - 4(-1x - 2) - 5)^2 + 5(-5(-1x - 2)^2 - 4(-1x - 2) - 5) - 4) + 3)/(-2(2(-5(-1x - 2)^2 - 4(-1x - 2) - 5)^2 + 5(-5(-1x - 2)^2 - 4(-1x - 2) - 5) - 4) + 3))^2 + 1((2(2(-5(-1x - 2)^2 - 4(-1x - 2) - 5)^2 + 5(-5(-1x - 2)^2 - 4(-1x - 2) - 5) - 4) + 3)/(-2(2(-5(-1x - 2)^2 - 4(-1x - 2) - 5)^2 + 5(-5(-1x - 2)^2 - 4(-1x - 2) - 5) - 4) + 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 rightmost local minimum of the function f(x) = 1(-3|((1((-3((2x - 1)/(-1x + 3)) - 1)/(-1((2x - 1)/(-1x + 3)) + 2)) - 1)/(3((-3((2x - 1)/(-1x + 3)) - 1)/(-1((2x - 1)/(-1x + 3)) + 2)) - 2)) - 2| - 1)^2 + 4(-3|((1((-3((2x - 1)/(-1x + 3)) - 1)/(-1((2x - 1)/(-1x + 3)) + 2)) - 1)/(3((-3((2x - 1)/(-1x + 3)) - 1)/(-1((2x - 1)/(-1x + 3)) + 2)) - 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": "-2", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the leftmost local extremum of the function f(x) = 5(-1(1(1cos(2\u03c0((2x - 2)/(-1x + 2)) + 3) + 3)^2 - 5(1cos(2\u03c0((2x - 2)/(-1x + 2)) + 3) + 3) + 3) + 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": "-9", "dataset": "MATH"}
{"messages": [{"content": "Find the average of all x-coordinates of local extrema of the function f(x) = -5(2cos(1\u03c0(-3|((-1((-2x - 1)/(1x + 3)) - 2)/(3((-2x - 1)/(1x + 3)) + 3)) - 3| + 1) - 2) + 2)^2 + 2(2cos(1\u03c0(-3|((-1((-2x - 1)/(1x + 3)) - 2)/(3((-2x - 1)/(1x + 3)) + 3)) - 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": "2", "dataset": "MATH"}
{"messages": [{"content": "How many local maxima does the function f(x) = -1|(3sin(2\u03c0(-1|((1((-1x)/(-3x - 3)) + 3)/(2((-1x)/(-3x - 3)) + 2)) + 3| + 1) + 2) - 2) + 2| - 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 largest y-value of the function f(x) = -2|(3(-5(-1(-1|x + 2| - 2) - 4)^2 + 4(-1(-1|x + 2| - 2) - 4) + 3) - 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": "-4", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local minimum of the function f(x) = -4((-3((1(-1(-3x - 4)^2 + 4(-3x - 4)))/(-3(-1(-3x - 4)^2 + 4(-3x - 4)) - 2)))/(2((1(-1(-3x - 4)^2 + 4(-3x - 4)))/(-3(-1(-3x - 4)^2 + 4(-3x - 4)) - 2)) - 3))^2 + 1((-3((1(-1(-3x - 4)^2 + 4(-3x - 4)))/(-3(-1(-3x - 4)^2 + 4(-3x - 4)) - 2)))/(2((1(-1(-3x - 4)^2 + 4(-3x - 4)))/(-3(-1(-3x - 4)^2 + 4(-3x - 4)) - 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": "-2", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local extremum with the smallest y-value of the function f(x) = -3|(2(5(-1|(4x^2 - 1) - 3| - 2)^2 + 3(-1|(4x^2 - 1) - 3| - 2) - 4)^2 + 4(5(-1|(4x^2 - 1) - 3| - 2)^2 + 3(-1|(4x^2 - 1) - 3| - 2) - 4) - 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": "0", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the leftmost local minimum of the function f(x) = 1((2(1(3cos(3\u03c0(-2x - 3) - 1) - 1) - 3) + 2)/(-1(1(3cos(3\u03c0(-2x - 3) - 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": "-10", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the rightmost local minimum of the function f(x) = -1|((3(4(-1|(2x^2 + 1x - 4) + 2| + 3) + 1))/(1(4(-1|(2x^2 + 1x - 4) + 2| + 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": "1", "dataset": "MATH"}
{"messages": [{"content": "How many local extrema (both minima and maxima) does the function f(x) = 1(5(-2e^(2(2((-1x + 1)/(-3x + 4))^2 - 3((-1x + 1)/(-3x + 4)) - 1)) - 3) + 4)^2 + 2 have in the interval [-10, 10]?\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) = (1(5(2|(-2sin(2\u03c0(3|x + 2| + 2) + 1) - 1) + 2| - 2)^2 - 1) + 3)/(2(5(2|(-2sin(2\u03c0(3|x + 2| + 2) + 1) - 1) + 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 x-coordinate of the local maximum with the smallest y-value of the function f(x) = 1e^(1(-2|(-1((-3(-5x^2 + 3) - 3)/(2(-5x^2 + 3) + 1))^2 - 1((-3(-5x^2 + 3) - 3)/(2(-5x^2 + 3) + 1)) - 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": "-1", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the leftmost local extremum of the function f(x) = -3((-1(1((1((2x - 2)/(-1x - 2)))/(3((2x - 2)/(-1x - 2)) - 1)) - 3) + 3)/(2(1((1((2x - 2)/(-1x - 2)))/(3((2x - 2)/(-1x - 2)) - 1)) - 3) - 1))^2 - 5((-1(1((1((2x - 2)/(-1x - 2)))/(3((2x - 2)/(-1x - 2)) - 1)) - 3) + 3)/(2(1((1((2x - 2)/(-1x - 2)))/(3((2x - 2)/(-1x - 2)) - 1)) - 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 leftmost local extremum of the function f(x) = 4(3|(5(5((-2x)/(2x + 2))^2 + 5((-2x)/(2x + 2)) - 4)^2 + 5(5((-2x)/(2x + 2))^2 + 5((-2x)/(2x + 2)) - 4) + 3) - 1| - 1)^2 - 5(3|(5(5((-2x)/(2x + 2))^2 + 5((-2x)/(2x + 2)) - 4)^2 + 5(5((-2x)/(2x + 2))^2 + 5((-2x)/(2x + 2)) - 4) + 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": "-3", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local extremum with the largest y-value of the function f(x) = -1(1|(2(4(5x - 1)^2 - 5(5x - 1) - 1)^2 - 4(4(5x - 1)^2 - 5(5x - 1) - 1) - 3) + 3| + 3)^2 - 1(1|(2(4(5x - 1)^2 - 5(5x - 1) - 1)^2 - 4(4(5x - 1)^2 - 5(5x - 1) - 1) - 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": "0", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local maximum with the smallest y-value of the function f(x) = -3|(-3((2(3(-1sin(2\u03c0x + 2) + 3)^2 - 2(-1sin(2\u03c0x + 2) + 3) + 1) + 2)/(2(3(-1sin(2\u03c0x + 2) + 3)^2 - 2(-1sin(2\u03c0x + 2) + 3) + 1) - 1))^2 + 3((2(3(-1sin(2\u03c0x + 2) + 3)^2 - 2(-1sin(2\u03c0x + 2) + 3) + 1) + 2)/(2(3(-1sin(2\u03c0x + 2) + 3)^2 - 2(-1sin(2\u03c0x + 2) + 3) + 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": "-9", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local maximum of the function f(x) = 5(3|(-1|(2|(3|x| + 1) - 3| - 1) + 1| - 1) + 3| - 1)^2 + 4(3|(-1|(2|(3|x| + 1) - 3| - 1) + 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": "0", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local maximum of the function f(x) = (1(-5(-3|(3(2e^(-1x) - 1)^2 - 5(2e^(-1x) - 1) + 5) - 3| - 3)^2 + 1(-3|(3(2e^(-1x) - 1)^2 - 5(2e^(-1x) - 1) + 5) - 3| - 3) - 4) - 3)/(2(-5(-3|(3(2e^(-1x) - 1)^2 - 5(2e^(-1x) - 1) + 5) - 3| - 3)^2 + 1(-3|(3(2e^(-1x) - 1)^2 - 5(2e^(-1x) - 1) + 5) - 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 x-coordinate of the local extremum with the largest y-value of the function f(x) = (2(2cos(3\u03c0(2(-1(-4x + 4)^2 + 2(-4x + 4) - 5) - 3) - 3) - 3))/(-1(2cos(3\u03c0(2(-1(-4x + 4)^2 + 2(-4x + 4) - 5) - 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": "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(1(2x + 1)^2 - 4(2x + 1) + 3)^2 - 5(1(2x + 1)^2 - 4(2x + 1) + 3) + 1)^2 - 4(-2(1(2x + 1)^2 - 4(2x + 1) + 3)^2 - 5(1(2x + 1)^2 - 4(2x + 1) + 3) + 1) + 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": "How many local maxima does the function f(x) = 1(-3|((-1((-2((-3x + 3)/(1x + 2)) - 2)/(1((-3x + 3)/(1x + 2)) - 3)) - 1)/(2((-2((-3x + 3)/(1x + 2)) - 2)/(1((-3x + 3)/(1x + 2)) - 3)))) - 2| + 2)^2 - 4(-3|((-1((-2((-3x + 3)/(1x + 2)) - 2)/(1((-3x + 3)/(1x + 2)) - 3)) - 1)/(2((-2((-3x + 3)/(1x + 2)) - 2)/(1((-3x + 3)/(1x + 2)) - 3)))) - 2| + 2) + 5 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) = -1sin(1\u03c0(2((-1((-3(2x + 1) + 3)/(1(2x + 1) + 2)))/(1((-3(2x + 1) + 3)/(1(2x + 1) + 2)) + 3))^2 - 5((-1((-3(2x + 1) + 3)/(1(2x + 1) + 2)))/(1((-3(2x + 1) + 3)/(1(2x + 1) + 2)) + 3)) - 5) - 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 minimum with the smallest y-value of the function f(x) = 4(-3sin(1\u03c0(-3|(4(-1x^2 - 4x + 2)^2 - 3(-1x^2 - 4x + 2) + 4) - 3| + 3)) + 1)^2 - 2(-3sin(1\u03c0(-3|(4(-1x^2 - 4x + 2)^2 - 3(-1x^2 - 4x + 2) + 4) - 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": "-5", "dataset": "MATH"}
{"messages": [{"content": "How many local minima does the function f(x) = -2|((3((-2(2|(-3x + 4) + 3| + 1) + 2)/(-2(2|(-3x + 4) + 3| + 1) + 3)) + 3)/(-1((-2(2|(-3x + 4) + 3| + 1) + 2)/(-2(2|(-3x + 4) + 3| + 1) + 3)) - 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": "How many local minima does the function f(x) = -1e^(-1(5((-2(-2|(2x^2 + 5x + 5) + 1| - 3) - 3)/(3(-2|(2x^2 + 5x + 5) + 1| - 3) - 2)) + 2)) + 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|(1(-4(3sin(1\u03c0(5x^2 - 2) - 1) - 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 minimum with the smallest y-value of the function f(x) = -5((-2(1(2(-2cos(2\u03c0x - 1) - 2)^2 - 2(-2cos(2\u03c0x - 1) - 2) + 5)^2 - 2(2(-2cos(2\u03c0x - 1) - 2)^2 - 2(-2cos(2\u03c0x - 1) - 2) + 5)) - 3)/(2(1(2(-2cos(2\u03c0x - 1) - 2)^2 - 2(-2cos(2\u03c0x - 1) - 2) + 5)^2 - 2(2(-2cos(2\u03c0x - 1) - 2)^2 - 2(-2cos(2\u03c0x - 1) - 2) + 5)) + 1))^2 - 1((-2(1(2(-2cos(2\u03c0x - 1) - 2)^2 - 2(-2cos(2\u03c0x - 1) - 2) + 5)^2 - 2(2(-2cos(2\u03c0x - 1) - 2)^2 - 2(-2cos(2\u03c0x - 1) - 2) + 5)) - 3)/(2(1(2(-2cos(2\u03c0x - 1) - 2)^2 - 2(-2cos(2\u03c0x - 1) - 2) + 5)^2 - 2(2(-2cos(2\u03c0x - 1) - 2)^2 - 2(-2cos(2\u03c0x - 1) - 2) + 5)) + 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": "How many local minima does the function f(x) = -5(-3|(4((-1(-2x - 2))/(1(-2x - 2) - 2))^2 - 3((-1(-2x - 2))/(1(-2x - 2) - 2)) + 4)| - 3)^2 + 2(-3|(4((-1(-2x - 2))/(1(-2x - 2) - 2))^2 - 3((-1(-2x - 2))/(1(-2x - 2) - 2)) + 4)| - 3) + 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 maximum of the function f(x) = (-3(1(-2sin(3\u03c0((1(3|x - 1| + 2) - 3)/(2(3|x - 1| + 2) + 3))) - 2) + 5) + 3)/(2(1(-2sin(3\u03c0((1(3|x - 1| + 2) - 3)/(2(3|x - 1| + 2) + 3))) - 2) + 5) - 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 minima does the function f(x) = 3(-1|((3(3(-1x + 4)^2 + 4(-1x + 4) - 2) + 2)/(-3(3(-1x + 4)^2 + 4(-1x + 4) - 2) + 1)) - 2| - 3)^2 + 5(-1|((3(3(-1x + 4)^2 + 4(-1x + 4) - 2) + 2)/(-3(3(-1x + 4)^2 + 4(-1x + 4) - 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 average of all x-coordinates of local maxima of the function f(x) = (-2(-2|(1|(2cos(3\u03c0(-1|x + 1| - 2) + 2) - 3) - 2| + 3) + 2| - 1) + 1)/(-3(-2|(1|(2cos(3\u03c0(-1|x + 1| - 2) + 2) - 3) - 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": "How many local maxima does the function f(x) = (3(-1|(-1|(-1|(1|x + 2| + 3) + 2| + 3) + 2|) + 1| + 3) - 3)/(-2(-1|(-1|(-1|(1|x + 2| + 3) + 2| + 3) + 2|) + 1| + 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 average of all x-coordinates of local minima of the function f(x) = -1|(-1(-2(5(-2|x + 2| + 3)^2 - 3(-2|x + 2| + 3) - 3)^2 - 4(5(-2|x + 2| + 3)^2 - 3(-2|x + 2| + 3) - 3) - 5) + 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": "-2", "dataset": "MATH"}
{"messages": [{"content": "Find the average of all x-coordinates of local extrema of the function f(x) = -1|(-3(-3e^(1(3(2x^2 + 3x - 3)^2 - 1(2x^2 + 3x - 3) - 4))) + 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 extremum of the function f(x) = (-3(-2|(2(-1|(4x + 2) - 2| - 3) - 5) - 2| + 1) - 1)/(-3(-2|(2(-1|(4x + 2) - 2| - 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": "0", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local minimum with the smallest y-value of the function f(x) = -2|(-3cos(1\u03c0(-1(4(4x^2 + 5x - 2)^2 + 3(4x^2 + 5x - 2) - 2) - 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": "-6", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local extremum of the function f(x) = (3(1e^(1(-3((-2(5x^2 - 1x + 1) + 1)/(-1(5x^2 - 1x + 1) - 2))^2 + 1((-2(5x^2 - 1x + 1) + 1)/(-1(5x^2 - 1x + 1) - 2)) - 1)) - 3) + 3)/(-1(1e^(1(-3((-2(5x^2 - 1x + 1) + 1)/(-1(5x^2 - 1x + 1) - 2))^2 + 1((-2(5x^2 - 1x + 1) + 1)/(-1(5x^2 - 1x + 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": "0", "dataset": "MATH"}
{"messages": [{"content": "How many local minima does the function f(x) = (-2(2|((3(-1(-5x - 3)^2 - 1(-5x - 3) + 5) + 2)/(-2(-1(-5x - 3)^2 - 1(-5x - 3) + 5) + 3)) + 1|))/(2(2|((3(-1(-5x - 3)^2 - 1(-5x - 3) + 5) + 2)/(-2(-1(-5x - 3)^2 - 1(-5x - 3) + 5) + 3)) + 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 minima of the function f(x) = (-2((1(-1(-1sin(2\u03c0(-1x - 5)) + 2)^2 - 1(-1sin(2\u03c0(-1x - 5)) + 2) - 1) + 2)/(-3(-1(-1sin(2\u03c0(-1x - 5)) + 2)^2 - 1(-1sin(2\u03c0(-1x - 5)) + 2) - 1) + 1)) + 3)/(2((1(-1(-1sin(2\u03c0(-1x - 5)) + 2)^2 - 1(-1sin(2\u03c0(-1x - 5)) + 2) - 1) + 2)/(-3(-1(-1sin(2\u03c0(-1x - 5)) + 2)^2 - 1(-1sin(2\u03c0(-1x - 5)) + 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 x-coordinate of the leftmost local minimum of the function f(x) = 1(-1|((-3(4(-1e^(-1x) + 1)^2 - 3) - 2)/(1(4(-1e^(-1x) + 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": "0", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local extremum with the largest y-value of the function f(x) = 3(-3(1sin(2\u03c0(-3(2|x + 3| - 3) - 5) + 2) - 1)^2 + 2(1sin(2\u03c0(-3(2|x + 3| - 3) - 5) + 2) - 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": "-10", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the leftmost local maximum of the function f(x) = 2|(1sin(3\u03c0((-3(-2|(-2x - 1) - 3| + 1) + 2)/(-3(-2|(-2x - 1) - 3| + 1) - 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": "-4", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local minimum with the smallest y-value of the function f(x) = -3|(-1(-2cos(2\u03c0(2((-2x + 3)/(-1x - 3))^2 - 4((-2x + 3)/(-1x - 3)) + 3) + 3) - 1)^2 + 3(-2cos(2\u03c0(2((-2x + 3)/(-1x - 3))^2 - 4((-2x + 3)/(-1x - 3)) + 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 maximum of the function f(x) = (-1(2(-3|((1(-2x + 3) + 3)/(-1(-2x + 3) + 3)) - 3| + 3) + 5) - 2)/(-3(2(-3|((1(-2x + 3) + 3)/(-1(-2x + 3) + 3)) - 3| + 3) + 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 x-coordinate of the local maximum of the function f(x) = -4(-2cos(3\u03c0((-3(-3|(1x^2 + 1x + 4) - 2| - 2) - 1)/(-2(-3|(1x^2 + 1x + 4) - 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": "0", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the rightmost local maximum of the function f(x) = 3(-4(-1|((-2(-5x - 4) - 2)/(1(-5x - 4) - 2)) - 1| + 1)^2 - 4(-1|((-2(-5x - 4) - 2)/(1(-5x - 4) - 2)) - 1| + 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 x-coordinate of the leftmost local maximum of the function f(x) = 3|(2((3(3((1x - 1)/(3x + 3))^2 + 3((1x - 1)/(3x + 3)) - 5) - 3)/(-2(3((1x - 1)/(3x + 3))^2 + 3((1x - 1)/(3x + 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": "-1", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local extremum of the function f(x) = -1|(-3|(-3|((1(1|x| + 1) + 3)/(-1(1|x| + 1) - 1)) + 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": "0", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local extremum of the function f(x) = -1|((-3(-2e^(-1((-3(1x^2 + 1x) + 2)/(-2(1x^2 + 1x) - 2))) + 2) + 3)/(-1(-2e^(-1((-3(1x^2 + 1x) + 2)/(-2(1x^2 + 1x) - 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": "0", "dataset": "MATH"}
{"messages": [{"content": "Find the average of all x-coordinates of local extrema of the function f(x) = (-1((-1(-3cos(3\u03c0(2|(1x^2 - 2x + 2) - 3| + 3) - 2) - 1) - 3)/(-1(-3cos(3\u03c0(2|(1x^2 - 2x + 2) - 3| + 3) - 2) - 1) + 2)) + 1)/(2((-1(-3cos(3\u03c0(2|(1x^2 - 2x + 2) - 3| + 3) - 2) - 1) - 3)/(-1(-3cos(3\u03c0(2|(1x^2 - 2x + 2) - 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": "0", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local extremum of the function f(x) = 1(1|(1e^(1(2|((-1x - 1)/(3x - 2)) - 3| - 1)) + 2) + 1| - 2)^2 + 1(1|(1e^(1(2|((-1x - 1)/(3x - 2)) - 3| - 1)) + 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": "How many local extrema (both minima and maxima) does the function f(x) = 4(5(2|(-2|(4x + 2) - 2| + 3)| - 1) + 3)^2 + 1(5(2|(-2|(4x + 2) - 2| + 3)| - 1) + 3) + 4 have in the interval [-10, 10]?\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 maximum of the function f(x) = (2(1|(-1(-3cos(1\u03c0(-3|x + 2| - 2) + 3) + 3)^2 + 2(-3cos(1\u03c0(-3|x + 2| - 2) + 3) + 3) + 2)|) - 3)/(-2(1|(-1(-3cos(1\u03c0(-3|x + 2| - 2) + 3) + 3)^2 + 2(-3cos(1\u03c0(-3|x + 2| - 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 rightmost local extremum of the function f(x) = -4(1|(-1(-3cos(1\u03c0((2x)/(3x - 2)) - 1) + 1) - 4) - 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": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local maximum with the smallest y-value of the function f(x) = -2(-1sin(1\u03c0(1(3|((-2x - 2)/(1x - 3)) - 3| - 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": "-6", "dataset": "MATH"}
{"messages": [{"content": "Find the average of all x-coordinates of local minima of the function f(x) = (2(-3((2(1|(2|x + 3| - 1)|) - 2)/(-1(1|(2|x + 3| - 1)|) + 3))^2 + 2) - 1)/(3(-3((2(1|(2|x + 3| - 1)|) - 2)/(-1(1|(2|x + 3| - 1)|) + 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": "-3", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the leftmost local extremum of the function f(x) = (-1(3sin(3\u03c0((2((-2(4x^2 + 3x) + 3)/(-3(4x^2 + 3x) + 2)) - 2)/(2((-2(4x^2 + 3x) + 3)/(-3(4x^2 + 3x) + 2)))) - 2) - 3) + 2)/(-1(3sin(3\u03c0((2((-2(4x^2 + 3x) + 3)/(-3(4x^2 + 3x) + 2)) - 2)/(2((-2(4x^2 + 3x) + 3)/(-3(4x^2 + 3x) + 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": "-2", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the rightmost local maximum of the function f(x) = -1(-1|(-2|(-2cos(2\u03c0(1x^2 - 2x + 4) + 2) + 2)| - 2) + 3| - 1)^2 - 2(-1|(-2|(-2cos(2\u03c0(1x^2 - 2x + 4) + 2) + 2)| - 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": "10", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local minimum of the function f(x) = 1|(2|(-2(2|(2x^2 - 3x)| + 2) + 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 rightmost local extremum of the function f(x) = -2|((1(3(-5(1sin(3\u03c0x + 3) + 1)^2 - 5(1sin(3\u03c0x + 3) + 1) - 1) + 4))/(2(3(-5(1sin(3\u03c0x + 3) + 1)^2 - 5(1sin(3\u03c0x + 3) + 1) - 1) + 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": "10", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the rightmost local maximum of the function f(x) = (-1(-3(3|(2((1x + 2)/(1x))^2 + 2((1x + 2)/(1x)) - 4) - 2| + 3) - 4) - 3)/(-2(-3(3|(2((1x + 2)/(1x))^2 + 2((1x + 2)/(1x)) - 4) - 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": "0", "dataset": "MATH"}
{"messages": [{"content": "Find the average of all x-coordinates of local maxima of the function f(x) = -3cos(3\u03c0(2|((2(-4(-1x - 5)^2 + 2(-1x - 5) + 5) + 2)/(-1(-4(-1x - 5)^2 + 2(-1x - 5) + 5) + 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": "-5", "dataset": "MATH"}
{"messages": [{"content": "How many local maxima does the function f(x) = 3sin(1\u03c0((3(-3(-2|(-4x^2 + 3x + 4)| - 1) - 2) + 3)/(-2(-3(-2|(-4x^2 + 3x + 4)| - 1) - 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 rightmost local minimum of the function f(x) = 2(-5(5(1|(-4x^2 + 1x) + 2|)^2 + 1(1|(-4x^2 + 1x) + 2|) - 4)^2 + 3(5(1|(-4x^2 + 1x) + 2|)^2 + 1(1|(-4x^2 + 1x) + 2|) - 4)) + 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 local minimum of the function f(x) = 2e^(1((1((-1(3|(2x^2 + 5x + 4) + 1| - 1) + 1)/(-3(3|(2x^2 + 5x + 4) + 1| - 1) + 4)) - 3)/(-3((-1(3|(2x^2 + 5x + 4) + 1| - 1) + 1)/(-3(3|(2x^2 + 5x + 4) + 1| - 1) + 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": "-1", "dataset": "MATH"}
{"messages": [{"content": "Find the average of all x-coordinates of local extrema of the function f(x) = 2(2cos(3\u03c0(2|(5(-4x^2 - 5x - 3)^2 + 2(-4x^2 - 5x - 3) + 2)| + 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": "0", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the rightmost local extremum of the function f(x) = -2|(2|(-3cos(1\u03c0(2(3|x| - 2)^2 + 1(3|x| - 2) - 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": "10", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local maximum with the smallest y-value of the function f(x) = -1(4(3cos(2\u03c0(1((-3x - 3)/(2x + 3)) + 1) + 2) + 1) + 3)^2 - 5(4(3cos(2\u03c0(1((-3x - 3)/(2x + 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": "-5", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local extremum with the largest y-value of the function f(x) = 1(-3((3((2(-2cos(3\u03c0x - 2) + 1) - 1)/(1(-2cos(3\u03c0x - 2) + 1) + 3)) + 2)/(2((2(-2cos(3\u03c0x - 2) + 1) - 1)/(1(-2cos(3\u03c0x - 2) + 1) + 3))))^2 - 1((3((2(-2cos(3\u03c0x - 2) + 1) - 1)/(1(-2cos(3\u03c0x - 2) + 1) + 3)) + 2)/(2((2(-2cos(3\u03c0x - 2) + 1) - 1)/(1(-2cos(3\u03c0x - 2) + 1) + 3)))) + 1)^2 + 5(-3((3((2(-2cos(3\u03c0x - 2) + 1) - 1)/(1(-2cos(3\u03c0x - 2) + 1) + 3)) + 2)/(2((2(-2cos(3\u03c0x - 2) + 1) - 1)/(1(-2cos(3\u03c0x - 2) + 1) + 3))))^2 - 1((3((2(-2cos(3\u03c0x - 2) + 1) - 1)/(1(-2cos(3\u03c0x - 2) + 1) + 3)) + 2)/(2((2(-2cos(3\u03c0x - 2) + 1) - 1)/(1(-2cos(3\u03c0x - 2) + 1) + 3)))) + 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": "-9", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local minimum of the function f(x) = -2(2(-3|((-2((2x)/(-2x - 2)) - 2)/(1((2x)/(-2x - 2)))) - 3|)^2 - 1(-3|((-2((2x)/(-2x - 2)) - 2)/(1((2x)/(-2x - 2)))) - 3|) - 2)^2 + 3(2(-3|((-2((2x)/(-2x - 2)) - 2)/(1((2x)/(-2x - 2)))) - 3|)^2 - 1(-3|((-2((2x)/(-2x - 2)) - 2)/(1((2x)/(-2x - 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": "How many local minima does the function f(x) = (1((-2(-4((3(-3x^2 + 3x - 5) - 3)/(-1(-3x^2 + 3x - 5))) + 4) - 3)/(1(-4((3(-3x^2 + 3x - 5) - 3)/(-1(-3x^2 + 3x - 5))) + 4) - 2)) - 1)/(3((-2(-4((3(-3x^2 + 3x - 5) - 3)/(-1(-3x^2 + 3x - 5))) + 4) - 3)/(1(-4((3(-3x^2 + 3x - 5) - 3)/(-1(-3x^2 + 3x - 5))) + 4) - 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": "How many local maxima does the function f(x) = -3|(1(-3(2(2sin(2\u03c0x + 3) + 1) - 4) + 5) - 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 local extremum of the function f(x) = -2(-1|((-1(-4(-1x^2 + 3x - 3) - 1) + 2)/(3(-4(-1x^2 + 3x - 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": "2", "dataset": "MATH"}
{"messages": [{"content": "How many local maxima does the function f(x) = 3((2(1|(-3sin(3\u03c0((1x + 1)/(-1x - 2)) + 1) - 1) + 1| + 3) - 2)/(-3(1|(-3sin(3\u03c0((1x + 1)/(-1x - 2)) + 1) - 1) + 1| + 3) - 3)) + 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 maximum of the function f(x) = 2|(-3cos(2\u03c0(-3|(1|(1x + 5) + 1| - 3) - 3| + 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": "10", "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(2cos(1\u03c0(2|x| + 1) - 3) - 1) + 4) - 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": "Find the x-coordinate of the local extremum with the largest y-value of the function f(x) = -3|(-2(3(2|(2x^2 + 2x - 3) - 1| + 3) - 4)^2 + 2(3(2|(2x^2 + 2x - 3) - 1| + 3) - 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": "-2", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local extremum with the smallest y-value of the function f(x) = -5(-1e^(1(-4(3(4x^2 - 1x - 5) - 3)^2 - 1)))^2 - 3(-1e^(1(-4(3(4x^2 - 1x - 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 x-coordinate of the local maximum with the smallest y-value of the function f(x) = -2|((3(1cos(3\u03c0(-1(-5x^2 - 4x + 3)^2 - 5(-5x^2 - 4x + 3) + 1)) - 1))/(-1(1cos(3\u03c0(-1(-5x^2 - 4x + 3)^2 - 5(-5x^2 - 4x + 3) + 1)) - 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 maximum of the function f(x) = -3((-2((1(1|(-2x^2 + 4x + 3) - 3| - 3) + 1)/(-2(1|(-2x^2 + 4x + 3) - 3| - 3) + 3)) - 3)/(2((1(1|(-2x^2 + 4x + 3) - 3| - 3) + 1)/(-2(1|(-2x^2 + 4x + 3) - 3| - 3) + 3)) + 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": "0", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the leftmost local maximum of the function f(x) = 3(-2|(3sin(1\u03c0(-5(1x + 4) + 2) - 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 leftmost local maximum of the function f(x) = -5((-3(1(3sin(1\u03c0(-3x - 1) - 2) - 1)^2 + 5(3sin(1\u03c0(-3x - 1) - 2) - 1) - 3) + 1)/(-1(1(3sin(1\u03c0(-3x - 1) - 2) - 1)^2 + 5(3sin(1\u03c0(-3x - 1) - 2) - 1) - 3) - 2))^2 - 5((-3(1(3sin(1\u03c0(-3x - 1) - 2) - 1)^2 + 5(3sin(1\u03c0(-3x - 1) - 2) - 1) - 3) + 1)/(-1(1(3sin(1\u03c0(-3x - 1) - 2) - 1)^2 + 5(3sin(1\u03c0(-3x - 1) - 2) - 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 rightmost local extremum of the function f(x) = (2(-1((1(-2(1x^2 - 4x - 5)^2 - 2(1x^2 - 4x - 5) + 4) - 2)/(2(-2(1x^2 - 4x - 5)^2 - 2(1x^2 - 4x - 5) + 4) - 3))^2 - 5((1(-2(1x^2 - 4x - 5)^2 - 2(1x^2 - 4x - 5) + 4) - 2)/(2(-2(1x^2 - 4x - 5)^2 - 2(1x^2 - 4x - 5) + 4) - 3))) - 3)/(-2(-1((1(-2(1x^2 - 4x - 5)^2 - 2(1x^2 - 4x - 5) + 4) - 2)/(2(-2(1x^2 - 4x - 5)^2 - 2(1x^2 - 4x - 5) + 4) - 3))^2 - 5((1(-2(1x^2 - 4x - 5)^2 - 2(1x^2 - 4x - 5) + 4) - 2)/(2(-2(1x^2 - 4x - 5)^2 - 2(1x^2 - 4x - 5) + 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": "5", "dataset": "MATH"}
{"messages": [{"content": "Find the average of all x-coordinates of local maxima of the function f(x) = -2(-1cos(3\u03c0(3(2(-1x^2 + 4x + 1)^2 - 4(-1x^2 + 4x + 1) + 5)^2 - 2(2(-1x^2 + 4x + 1)^2 - 4(-1x^2 + 4x + 1) + 5) - 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": "2", "dataset": "MATH"}
{"messages": [{"content": "How many local minima does the function f(x) = -1|((-1(-1(-5(5x^2 - 3x - 5) + 2) + 4) + 3)/(2(-1(-5(5x^2 - 3x - 5) + 2) + 4))) - 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 maximum with the smallest y-value of the function f(x) = 1((-1(2|((2(-1x^2 - 4x + 1) - 3)/(3(-1x^2 - 4x + 1) - 2)) - 1| - 1) + 1)/(1(2|((2(-1x^2 - 4x + 1) - 3)/(3(-1x^2 - 4x + 1) - 2)) - 1| - 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": "-2", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local extremum of the function f(x) = 4(-2|((1((-2(-5x^2 - 2x + 5) + 3)/(-1(-5x^2 - 2x + 5) + 2)))/(-2((-2(-5x^2 - 2x + 5) + 3)/(-1(-5x^2 - 2x + 5) + 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": "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(3sin(1\u03c0(-2|x + 1| + 1) + 1) + 2)^2 - 2(3sin(1\u03c0(-2|x + 1| + 1) + 1) + 2) + 5) - 2| + 2) + 1)/(-1(-3|(-1(3sin(1\u03c0(-2|x + 1| + 1) + 1) + 2)^2 - 2(3sin(1\u03c0(-2|x + 1| + 1) + 1) + 2) + 5) - 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": "-9", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local maximum with the largest y-value of the function f(x) = -3cos(2\u03c0(-5(2(5(-1x - 4)^2 + 3(-1x - 4) + 2)^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": "-6", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local extremum with the largest y-value of the function f(x) = (-3(5(-2cos(2\u03c0(-4((2x - 2)/(2x))^2 - 2((2x - 2)/(2x)) - 2) - 1) - 3)^2 + 5(-2cos(2\u03c0(-4((2x - 2)/(2x))^2 - 2((2x - 2)/(2x)) - 2) - 1) - 3) - 4))/(-2(5(-2cos(2\u03c0(-4((2x - 2)/(2x))^2 - 2((2x - 2)/(2x)) - 2) - 1) - 3)^2 + 5(-2cos(2\u03c0(-4((2x - 2)/(2x))^2 - 2((2x - 2)/(2x)) - 2) - 1) - 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": "-6", "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(1(-1|(3|(3|x + 2| - 3)| - 3) - 1| + 2)^2 - 4(-1|(3|(3|x + 2| - 3)| - 3) - 1| + 2) - 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": "-1", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local maximum of the function f(x) = -5(-2sin(1\u03c0((-1(5(4x - 3)^2 + 3(4x - 3) - 1))/(2(5(4x - 3)^2 + 3(4x - 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 local maximum with the largest y-value of the function f(x) = -1|(4(1cos(3\u03c0(5(-4x^2 - 2)^2 + 2(-4x^2 - 2) + 2) - 1) + 3) + 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": "-3", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the leftmost local maximum of the function f(x) = -1|(1sin(3\u03c0(4(-2(-3|x - 2| - 2) + 2)^2 - 2(-2(-3|x - 2| - 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": "-10", "dataset": "MATH"}
{"messages": [{"content": "Find the average of all x-coordinates of local maxima of the function f(x) = -2cos(2\u03c0(-2|(-5((2(2x - 2) + 1)/(3(2x - 2) - 1))^2 - 5((2(2x - 2) + 1)/(3(2x - 2) - 1)) - 2) + 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": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the average of all x-coordinates of local minima of the function f(x) = (-1(-2sin(2\u03c0(5(-3((-3x - 3)/(3x + 2)) + 1)^2 - 4(-3((-3x - 3)/(3x + 2)) + 1))) - 2) + 3)/(-1(-2sin(2\u03c0(5(-3((-3x - 3)/(3x + 2)) + 1)^2 - 4(-3((-3x - 3)/(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": "-1", "dataset": "MATH"}
{"messages": [{"content": "How many local minima does the function f(x) = (-3(1(-1|(1|(3|x + 2| - 2)| + 2) + 1| + 1)^2 + 5(-1|(1|(3|x + 2| - 2)| + 2) + 1| + 1) - 2) + 3)/(1(1(-1|(1|(3|x + 2| - 2)| + 2) + 1| + 1)^2 + 5(-1|(1|(3|x + 2| - 2)| + 2) + 1| + 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 x-coordinate of the local minimum with the smallest y-value of the function f(x) = -2(-2|((2(-1|(2sin(1\u03c0x - 1) + 2) - 1| + 2))/(-1(-1|(2sin(1\u03c0x - 1) + 2) - 1| + 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": "-9", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local maximum with the smallest y-value of the function f(x) = (-3(-1|(-1(-3cos(1\u03c0(1x + 3) + 3) - 3)^2 + 2(-3cos(1\u03c0(1x + 3) + 3) - 3) + 3) + 2| + 1))/(1(-1|(-1(-3cos(1\u03c0(1x + 3) + 3) - 3)^2 + 2(-3cos(1\u03c0(1x + 3) + 3) - 3) + 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": "-9", "dataset": "MATH"}
{"messages": [{"content": "Find the average of all x-coordinates of local maxima of the function f(x) = -4(-1(-2|(-1(3|x| - 1)^2 + 1(3|x| - 1) - 5)| - 2) + 5)^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 rightmost local maximum of the function f(x) = 3|(-1cos(2\u03c0(-2|(-2(-1|x + 3| + 1)) - 2| - 1) + 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": "10", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the leftmost local extremum of the function f(x) = 3|((-2(-2(-2((-1x + 3)/(-3x - 1))^2 + 1((-1x + 3)/(-3x - 1)) + 1) + 2) - 1)/(-2(-2(-2((-1x + 3)/(-3x - 1))^2 + 1((-1x + 3)/(-3x - 1)) + 1) + 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 leftmost local minimum of the function f(x) = -4(-1(1|(-1sin(2\u03c0(1x^2 - 4x + 3) - 3) - 1)| + 2)^2 - 4(1|(-1sin(2\u03c0(1x^2 - 4x + 3) - 3) - 1)| + 2) - 3)^2 + 5(-1(1|(-1sin(2\u03c0(1x^2 - 4x + 3) - 3) - 1)| + 2)^2 - 4(1|(-1sin(2\u03c0(1x^2 - 4x + 3) - 3) - 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": "How many local maxima does the function f(x) = -1|(3((-3(5((1x - 2)/(-2x - 1)) + 3))/(-3(5((1x - 2)/(-2x - 1)) + 3) - 1))^2 - 5((-3(5((1x - 2)/(-2x - 1)) + 3))/(-3(5((1x - 2)/(-2x - 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": "0", "dataset": "MATH"}
{"messages": [{"content": "How many local extrema (both minima and maxima) does the function f(x) = 4(1|(2|(-1sin(2\u03c0((-1x - 2)/(3x - 2)) + 3) + 2)| - 2) - 1| - 1)^2 - 2(1|(2|(-1sin(2\u03c0((-1x - 2)/(3x - 2)) + 3) + 2)| - 2) - 1| - 1) + 3 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "48", "dataset": "MATH"}
{"messages": [{"content": "How many local maxima does the function f(x) = 4(1(-2((3(2x - 4))/(1(2x - 4) + 3)) + 3)^2 + 2(-2((3(2x - 4))/(1(2x - 4) + 3)) + 3) + 2)^2 - 5(1(-2((3(2x - 4))/(1(2x - 4) + 3)) + 3)^2 + 2(-2((3(2x - 4))/(1(2x - 4) + 3)) + 3) + 2) - 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 local minimum with the smallest y-value of the function f(x) = -1|(1(-1(3(-2x^2 + 2x + 1) - 4)^2 - 4(3(-2x^2 + 2x + 1) - 4) + 3)^2 + 2(-1(3(-2x^2 + 2x + 1) - 4)^2 - 4(3(-2x^2 + 2x + 1) - 4) + 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 average of all x-coordinates of local minima of the function f(x) = 2(5((-3(-5(3sin(1\u03c0x) - 3) - 1) + 2)/(-2(-5(3sin(1\u03c0x) - 3) - 1) - 1)) + 2)^2 + 2(5((-3(-5(3sin(1\u03c0x) - 3) - 1) + 2)/(-2(-5(3sin(1\u03c0x) - 3) - 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": "0", "dataset": "MATH"}
{"messages": [{"content": "How many local maxima does the function f(x) = 5(3(2((-3(-2e^(-1x) + 2) + 2)/(1(-2e^(-1x) + 2) - 2))^2 - 5((-3(-2e^(-1x) + 2) + 2)/(1(-2e^(-1x) + 2) - 2)) + 5)^2 + 5(2((-3(-2e^(-1x) + 2) + 2)/(1(-2e^(-1x) + 2) - 2))^2 - 5((-3(-2e^(-1x) + 2) + 2)/(1(-2e^(-1x) + 2) - 2)) + 5) + 5) - 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 minimum of the function f(x) = (3(-2|((-2((3(-3|x - 3|) - 2)/(-2(-3|x - 3|) - 1)) - 2)/(-3((3(-3|x - 3|) - 2)/(-2(-3|x - 3|) - 1)) - 3)) + 3| - 1) - 2)/(2(-2|((-2((3(-3|x - 3|) - 2)/(-2(-3|x - 3|) - 1)) - 2)/(-3((3(-3|x - 3|) - 2)/(-2(-3|x - 3|) - 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": "10", "dataset": "MATH"}
{"messages": [{"content": "How many local minima does the function f(x) = 1(-2|(2e^(-1(-1|(1|x + 3| + 3) + 1| + 1)) + 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 local minimum with the smallest y-value of the function f(x) = (1(5(-2sin(2\u03c0(-1(1x + 5) + 1) - 2) - 3)^2 - 1(-2sin(2\u03c0(-1(1x + 5) + 1) - 2) - 3) + 5) - 1)/(-3(5(-2sin(2\u03c0(-1(1x + 5) + 1) - 2) - 3)^2 - 1(-2sin(2\u03c0(-1(1x + 5) + 1) - 2) - 3) + 5) - 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) = 5(-1(4(2|(-2sin(1\u03c0x) - 2) + 3| - 2) + 2)^2 - 1(4(2|(-2sin(1\u03c0x) - 2) + 3| - 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": "-8", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local extremum with the smallest y-value of the function f(x) = -4(3sin(1\u03c0((-2(-3(5x^2 - 3x - 2) - 4) + 1)/(1(-3(5x^2 - 3x - 2) - 4) + 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": "-1", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local extremum with the smallest y-value of the function f(x) = 3((2(2((-1((-2x + 1)/(-2x - 1)) + 1)/(-1((-2x + 1)/(-2x - 1)) - 1))^2 - 4((-1((-2x + 1)/(-2x - 1)) + 1)/(-1((-2x + 1)/(-2x - 1)) - 1))) - 2)/(2(2((-1((-2x + 1)/(-2x - 1)) + 1)/(-1((-2x + 1)/(-2x - 1)) - 1))^2 - 4((-1((-2x + 1)/(-2x - 1)) + 1)/(-1((-2x + 1)/(-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) = 1cos(2\u03c0(1(-3((1(-1x + 4) - 2)/(1(-1x + 4) + 2)) - 1)^2 + 2(-3((1(-1x + 4) - 2)/(1(-1x + 4) + 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": "-9", "dataset": "MATH"}
{"messages": [{"content": "How many local minima does the function f(x) = 1|(2|((2(3(-2x^2 - 5x - 5)^2 + 2))/(2(3(-2x^2 - 5x - 5)^2 + 2) - 1)) + 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 maximum of the function f(x) = (-2(1(-1cos(3\u03c0((2(-1x^2 + 3))/(2(-1x^2 + 3) + 2)) - 3) + 2)^2 + 1(-1cos(3\u03c0((2(-1x^2 + 3))/(2(-1x^2 + 3) + 2)) - 3) + 2) - 2))/(-3(1(-1cos(3\u03c0((2(-1x^2 + 3))/(2(-1x^2 + 3) + 2)) - 3) + 2)^2 + 1(-1cos(3\u03c0((2(-1x^2 + 3))/(2(-1x^2 + 3) + 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": "-2", "dataset": "MATH"}
{"messages": [{"content": "Find the average of all x-coordinates of local minima of the function f(x) = 2|((3(-3(1cos(3\u03c0(-1x - 2) + 2) + 3)^2 - 5(1cos(3\u03c0(-1x - 2) + 2) + 3) - 4) - 3)/(2(-3(1cos(3\u03c0(-1x - 2) + 2) + 3)^2 - 5(1cos(3\u03c0(-1x - 2) + 2) + 3) - 4) + 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": "0", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the rightmost local maximum of the function f(x) = -1|((2(-4((1(1cos(3\u03c0x + 2)) - 1)/(2(1cos(3\u03c0x + 2)))) - 4) + 1)/(3(-4((1(1cos(3\u03c0x + 2)) - 1)/(2(1cos(3\u03c0x + 2)))) - 4) + 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": "Find the x-coordinate of the rightmost local minimum of the function f(x) = -3(2|(1(1(-3|x + 3| - 3) + 3)^2 + 5(1(-3|x + 3| - 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": "-2", "dataset": "MATH"}
{"messages": [{"content": "How many local minima does the function f(x) = (1(3cos(2\u03c0((3(-5(-3x - 2) - 3) + 3)/(-2(-5(-3x - 2) - 3) - 1))) + 2) - 3)/(3(3cos(2\u03c0((3(-5(-3x - 2) - 3) + 3)/(-2(-5(-3x - 2) - 3) - 1))) + 2) + 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) = -3cos(3\u03c0((-3((2(-5(-4x)^2 + 4(-4x) - 2) + 2)/(3(-5(-4x)^2 + 4(-4x) - 2) - 2)) - 3)/(-1((2(-5(-4x)^2 + 4(-4x) - 2) + 2)/(3(-5(-4x)^2 + 4(-4x) - 2) - 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": "How many local minima does the function f(x) = -2e^(1(5((-1((1((2x + 3)/(-1x + 2)) - 1)/(2((2x + 3)/(-1x + 2)) - 1)) + 3)/(-2((1((2x + 3)/(-1x + 2)) - 1)/(2((2x + 3)/(-1x + 2)) - 1)) - 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 leftmost local minimum of the function f(x) = 1|(2|(-1cos(2\u03c0(3|((3x + 1)/(-1x + 2)) - 3| - 2) + 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": "-6", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local extremum of the function f(x) = 4(-4(2|((1(5x^2 + 2x - 2))/(-2(5x^2 + 2x - 2) - 1)) - 2| + 3)^2 + 1(2|((1(5x^2 + 2x - 2))/(-2(5x^2 + 2x - 2) - 1)) - 2| + 3) - 1)^2 - 2(-4(2|((1(5x^2 + 2x - 2))/(-2(5x^2 + 2x - 2) - 1)) - 2| + 3)^2 + 1(2|((1(5x^2 + 2x - 2))/(-2(5x^2 + 2x - 2) - 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": "0", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the rightmost local maximum of the function f(x) = -3(-3sin(2\u03c0((3((-1(-3x^2 + 2x - 4) - 2)/(-2(-3x^2 + 2x - 4) - 2)) + 2)/(2((-1(-3x^2 + 2x - 4) - 2)/(-2(-3x^2 + 2x - 4) - 2)) - 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": "How many local extrema (both minima and maxima) does the function f(x) = (-3(-2(3|(2(3x + 5) - 4) - 2| - 1)^2 + 4(3|(2(3x + 5) - 4) - 2| - 1) + 4) + 2)/(-1(-2(3|(2(3x + 5) - 4) - 2| - 1)^2 + 4(3|(2(3x + 5) - 4) - 2| - 1) + 4)) 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 maximum with the smallest y-value of the function f(x) = 4(4(-3|(-4(-1x^2 - 4x - 1) - 4) + 1| + 2)^2 - 2(-3|(-4(-1x^2 - 4x - 1) - 4) + 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": "-4", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the rightmost local maximum of the function f(x) = -3cos(3\u03c0(-2|(4(3(1x^2 + 5x - 3) + 5) + 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": "10", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the rightmost local maximum of the function f(x) = 2(3|(2cos(3\u03c0(-2(-2|x - 3| + 2) - 2) - 3) + 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 local extremum with the smallest y-value of the function f(x) = -3((2(-3|(-1e^(1(-5x - 4)) - 2) + 3| + 1) - 1)/(1(-3|(-1e^(1(-5x - 4)) - 2) + 3| + 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 average of all x-coordinates of local minima of the function f(x) = -2|(-1(2sin(3\u03c0(3|(-1x - 4) - 1| - 2) + 2)) + 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": "0", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local minimum of the function f(x) = 2e^(2(-1|((1((3(-3x - 1) + 3)/(-2(-3x - 1) - 2)) + 1)/(-2((3(-3x - 1) + 3)/(-2(-3x - 1) - 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": "0", "dataset": "MATH"}
{"messages": [{"content": "How many local extrema (both minima and maxima) does the function f(x) = -2|(-1((1(5(2|x + 3| - 1)^2 + 1(2|x + 3| - 1) - 3) - 2)/(-3(5(2|x + 3| - 1)^2 + 1(2|x + 3| - 1) - 3) + 2))^2 + 5((1(5(2|x + 3| - 1)^2 + 1(2|x + 3| - 1) - 3) - 2)/(-3(5(2|x + 3| - 1)^2 + 1(2|x + 3| - 1) - 3) + 2)) + 5) - 2| - 1 have in the interval [-10, 10]?\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) = (-3(3(1|(-1(-3cos(3\u03c0x - 2) - 3) - 4) + 3| + 2) + 1) - 1)/(2(3(1|(-1(-3cos(3\u03c0x - 2) - 3) - 4) + 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) = (3(-1(-2|(1(-4x^2 + 1x - 2)^2 - 4(-4x^2 + 1x - 2) - 4) - 1| + 2) + 4) + 3)/(-2(-1(-2|(1(-4x^2 + 1x - 2)^2 - 4(-4x^2 + 1x - 2) - 4) - 1| + 2) + 4) + 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 minima does the function f(x) = (-1(1(2(1|(-3e^(-1x) + 2)| + 2)^2 - 3(1|(-3e^(-1x) + 2)| + 2) + 2)^2 + 3(2(1|(-3e^(-1x) + 2)| + 2)^2 - 3(1|(-3e^(-1x) + 2)| + 2) + 2) - 1))/(1(1(2(1|(-3e^(-1x) + 2)| + 2)^2 - 3(1|(-3e^(-1x) + 2)| + 2) + 2)^2 + 3(2(1|(-3e^(-1x) + 2)| + 2)^2 - 3(1|(-3e^(-1x) + 2)| + 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 minima of the function f(x) = 3(-2(-5(2|(1cos(3\u03c0x + 2) + 1) + 3|) + 4)^2 - 5(-5(2|(1cos(3\u03c0x + 2) + 1) + 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": "0", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local maximum with the largest y-value of the function f(x) = -1(-2|((-1(3e^(-1(-2|x + 3| - 1)) + 1) - 3)/(2(3e^(-1(-2|x + 3| - 1)) + 1))) + 1| - 3)^2 + 3(-2|((-1(3e^(-1(-2|x + 3| - 1)) + 1) - 3)/(2(3e^(-1(-2|x + 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": "9", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the leftmost local maximum of the function f(x) = 1|(2((-1(2|(-5x) + 2|) - 3)/(-3(2|(-5x) + 2|)))^2 - 2((-1(2|(-5x) + 2|) - 3)/(-3(2|(-5x) + 2|))) - 4) - 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 of the function f(x) = -1(-2(-1((-3(-4x^2 - 2x - 1) - 2)/(2(-4x^2 - 2x - 1) + 2))^2 - 3((-3(-4x^2 - 2x - 1) - 2)/(2(-4x^2 - 2x - 1) + 2)) + 5)^2 + 2(-1((-3(-4x^2 - 2x - 1) - 2)/(2(-4x^2 - 2x - 1) + 2))^2 - 3((-3(-4x^2 - 2x - 1) - 2)/(2(-4x^2 - 2x - 1) + 2)) + 5) + 5) - 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 maximum with the largest y-value of the function f(x) = -1cos(1\u03c0(1((-1(2|((2x + 1)/(-1x + 2)) + 2| - 2))/(-2(2|((2x + 1)/(-1x + 2)) + 2| - 2) + 1))^2 + 5((-1(2|((2x + 1)/(-1x + 2)) + 2| - 2))/(-2(2|((2x + 1)/(-1x + 2)) + 2| - 2) + 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": "-3", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the leftmost local minimum of the function f(x) = 1(-1|(1|(-1((-3x - 3)/(-3x + 2)) - 1) - 1| - 3) + 1|)^2 - 1(-1|(1|(-1((-3x - 3)/(-3x + 2)) - 1) - 1| - 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": "0", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the rightmost local minimum of the function f(x) = (-3(5(-4(4(-2cos(3\u03c0x - 1) - 2) + 1)^2 - 4(4(-2cos(3\u03c0x - 1) - 2) + 1) - 3) + 4) - 3)/(1(5(-4(4(-2cos(3\u03c0x - 1) - 2) + 1)^2 - 4(4(-2cos(3\u03c0x - 1) - 2) + 1) - 3) + 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": "10", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the leftmost local extremum of the function f(x) = 2cos(3\u03c0(-2|((1(-3((-2x + 1)/(-1x + 2))^2 - 1((-2x + 1)/(-1x + 2)) - 5) - 3)/(3(-3((-2x + 1)/(-1x + 2))^2 - 1((-2x + 1)/(-1x + 2)) - 5) + 2)) - 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 local minimum with the largest y-value of the function f(x) = 3(3(1|(-3(1cos(1\u03c0x - 2) - 3)^2 + 4(1cos(1\u03c0x - 2) - 3) - 2) - 2| - 3)^2 + 2(1|(-3(1cos(1\u03c0x - 2) - 3)^2 + 4(1cos(1\u03c0x - 2) - 3) - 2) - 2| - 3) + 3)^2 - 1(3(1|(-3(1cos(1\u03c0x - 2) - 3)^2 + 4(1cos(1\u03c0x - 2) - 3) - 2) - 2| - 3)^2 + 2(1|(-3(1cos(1\u03c0x - 2) - 3)^2 + 4(1cos(1\u03c0x - 2) - 3) - 2) - 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": "-7", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local minimum of the function f(x) = (3(-3(5(-1(-5x^2 + 3x - 2) - 5)^2 - 3(-1(-5x^2 + 3x - 2) - 5) - 1) - 1) + 3)/(-3(-3(5(-1(-5x^2 + 3x - 2) - 5)^2 - 3(-1(-5x^2 + 3x - 2) - 5) - 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 rightmost local maximum of the function f(x) = (2(5(4(3|(-5x^2 + 3x + 5) - 3| + 3)^2 - 4(3|(-5x^2 + 3x + 5) - 3| + 3) + 1)^2 - 1(4(3|(-5x^2 + 3x + 5) - 3| + 3)^2 - 4(3|(-5x^2 + 3x + 5) - 3| + 3) + 1) + 5) + 1)/(1(5(4(3|(-5x^2 + 3x + 5) - 3| + 3)^2 - 4(3|(-5x^2 + 3x + 5) - 3| + 3) + 1)^2 - 1(4(3|(-5x^2 + 3x + 5) - 3| + 3)^2 - 4(3|(-5x^2 + 3x + 5) - 3| + 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": "9", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the leftmost local minimum of the function f(x) = (2((-3(-3(-2sin(2\u03c0((-2x - 2)/(2x + 3)) - 1)) - 2) + 1)/(2(-3(-2sin(2\u03c0((-2x - 2)/(2x + 3)) - 1)) - 2) - 1)) + 1)/(-3((-3(-3(-2sin(2\u03c0((-2x - 2)/(2x + 3)) - 1)) - 2) + 1)/(2(-3(-2sin(2\u03c0((-2x - 2)/(2x + 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": "-2", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local minimum of the function f(x) = -4((2(-1(-1|((-2x - 3)/(-2x)) + 1| + 2) - 2))/(2(-1(-1|((-2x - 3)/(-2x)) + 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": "0", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the leftmost local maximum of the function f(x) = (-1(5((-3(-1e^(-2((-1x)/(2x - 1))) + 3) + 3)/(-2(-1e^(-2((-1x)/(2x - 1))) + 3) + 3)) - 3) - 2)/(2(5((-3(-1e^(-2((-1x)/(2x - 1))) + 3) + 3)/(-2(-1e^(-2((-1x)/(2x - 1))) + 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": "0", "dataset": "MATH"}
{"messages": [{"content": "How many local maxima does the function f(x) = 5(1|(2e^(1(1(-1x - 3)^2)) + 2) + 2| + 3)^2 - 2(1|(2e^(1(1(-1x - 3)^2)) + 2) + 2| + 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 local maximum with the largest y-value of the function f(x) = 2|(-3(-3(-2(-2cos(3\u03c0x) - 2)^2 - 2(-2cos(3\u03c0x) - 2) - 5) - 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 maximum with the smallest y-value of the function f(x) = -3((1((-2((2(2x + 5) - 3)/(-1(2x + 5) - 3)) - 3)/(2((2(2x + 5) - 3)/(-1(2x + 5) - 3)) - 3)) + 3)/(-2((-2((2(2x + 5) - 3)/(-1(2x + 5) - 3)) - 3)/(2((2(2x + 5) - 3)/(-1(2x + 5) - 3)) - 3)) + 1))^2 - 5((1((-2((2(2x + 5) - 3)/(-1(2x + 5) - 3)) - 3)/(2((2(2x + 5) - 3)/(-1(2x + 5) - 3)) - 3)) + 3)/(-2((-2((2(2x + 5) - 3)/(-1(2x + 5) - 3)) - 3)/(2((2(2x + 5) - 3)/(-1(2x + 5) - 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": "-3", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the leftmost local extremum of the function f(x) = -1((-2(-1(1|((1x - 3)/(-3x - 2)) + 3| + 3)^2 - 2(1|((1x - 3)/(-3x - 2)) + 3| + 3) + 3) + 2)/(-3(-1(1|((1x - 3)/(-3x - 2)) + 3| + 3)^2 - 2(1|((1x - 3)/(-3x - 2)) + 3| + 3) + 3) - 2))^2 - 4((-2(-1(1|((1x - 3)/(-3x - 2)) + 3| + 3)^2 - 2(1|((1x - 3)/(-3x - 2)) + 3| + 3) + 3) + 2)/(-3(-1(1|((1x - 3)/(-3x - 2)) + 3| + 3)^2 - 2(1|((1x - 3)/(-3x - 2)) + 3| + 3) + 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": "How many local maxima does the function f(x) = (-2((3(-2(1(-1x - 5)^2 + 1(-1x - 5) + 3)))/(2(-2(1(-1x - 5)^2 + 1(-1x - 5) + 3)) - 1)) + 2)/(2((3(-2(1(-1x - 5)^2 + 1(-1x - 5) + 3)))/(2(-2(1(-1x - 5)^2 + 1(-1x - 5) + 3)) - 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 rightmost local extremum of the function f(x) = -2(5(5((-2(-5x^2 + 4x + 1) - 1)/(-2(-5x^2 + 4x + 1) - 2))^2 + 2((-2(-5x^2 + 4x + 1) - 1)/(-2(-5x^2 + 4x + 1) - 2)) - 4) - 4)^2 - 2(5(5((-2(-5x^2 + 4x + 1) - 1)/(-2(-5x^2 + 4x + 1) - 2))^2 + 2((-2(-5x^2 + 4x + 1) - 1)/(-2(-5x^2 + 4x + 1) - 2)) - 4) - 4) + 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": "How many local extrema (both minima and maxima) does the function f(x) = 1|(-2(5(3e^(1((-1x - 1)/(-1x + 2))) - 3)^2 + 1(3e^(1((-1x - 1)/(-1x + 2))) - 3) - 2) + 4) + 3| - 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 maximum of the function f(x) = (-1(-2|(-2((-3((1x)/(-1x + 2)) + 1)/(2((1x)/(-1x + 2)) - 3))^2 + 3((-3((1x)/(-1x + 2)) + 1)/(2((1x)/(-1x + 2)) - 3)) - 5) - 3| - 3))/(-2(-2|(-2((-3((1x)/(-1x + 2)) + 1)/(2((1x)/(-1x + 2)) - 3))^2 + 3((-3((1x)/(-1x + 2)) + 1)/(2((1x)/(-1x + 2)) - 3)) - 5) - 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(-4((-3(2sin(3\u03c0(1x + 2) + 3)) - 3)/(-2(2sin(3\u03c0(1x + 2) + 3)) + 3))^2 + 1((-3(2sin(3\u03c0(1x + 2) + 3)) - 3)/(-2(2sin(3\u03c0(1x + 2) + 3)) + 3)) + 1)^2 + 1(-4((-3(2sin(3\u03c0(1x + 2) + 3)) - 3)/(-2(2sin(3\u03c0(1x + 2) + 3)) + 3))^2 + 1((-3(2sin(3\u03c0(1x + 2) + 3)) - 3)/(-2(2sin(3\u03c0(1x + 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": "-10", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local maximum of the function f(x) = 1((-1(5(-3((-3x - 1)/(-2x + 1))^2 + 2((-3x - 1)/(-2x + 1)) - 3) - 2) + 1)/(-3(5(-3((-3x - 1)/(-2x + 1))^2 + 2((-3x - 1)/(-2x + 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": "-1", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local minimum of the function f(x) = (3((-1(-3|((-1(-5x^2 + 5x + 1) - 1)/(2(-5x^2 + 5x + 1) - 1)) + 2| - 3))/(-3(-3|((-1(-5x^2 + 5x + 1) - 1)/(2(-5x^2 + 5x + 1) - 1)) + 2| - 3) - 1)) + 2)/(2((-1(-3|((-1(-5x^2 + 5x + 1) - 1)/(2(-5x^2 + 5x + 1) - 1)) + 2| - 3))/(-3(-3|((-1(-5x^2 + 5x + 1) - 1)/(2(-5x^2 + 5x + 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 extremum with the smallest y-value of the function f(x) = -5(1(-3|(2(-3sin(1\u03c0x) - 2)) - 3| + 2)^2 - 1(-3|(2(-3sin(1\u03c0x) - 2)) - 3| + 2) + 3)^2 + 2(1(-3|(2(-3sin(1\u03c0x) - 2)) - 3| + 2)^2 - 1(-3|(2(-3sin(1\u03c0x) - 2)) - 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": "-10", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local extremum with the smallest y-value of the function f(x) = (1(-1(-5(-2sin(1\u03c0((1x)/(-2x - 1)) + 2) + 1))^2 - 1(-5(-2sin(1\u03c0((1x)/(-2x - 1)) + 2) + 1)) - 1) + 3)/(3(-1(-5(-2sin(1\u03c0((1x)/(-2x - 1)) + 2) + 1))^2 - 1(-5(-2sin(1\u03c0((1x)/(-2x - 1)) + 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": "-1", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local maximum of the function f(x) = (3((-1(-1(1((3x + 2)/(2x + 3)) - 5)^2 + 3(1((3x + 2)/(2x + 3)) - 5) - 1) + 2)/(-1(-1(1((3x + 2)/(2x + 3)) - 5)^2 + 3(1((3x + 2)/(2x + 3)) - 5) - 1) - 1)) + 3)/(-1((-1(-1(1((3x + 2)/(2x + 3)) - 5)^2 + 3(1((3x + 2)/(2x + 3)) - 5) - 1) + 2)/(-1(-1(1((3x + 2)/(2x + 3)) - 5)^2 + 3(1((3x + 2)/(2x + 3)) - 5) - 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 x-coordinate of the local extremum with the smallest y-value of the function f(x) = 3sin(3\u03c0(5(-2(-2|((-1x - 2)/(1x)) - 1|) + 4)^2 + 1(-2(-2|((-1x - 2)/(1x)) - 1|) + 4) - 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 leftmost local minimum of the function f(x) = (3(5(1|(-2cos(3\u03c0(-3|x - 2| + 3) - 3) + 2) - 3|) - 1) + 1)/(-2(5(1|(-2cos(3\u03c0(-3|x - 2| + 3) - 3) + 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 x-coordinate of the local minimum with the largest y-value of the function f(x) = -1(-2sin(2\u03c0(-2|((2(-5x + 4) + 1)/(-3(-5x + 4) + 1)) - 2| + 2) + 2) + 2)^2 - 2(-2sin(2\u03c0(-2|((2(-5x + 4) + 1)/(-3(-5x + 4) + 1)) - 2| + 2) + 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": "0", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local maximum with the largest y-value of the function f(x) = -4((-3(4(2e^(-2(-1x^2 - 4x - 3)) + 2) - 4))/(1(4(2e^(-2(-1x^2 - 4x - 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": "-2", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the rightmost local minimum of the function f(x) = -1sin(3\u03c0(5(2|(1((-2x)/(3x - 2))^2 - 4((-2x)/(3x - 2)) + 2) + 3| - 2)^2 + 1(2|(1((-2x)/(3x - 2))^2 - 4((-2x)/(3x - 2)) + 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": "How many local minima does the function f(x) = 2|(-3(1|(-1|(-4x)| + 1) - 1| - 3) + 3) + 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 extremum with the smallest y-value of the function f(x) = -3e^(1(-1|(-3(-1(-4x^2 - 2x - 5)^2 - 2(-4x^2 - 2x - 5) - 4) - 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(-1(-2|(5((-1x + 1)/(-1x - 1))^2 - 4((-1x + 1)/(-1x - 1)) + 2) + 3| + 1) + 4) + 1)/(3(-1(-2|(5((-1x + 1)/(-1x - 1))^2 - 4((-1x + 1)/(-1x - 1)) + 2) + 3| + 1) + 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": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the average of all x-coordinates of local maxima of the function f(x) = -1(-1((2(-2(1x^2 - 3x)^2 - 4(1x^2 - 3x) - 2) - 1)/(-1(-2(1x^2 - 3x)^2 - 4(1x^2 - 3x) - 2) - 2)) - 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": "2", "dataset": "MATH"}
{"messages": [{"content": "How many local maxima does the function f(x) = (-1(-2e^(1(5((1(-3x^2 + 1x - 5) + 1)/(-3(-3x^2 + 1x - 5) - 1))^2 - 5((1(-3x^2 + 1x - 5) + 1)/(-3(-3x^2 + 1x - 5) - 1)) - 4)) + 2) - 1)/(-1(-2e^(1(5((1(-3x^2 + 1x - 5) + 1)/(-3(-3x^2 + 1x - 5) - 1))^2 - 5((1(-3x^2 + 1x - 5) + 1)/(-3(-3x^2 + 1x - 5) - 1)) - 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 x-coordinate of the local extremum of the function f(x) = -2|((-2(-1(2(1x^2 - 1x + 2)^2 + 5(1x^2 - 1x + 2) - 4) - 5) - 3)/(3(-1(2(1x^2 - 1x + 2)^2 + 5(1x^2 - 1x + 2) - 4) - 5) - 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": "0", "dataset": "MATH"}
{"messages": [{"content": "Find the average of all x-coordinates of local minima of the function f(x) = 1(-1(-1((3(-1x^2 - 5x - 1) - 3)/(-3(-1x^2 - 5x - 1) - 3)) - 4)^2 + 4)^2 - 1(-1(-1((3(-1x^2 - 5x - 1) - 3)/(-3(-1x^2 - 5x - 1) - 3)) - 4)^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": "-3", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local maximum of the function f(x) = -2((2(3(-4((-1x + 3)/(-1x + 2))) - 2) + 2)/(2(3(-4((-1x + 3)/(-1x + 2))) - 2) + 3))^2 - 4((2(3(-4((-1x + 3)/(-1x + 2))) - 2) + 2)/(2(3(-4((-1x + 3)/(-1x + 2))) - 2) + 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": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local minimum with the largest y-value of the function f(x) = -2sin(3\u03c0(-1(3(-1(-2x^2 + 2x - 4) + 4)^2 + 3(-1(-2x^2 + 2x - 4) + 4))^2 + 2(3(-1(-2x^2 + 2x - 4) + 4)^2 + 3(-1(-2x^2 + 2x - 4) + 4)) + 5) - 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 of the function f(x) = -4((-2(1|((-2(-4x^2 - 1x + 1) + 2)/(-1(-4x^2 - 1x + 1) + 3)) - 2| - 3))/(-3(1|((-2(-4x^2 - 1x + 1) + 2)/(-1(-4x^2 - 1x + 1) + 3)) - 2| - 3) + 2))^2 - 2((-2(1|((-2(-4x^2 - 1x + 1) + 2)/(-1(-4x^2 - 1x + 1) + 3)) - 2| - 3))/(-3(1|((-2(-4x^2 - 1x + 1) + 2)/(-1(-4x^2 - 1x + 1) + 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": "0", "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|(1((-3((-1x - 1)/(-3x + 1)) - 1)/(-1((-1x - 1)/(-3x + 1)) - 2))^2 + 3((-3((-1x - 1)/(-3x + 1)) - 1)/(-1((-1x - 1)/(-3x + 1)) - 2)) + 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": "-6", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local maximum with the largest y-value of the function f(x) = (-2(2sin(3\u03c0(1(1(1|x - 2| + 2) + 1)^2 - 4(1(1|x - 2| + 2) + 1) - 2) - 1)) - 2)/(3(2sin(3\u03c0(1(1(1|x - 2| + 2) + 1)^2 - 4(1(1|x - 2| + 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 minimum of the function f(x) = -2(4((-3((-2(-1x - 4) + 2)/(3(-1x - 4) + 3)) + 1)/(-1((-2(-1x - 4) + 2)/(3(-1x - 4) + 3))))^2 - 5((-3((-2(-1x - 4) + 2)/(3(-1x - 4) + 3)) + 1)/(-1((-2(-1x - 4) + 2)/(3(-1x - 4) + 3)))) + 2)^2 + 2(4((-3((-2(-1x - 4) + 2)/(3(-1x - 4) + 3)) + 1)/(-1((-2(-1x - 4) + 2)/(3(-1x - 4) + 3))))^2 - 5((-3((-2(-1x - 4) + 2)/(3(-1x - 4) + 3)) + 1)/(-1((-2(-1x - 4) + 2)/(3(-1x - 4) + 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": "-4", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local maximum with the largest y-value of the function f(x) = (-1(-1|(2(-3e^(1(-3x - 4)))^2 + 3) - 2|) - 1)/(-2(-1|(2(-3e^(1(-3x - 4)))^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": "-7", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local maximum with the largest y-value of the function f(x) = 1(2|((2(-3|(-2x^2 + 1x + 5) + 1| + 2) + 1)/(-1(-3|(-2x^2 + 1x + 5) + 1| + 2) - 1)) + 1| - 1)^2 + 4(2|((2(-3|(-2x^2 + 1x + 5) + 1| + 2) + 1)/(-1(-3|(-2x^2 + 1x + 5) + 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": "-2", "dataset": "MATH"}
{"messages": [{"content": "Find the average of all x-coordinates of local maxima of the function f(x) = 2|(-3(-3|(3sin(2\u03c0(1x^2 + 2x + 4) - 1) - 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": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local minimum with the largest y-value of the function f(x) = -5((-3(-3cos(1\u03c0(-2(-3|x| - 3)^2 - 1(-3|x| - 3) + 4)) - 1))/(-1(-3cos(1\u03c0(-2(-3|x| - 3)^2 - 1(-3|x| - 3) + 4)) - 1) + 2))^2 - 5((-3(-3cos(1\u03c0(-2(-3|x| - 3)^2 - 1(-3|x| - 3) + 4)) - 1))/(-1(-3cos(1\u03c0(-2(-3|x| - 3)^2 - 1(-3|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": "-10", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local extremum of the function f(x) = -1(3|(1(-3|(1x^2 + 1x + 2) - 1| - 3) - 4) + 2| + 1)^2 - 2(3|(1(-3|(1x^2 + 1x + 2) - 1| - 3) - 4) + 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": "0", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local extremum of the function f(x) = -4(-1|(-5(2((-2x)/(2x - 3))^2 + 3((-2x)/(2x - 3)) + 2)^2 - 4(2((-2x)/(2x - 3))^2 + 3((-2x)/(2x - 3)) + 2) - 5) - 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 extremum with the largest y-value of the function f(x) = 3e^(-1(2(-4(2(2x^2 - 5x + 3)^2 + 1(2x^2 - 5x + 3) - 5)^2 - 1(2(2x^2 - 5x + 3)^2 + 1(2x^2 - 5x + 3) - 5) + 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": "0", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local maximum with the largest y-value of the function f(x) = -2(-3(5((-2(5x - 5) - 2)/(3(5x - 5) + 2)) - 2)^2 + 3(5((-2(5x - 5) - 2)/(3(5x - 5) + 2)) - 2) + 3)^2 + 2(-3(5((-2(5x - 5) - 2)/(3(5x - 5) + 2)) - 2)^2 + 3(5((-2(5x - 5) - 2)/(3(5x - 5) + 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": "1", "dataset": "MATH"}
{"messages": [{"content": "How many local extrema (both minima and maxima) does the function f(x) = (-2(2(-5(1(2e^(-2x))^2 + 1(2e^(-2x)) - 3) - 1)^2 - 4(-5(1(2e^(-2x))^2 + 1(2e^(-2x)) - 3) - 1) + 4) + 1)/(-1(2(-5(1(2e^(-2x))^2 + 1(2e^(-2x)) - 3) - 1)^2 - 4(-5(1(2e^(-2x))^2 + 1(2e^(-2x)) - 3) - 1) + 4) - 3) have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local extremum of the function f(x) = 2|(-2(3(-3|(2|x| - 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": "0", "dataset": "MATH"}
{"messages": [{"content": "How many local extrema (both minima and maxima) does the function f(x) = (2(5(1(5(-1sin(2\u03c0x + 3) + 3) - 1) - 4) + 2) + 1)/(2(5(1(5(-1sin(2\u03c0x + 3) + 3) - 1) - 4) + 2) - 1) 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 leftmost local maximum of the function f(x) = -5(1e^(2(3|((1(1x^2 - 4x - 5) - 1)/(-3(1x^2 - 4x - 5) - 3)) - 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": "-1", "dataset": "MATH"}
{"messages": [{"content": "Find the average of all x-coordinates of local minima of the function f(x) = 3|((-2(-2|(2(-2x^2 - 1x + 2)^2 + 5(-2x^2 - 1x + 2) - 1) + 2| + 2))/(3(-2|(2(-2x^2 - 1x + 2)^2 + 5(-2x^2 - 1x + 2) - 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": "0", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local maximum of the function f(x) = 3e^(1((-1((2((-2(-3|x + 1| + 3) - 1)/(-2(-3|x + 1| + 3) + 3)) + 2)/(2((-2(-3|x + 1| + 3) - 1)/(-2(-3|x + 1| + 3) + 3)) + 1)) + 3)/(-2((2((-2(-3|x + 1| + 3) - 1)/(-2(-3|x + 1| + 3) + 3)) + 2)/(2((-2(-3|x + 1| + 3) - 1)/(-2(-3|x + 1| + 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 local extremum with the largest y-value of the function f(x) = -5(-3|(1|((1(2|x - 3| - 3) - 3)/(-2(2|x - 3| - 3) + 3)) + 1| - 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": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the leftmost local extremum of the function f(x) = 4(3(3(3(-3sin(1\u03c0x - 1) - 3)^2 + 4(-3sin(1\u03c0x - 1) - 3) - 2) + 4)^2 - 1(3(3(-3sin(1\u03c0x - 1) - 3)^2 + 4(-3sin(1\u03c0x - 1) - 3) - 2) + 4) + 1)^2 - 5(3(3(3(-3sin(1\u03c0x - 1) - 3)^2 + 4(-3sin(1\u03c0x - 1) - 3) - 2) + 4)^2 - 1(3(3(-3sin(1\u03c0x - 1) - 3)^2 + 4(-3sin(1\u03c0x - 1) - 3) - 2) + 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": "-10", "dataset": "MATH"}
{"messages": [{"content": "How many local minima does the function f(x) = 5(3|(-3((-2(1x - 1) - 1)/(3(1x - 1) - 2))^2 - 2((-2(1x - 1) - 1)/(3(1x - 1) - 2)) + 3) - 2| - 1) - 5 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 minima does the function f(x) = 2(-5((1(2|(1x + 4) - 1| - 3))/(-2(2|(1x + 4) - 1| - 3) - 1))^2 - 4((1(2|(1x + 4) - 1| - 3))/(-2(2|(1x + 4) - 1| - 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 x-coordinate of the leftmost local extremum of the function f(x) = -2(1(-1(-2|(1|x + 2| - 3) - 1| - 1))^2 - 5(-1(-2|(1|x + 2| - 3) - 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": "-7", "dataset": "MATH"}
{"messages": [{"content": "Find the average of all x-coordinates of local minima of the function f(x) = 5(-3cos(2\u03c0(2(-5(3|x + 3| - 3) - 3)^2 - 3(-5(3|x + 3| - 3) - 3) - 1) - 1) + 1)^2 - 2(-3cos(2\u03c0(2(-5(3|x + 3| - 3) - 3)^2 - 3(-5(3|x + 3| - 3) - 3) - 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 rightmost local extremum of the function f(x) = 3(2|(-1((-2(-3|x + 1| + 1))/(2(-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": "-1", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the leftmost local maximum of the function f(x) = -1((-1(4(-5(-3sin(1\u03c0x) + 3)^2 - 1(-3sin(1\u03c0x) + 3) - 1) + 1) + 3)/(-3(4(-5(-3sin(1\u03c0x) + 3)^2 - 1(-3sin(1\u03c0x) + 3) - 1) + 1) - 3))^2 + 4((-1(4(-5(-3sin(1\u03c0x) + 3)^2 - 1(-3sin(1\u03c0x) + 3) - 1) + 1) + 3)/(-3(4(-5(-3sin(1\u03c0x) + 3)^2 - 1(-3sin(1\u03c0x) + 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": "-10", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the rightmost local maximum of the function f(x) = 1|((-1(3(1(4x + 1)^2 - 5(4x + 1) - 4)^2 + 1(1(4x + 1)^2 - 5(4x + 1) - 4) + 5) + 3)/(1(3(1(4x + 1)^2 - 5(4x + 1) - 4)^2 + 1(1(4x + 1)^2 - 5(4x + 1) - 4) + 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": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the average of all x-coordinates of local maxima of the function f(x) = 4(-1(-1sin(2\u03c0((1(3x^2 - 1x))/(-3(3x^2 - 1x) + 1)) - 1) + 2) + 5)^2 - 5(-1(-1sin(2\u03c0((1(3x^2 - 1x))/(-3(3x^2 - 1x) + 1)) - 1) + 2) + 5) - 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 minimum with the largest y-value of the function f(x) = 3e^(-1(-3|(-1((1(1|x + 1| - 3) + 2)/(-2(1|x + 1| - 3) - 3)) - 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 local maximum with the largest y-value of the function f(x) = (-2(1(2sin(2\u03c0((1(-2|x + 2| - 1) - 1)/(3(-2|x + 2| - 1) + 3)) - 3) + 2) - 1) - 3)/(-1(1(2sin(2\u03c0((1(-2|x + 2| - 1) - 1)/(3(-2|x + 2| - 1) + 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": "-2", "dataset": "MATH"}
{"messages": [{"content": "Find the average of all x-coordinates of local extrema of the function f(x) = (1(-2(-3|(-1|(-3x^2 - 5) + 2| + 1) + 3| + 1)) + 2)/(3(-2(-3|(-1|(-3x^2 - 5) + 2| + 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 leftmost local extremum of the function f(x) = (1((1(-4(3|(5x^2 - 3x + 1) - 2| - 3) - 2) + 1)/(1(-4(3|(5x^2 - 3x + 1) - 2| - 3) - 2) + 2)) + 2)/(-2((1(-4(3|(5x^2 - 3x + 1) - 2| - 3) - 2) + 1)/(1(-4(3|(5x^2 - 3x + 1) - 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": "0", "dataset": "MATH"}
{"messages": [{"content": "How many local maxima does the function f(x) = 1|((1(1(-2|(1x + 4)| + 3) - 2) + 3)/(3(1(-2|(1x + 4)| + 3) - 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 local maximum of the function f(x) = (-1((-1(1(-3(-5x^2 - 3x - 4)^2 + 3(-5x^2 - 3x - 4) + 3) + 1) - 2)/(-1(1(-3(-5x^2 - 3x - 4)^2 + 3(-5x^2 - 3x - 4) + 3) + 1) + 2)) - 3)/(-1((-1(1(-3(-5x^2 - 3x - 4)^2 + 3(-5x^2 - 3x - 4) + 3) + 1) - 2)/(-1(1(-3(-5x^2 - 3x - 4)^2 + 3(-5x^2 - 3x - 4) + 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 local extremum with the smallest y-value of the function f(x) = 3(1|((3(2|(1sin(2\u03c0x - 2) + 1) - 1| - 1) - 3)/(-2(2|(1sin(2\u03c0x - 2) + 1) - 1| - 1) - 1)) + 3| + 1)^2 + 3(1|((3(2|(1sin(2\u03c0x - 2) + 1) - 1| - 1) - 3)/(-2(2|(1sin(2\u03c0x - 2) + 1) - 1| - 1) - 1)) + 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 leftmost local minimum of the function f(x) = (-2(-1|(-2(1|(-2sin(1\u03c0x - 1) - 1) - 3| - 3) + 5) + 2| - 3) + 1)/(3(-1|(-2(1|(-2sin(1\u03c0x - 1) - 1) - 3| - 3) + 5) + 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": "-9", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local maximum with the smallest y-value of the function f(x) = -4(2(2e^(2(-2|((3x + 3)/(-3x - 1)) + 1| + 1)) - 2) - 1)^2 - 4(2(2e^(2(-2|((3x + 3)/(-3x - 1)) + 1| + 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": "0", "dataset": "MATH"}
{"messages": [{"content": "How many local maxima does the function f(x) = (2((1((-1((-1(-1x^2 - 2x - 4) - 2)/(1(-1x^2 - 2x - 4))))/(2((-1(-1x^2 - 2x - 4) - 2)/(1(-1x^2 - 2x - 4))) + 2)) + 2)/(3((-1((-1(-1x^2 - 2x - 4) - 2)/(1(-1x^2 - 2x - 4))))/(2((-1(-1x^2 - 2x - 4) - 2)/(1(-1x^2 - 2x - 4))) + 2)) - 2)) + 2)/(-1((1((-1((-1(-1x^2 - 2x - 4) - 2)/(1(-1x^2 - 2x - 4))))/(2((-1(-1x^2 - 2x - 4) - 2)/(1(-1x^2 - 2x - 4))) + 2)) + 2)/(3((-1((-1(-1x^2 - 2x - 4) - 2)/(1(-1x^2 - 2x - 4))))/(2((-1(-1x^2 - 2x - 4) - 2)/(1(-1x^2 - 2x - 4))) + 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": "How many local maxima does the function f(x) = -3(-1|(-1e^(-1(-2(2|x - 2| - 3)^2 - 3(2|x - 2| - 3) + 4)) - 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 local maximum with the smallest y-value of the function f(x) = 2sin(3\u03c0(-1(-3|(-2((-3x)/(1x + 1)) - 3)| + 2)^2 + 4(-3|(-2((-3x)/(1x + 1)) - 3)| + 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": "1", "dataset": "MATH"}
{"messages": [{"content": "How many local minima does the function f(x) = 5(2|(-2(2(2cos(3\u03c0x - 1) + 1)^2 - 1(2cos(3\u03c0x - 1) + 1) - 4)^2 - 4(2(2cos(3\u03c0x - 1) + 1)^2 - 1(2cos(3\u03c0x - 1) + 1) - 4) - 1) + 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 x-coordinate of the local maximum with the smallest y-value of the function f(x) = 1(-2cos(2\u03c0((-3((1(-3x^2 + 2x + 2))/(2(-3x^2 + 2x + 2) - 1)) - 1)/(-1((1(-3x^2 + 2x + 2))/(2(-3x^2 + 2x + 2) - 1)) + 2)) - 3) + 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": "0", "dataset": "MATH"}
{"messages": [{"content": "How many local minima does the function f(x) = -1e^(2(-3|(-1((-3(-5x + 1) + 3)/(2(-5x + 1) - 1)) + 5) - 1| - 2)) - 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": "How many local maxima does the function f(x) = 1|(3|(-3|(-2(1x^2 - 2x + 3) - 5) - 3| - 3) - 1| - 3)| + 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 minimum of the function f(x) = -1(-2|(3sin(2\u03c0(-1|(5x^2 - 2x - 5) - 2| - 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": "How many local maxima does the function f(x) = 2(-2|(4((3(-3|x - 2| + 1))/(-2(-3|x - 2| + 1) + 3))^2 - 1((3(-3|x - 2| + 1))/(-2(-3|x - 2| + 1) + 3))) + 1| - 1)^2 - 2(-2|(4((3(-3|x - 2| + 1))/(-2(-3|x - 2| + 1) + 3))^2 - 1((3(-3|x - 2| + 1))/(-2(-3|x - 2| + 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 local extremum of the function f(x) = 1(1(1|((-1(-2|x| + 1))/(-1(-2|x| + 1) + 2)) - 1| - 2)^2 - 5(1|((-1(-2|x| + 1))/(-1(-2|x| + 1) + 2)) - 1| - 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": "0", "dataset": "MATH"}
{"messages": [{"content": "Find the average of all x-coordinates of local maxima of the function f(x) = 3(3cos(3\u03c0(-1(-4(1|x| + 1) + 5)^2 - 3) - 3) - 3)^2 - 3(3cos(3\u03c0(-1(-4(1|x| + 1) + 5)^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": "0", "dataset": "MATH"}
{"messages": [{"content": "Find the average of all x-coordinates of local extrema of the function f(x) = -2|((1(3|(3|(1sin(3\u03c0x + 3) + 1) + 2| - 3)| - 1) + 2)/(-1(3|(3|(1sin(3\u03c0x + 3) + 1) + 2| - 3)| - 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 minimum of the function f(x) = (3((2((2(1|(3x + 2)| - 1) - 2)/(-1(1|(3x + 2)| - 1))))/(1((2(1|(3x + 2)| - 1) - 2)/(-1(1|(3x + 2)| - 1))) + 1)) + 2)/(2((2((2(1|(3x + 2)| - 1) - 2)/(-1(1|(3x + 2)| - 1))))/(1((2(1|(3x + 2)| - 1) - 2)/(-1(1|(3x + 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": "-1", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local extremum with the smallest y-value of the function f(x) = -2|(-5((-2(2|(-3x + 3) + 3| - 2))/(3(2|(-3x + 3) + 3| - 2) - 2))^2 + 1((-2(2|(-3x + 3) + 3| - 2))/(3(2|(-3x + 3) + 3| - 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 x-coordinate of the local extremum of the function f(x) = 1|(-2|(-1|(2e^(1((-1x - 3)/(1x + 2))) + 1) - 1| + 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 of the function f(x) = 1|(1|(3e^(1(3((1x - 3)/(-2x + 3))^2 + 4((1x - 3)/(-2x + 3)) + 5)) - 1) - 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": "-3", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local extremum of the function f(x) = 3(-4(2(-2|((-2x - 3)/(3x + 1)) + 2| - 2)^2 - 5(-2|((-2x - 3)/(3x + 1)) + 2| - 2))^2 - 5(2(-2|((-2x - 3)/(3x + 1)) + 2| - 2)^2 - 5(-2|((-2x - 3)/(3x + 1)) + 2| - 2)) - 3)^2 + 2(-4(2(-2|((-2x - 3)/(3x + 1)) + 2| - 2)^2 - 5(-2|((-2x - 3)/(3x + 1)) + 2| - 2))^2 - 5(2(-2|((-2x - 3)/(3x + 1)) + 2| - 2)^2 - 5(-2|((-2x - 3)/(3x + 1)) + 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": "0", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local minimum with the largest y-value of the function f(x) = (-3(3(-1|(1((-2x + 1)/(2x + 3)) + 2) + 1| + 3)^2 + 3) + 1)/(3(3(-1|(1((-2x + 1)/(2x + 3)) + 2) + 1| + 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": "-2", "dataset": "MATH"}
{"messages": [{"content": "Find the average of all x-coordinates of local minima of the function f(x) = -1|((3(-3(5(2cos(1\u03c0x + 1)))^2 - 5(5(2cos(1\u03c0x + 1)))))/(3(-3(5(2cos(1\u03c0x + 1)))^2 - 5(5(2cos(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": "-1", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local maximum with the smallest y-value of the function f(x) = -1|((-1((-1(1cos(1\u03c0(-2|x| - 1) - 3) + 1) - 1)/(-3(1cos(1\u03c0(-2|x| - 1) - 3) + 1) - 1)) + 1)/(-3((-1(1cos(1\u03c0(-2|x| - 1) - 3) + 1) - 1)/(-3(1cos(1\u03c0(-2|x| - 1) - 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": "-9", "dataset": "MATH"}
{"messages": [{"content": "How many local extrema (both minima and maxima) does the function f(x) = (-3(3|(-3((3(4x - 5) + 2)/(2(4x - 5)))^2 + 2((3(4x - 5) + 2)/(2(4x - 5))) + 5) - 1| + 3) - 3)/(-1(3|(-3((3(4x - 5) + 2)/(2(4x - 5)))^2 + 2((3(4x - 5) + 2)/(2(4x - 5))) + 5) - 1| + 3) - 3) 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 extremum with the largest y-value of the function f(x) = -5(-2(-3e^(2(5(-4x^2 - 5x + 2)^2 - 5(-4x^2 - 5x + 2))) - 1)^2 + 5(-3e^(2(5(-4x^2 - 5x + 2)^2 - 5(-4x^2 - 5x + 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": "-2", "dataset": "MATH"}
{"messages": [{"content": "How many local extrema (both minima and maxima) does the function f(x) = 3(-2e^(-1(-1((3((-2x - 3)/(-2x + 3)) + 1)/(-2((-2x - 3)/(-2x + 3)) + 3))^2 - 4((3((-2x - 3)/(-2x + 3)) + 1)/(-2((-2x - 3)/(-2x + 3)) + 3)) - 3)) + 2)^2 + 1(-2e^(-1(-1((3((-2x - 3)/(-2x + 3)) + 1)/(-2((-2x - 3)/(-2x + 3)) + 3))^2 - 4((3((-2x - 3)/(-2x + 3)) + 1)/(-2((-2x - 3)/(-2x + 3)) + 3)) - 3)) + 2) - 3 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 of the function f(x) = -3((-3(2|((3(-1x^2 + 5x + 5) - 2)/(2(-1x^2 + 5x + 5) + 3)) + 2| - 1))/(2(2|((3(-1x^2 + 5x + 5) - 2)/(2(-1x^2 + 5x + 5) + 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": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local extremum of the function f(x) = 2|(-1(3|(1((-2x + 1)/(1x - 2))^2 + 5) - 2| + 3)^2 - 2(3|(1((-2x + 1)/(1x - 2))^2 + 5) - 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 extremum with the smallest y-value of the function f(x) = 3cos(1\u03c0(2((-2(5(2|x + 1| - 1) - 4) - 1)/(-1(5(2|x + 1| - 1) - 4) - 2))^2 + 3((-2(5(2|x + 1| - 1) - 4) - 1)/(-1(5(2|x + 1| - 1) - 4) - 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 extremum of the function f(x) = -1(-4(-5(2|(1x + 2)| - 1)^2 - 2(2|(1x + 2)| - 1) + 3)^2 + 1(-5(2|(1x + 2)| - 1)^2 - 2(2|(1x + 2)| - 1) + 3) + 1)^2 + 4(-4(-5(2|(1x + 2)| - 1)^2 - 2(2|(1x + 2)| - 1) + 3)^2 + 1(-5(2|(1x + 2)| - 1)^2 - 2(2|(1x + 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": "-3", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local extremum of the function f(x) = -1|(3|(-1(2e^(-1((1x + 3)/(-2x - 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": "-1", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local minimum with the largest y-value of the function f(x) = -5(3((2(3sin(1\u03c0(-3x - 2)) - 3) - 2)/(-2(3sin(1\u03c0(-3x - 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": "-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((3(3cos(2\u03c0(2x^2 + 5x + 1) + 2) - 2) - 3)/(-1(3cos(2\u03c0(2x^2 + 5x + 1) + 2) - 2) - 1))^2 + 1((3(3cos(2\u03c0(2x^2 + 5x + 1) + 2) - 2) - 3)/(-1(3cos(2\u03c0(2x^2 + 5x + 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": "-1", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the leftmost local maximum of the function f(x) = -5(-1|(-2(-2|(5x^2 + 4x - 5) - 1| - 2)) + 1| + 1)^2 + 4(-1|(-2(-2|(5x^2 + 4x - 5) - 1| - 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": "-2", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the rightmost local maximum of the function f(x) = (2(-1|(2sin(1\u03c0(-3|(-1x + 1) + 1|)) - 2) + 1|) + 3)/(-2(-1|(2sin(1\u03c0(-3|(-1x + 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 local extremum with the smallest y-value of the function f(x) = -5(1cos(2\u03c0((-2(3|(-1x^2 + 5x + 1) - 3| - 3) - 1)/(-2(3|(-1x^2 + 5x + 1) - 3| - 3) + 1)) + 2))^2 + 2(1cos(2\u03c0((-2(3|(-1x^2 + 5x + 1) - 3| - 3) - 1)/(-2(3|(-1x^2 + 5x + 1) - 3| - 3) + 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": "0", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local maximum of the function f(x) = 1(2|(1|((2(-3x^2 - 5x) + 1)/(-1(-3x^2 - 5x) - 2)) - 3| + 1) - 3|)^2 - 5(2|(1|((2(-3x^2 - 5x) + 1)/(-1(-3x^2 - 5x) - 2)) - 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 local minimum with the smallest y-value of the function f(x) = -1(-1(-1(-1sin(2\u03c0(1|x - 2| - 1) - 1) + 2)^2 - 5(-1sin(2\u03c0(1|x - 2| - 1) - 1) + 2) + 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": "-10", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local minimum of the function f(x) = (1((-1(-5(3((2x + 1)/(-2x + 3))^2 + 4((2x + 1)/(-2x + 3)) + 2) - 4) - 1)/(-3(-5(3((2x + 1)/(-2x + 3))^2 + 4((2x + 1)/(-2x + 3)) + 2) - 4) - 2)) + 2)/(2((-1(-5(3((2x + 1)/(-2x + 3))^2 + 4((2x + 1)/(-2x + 3)) + 2) - 4) - 1)/(-3(-5(3((2x + 1)/(-2x + 3))^2 + 4((2x + 1)/(-2x + 3)) + 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": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local maximum of the function f(x) = (-3((-1((1(-1(1x^2 - 2x + 1)^2 - 3(1x^2 - 2x + 1) - 1) + 2)/(-3(-1(1x^2 - 2x + 1)^2 - 3(1x^2 - 2x + 1) - 1) + 1)) + 2)/(-1((1(-1(1x^2 - 2x + 1)^2 - 3(1x^2 - 2x + 1) - 1) + 2)/(-3(-1(1x^2 - 2x + 1)^2 - 3(1x^2 - 2x + 1) - 1) + 1)) - 1)))/(-2((-1((1(-1(1x^2 - 2x + 1)^2 - 3(1x^2 - 2x + 1) - 1) + 2)/(-3(-1(1x^2 - 2x + 1)^2 - 3(1x^2 - 2x + 1) - 1) + 1)) + 2)/(-1((1(-1(1x^2 - 2x + 1)^2 - 3(1x^2 - 2x + 1) - 1) + 2)/(-3(-1(1x^2 - 2x + 1)^2 - 3(1x^2 - 2x + 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": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the average of all x-coordinates of local maxima of the function f(x) = 1|(4((1((2(-3cos(1\u03c0x - 2) - 3) - 1)/(-2(-3cos(1\u03c0x - 2) - 3) - 3)) - 1)/(2((2(-3cos(1\u03c0x - 2) - 3) - 1)/(-2(-3cos(1\u03c0x - 2) - 3) - 3)) + 2))^2 + 2((1((2(-3cos(1\u03c0x - 2) - 3) - 1)/(-2(-3cos(1\u03c0x - 2) - 3) - 3)) - 1)/(2((2(-3cos(1\u03c0x - 2) - 3) - 1)/(-2(-3cos(1\u03c0x - 2) - 3) - 3)) + 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 extremum with the smallest y-value of the function f(x) = 3|((-1((2(2(-2cos(2\u03c0x + 3) + 2)^2 - 2(-2cos(2\u03c0x + 3) + 2) + 3) - 2)/(2(2(-2cos(2\u03c0x + 3) + 2)^2 - 2(-2cos(2\u03c0x + 3) + 2) + 3))))/(-3((2(2(-2cos(2\u03c0x + 3) + 2)^2 - 2(-2cos(2\u03c0x + 3) + 2) + 3) - 2)/(2(2(-2cos(2\u03c0x + 3) + 2)^2 - 2(-2cos(2\u03c0x + 3) + 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 local extremum with the smallest y-value of the function f(x) = -3(-4((-3(4(1|x + 2|) - 4))/(-2(4(1|x + 2|) - 4) - 2))^2 + 4((-3(4(1|x + 2|) - 4))/(-2(4(1|x + 2|) - 4) - 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": "-3", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local maximum with the smallest y-value of the function f(x) = 1|(3((2(5(1x^2 + 5x - 4) + 5) + 3)/(2(5(1x^2 + 5x - 4) + 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": "-2", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the rightmost local minimum of the function f(x) = -1(-2(-1(3|((1x + 1)/(3x - 2)) + 2|)^2 - 3(3|((1x + 1)/(3x - 2)) + 2|) + 2)^2 - 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 x-coordinate of the leftmost local minimum of the function f(x) = 2(-3((3(3(-2x^2 - 3x + 2)^2 + 5(-2x^2 - 3x + 2) - 4) + 1)/(3(3(-2x^2 - 3x + 2)^2 + 5(-2x^2 - 3x + 2) - 4) - 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": "-2", "dataset": "MATH"}
{"messages": [{"content": "How many local minima does the function f(x) = 3|((-2(3(-4(1x^2 - 1x + 3)^2 + 4(1x^2 - 1x + 3) + 5)^2 - 5(-4(1x^2 - 1x + 3)^2 + 4(1x^2 - 1x + 3) + 5) + 2) - 1)/(3(3(-4(1x^2 - 1x + 3)^2 + 4(1x^2 - 1x + 3) + 5)^2 - 5(-4(1x^2 - 1x + 3)^2 + 4(1x^2 - 1x + 3) + 5) + 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 extremum with the largest y-value of the function f(x) = -3(2(1sin(3\u03c0(-1(-1|x - 1| - 1)^2 - 1(-1|x - 1| - 1) - 3) - 1))^2 + 5(1sin(3\u03c0(-1(-1|x - 1| - 1)^2 - 1(-1|x - 1| - 1) - 3) - 1)) - 1)^2 - 3(2(1sin(3\u03c0(-1(-1|x - 1| - 1)^2 - 1(-1|x - 1| - 1) - 3) - 1))^2 + 5(1sin(3\u03c0(-1(-1|x - 1| - 1)^2 - 1(-1|x - 1| - 1) - 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": "-10", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local minimum with the largest y-value of the function f(x) = -5(2cos(1\u03c0(-5(4(-1|x|) + 5)^2 + 3(4(-1|x|) + 5) - 2) - 1) + 2)^2 + 1(2cos(1\u03c0(-5(4(-1|x|) + 5)^2 + 3(4(-1|x|) + 5) - 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 average of all x-coordinates of local maxima of the function f(x) = -1|(-2cos(1\u03c0(2|(-2(4x^2 + 3x - 2)^2 - 1(4x^2 + 3x - 2) - 3) - 2| + 3) + 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": "0", "dataset": "MATH"}
{"messages": [{"content": "How many local minima does the function f(x) = (-1((-2((1((-3(-3x^2 + 3x - 1) - 2)/(-2(-3x^2 + 3x - 1) - 2)) + 3)/(1((-3(-3x^2 + 3x - 1) - 2)/(-2(-3x^2 + 3x - 1) - 2)))) + 1)/(3((1((-3(-3x^2 + 3x - 1) - 2)/(-2(-3x^2 + 3x - 1) - 2)) + 3)/(1((-3(-3x^2 + 3x - 1) - 2)/(-2(-3x^2 + 3x - 1) - 2)))) - 2)) + 3)/(2((-2((1((-3(-3x^2 + 3x - 1) - 2)/(-2(-3x^2 + 3x - 1) - 2)) + 3)/(1((-3(-3x^2 + 3x - 1) - 2)/(-2(-3x^2 + 3x - 1) - 2)))) + 1)/(3((1((-3(-3x^2 + 3x - 1) - 2)/(-2(-3x^2 + 3x - 1) - 2)) + 3)/(1((-3(-3x^2 + 3x - 1) - 2)/(-2(-3x^2 + 3x - 1) - 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 rightmost local extremum of the function f(x) = -4(4(-1((1(-2|x + 3| + 1) - 2)/(1(-2|x + 3| + 1)))^2 + 4((1(-2|x + 3| + 1) - 2)/(1(-2|x + 3| + 1))) - 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": "-2", "dataset": "MATH"}
{"messages": [{"content": "Find the average of all x-coordinates of local extrema of the function f(x) = -1(3((1(-3(2x + 5)^2 + 3) + 2)/(-1(-3(2x + 5)^2 + 3) - 1))^2 - 2((1(-3(2x + 5)^2 + 3) + 2)/(-1(-3(2x + 5)^2 + 3) - 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": "-2", "dataset": "MATH"}
{"messages": [{"content": "Find the average of all x-coordinates of local extrema of the function f(x) = (-3(1(-3(2(-5x^2 + 3) + 2)^2 - 3(2(-5x^2 + 3) + 2) - 4)^2 + 5(-3(2(-5x^2 + 3) + 2)^2 - 3(2(-5x^2 + 3) + 2) - 4) - 1) + 3)/(1(1(-3(2(-5x^2 + 3) + 2)^2 - 3(2(-5x^2 + 3) + 2) - 4)^2 + 5(-3(2(-5x^2 + 3) + 2)^2 - 3(2(-5x^2 + 3) + 2) - 4) - 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 rightmost local maximum of the function f(x) = -2sin(2\u03c0(-2((-3(3|(3x^2 - 1x) - 1|) + 2)/(-1(3|(3x^2 - 1x) - 1|) + 2))^2 + 4((-3(3|(3x^2 - 1x) - 1|) + 2)/(-1(3|(3x^2 - 1x) - 1|) + 2)) + 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": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local maximum with the smallest y-value of the function f(x) = (2(-1(2(1|(2e^(2x) + 3) + 2| - 1) - 1)^2 - 1(2(1|(2e^(2x) + 3) + 2| - 1) - 1)) - 1)/(3(-1(2(1|(2e^(2x) + 3) + 2| - 1) - 1)^2 - 1(2(1|(2e^(2x) + 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": "6", "dataset": "MATH"}
{"messages": [{"content": "How many local extrema (both minima and maxima) does the function f(x) = 2|((3((2(1(3|x| - 3)) + 3)/(-2(1(3|x| - 3)))) - 1)/(-3((2(1(3|x| - 3)) + 3)/(-2(1(3|x| - 3)))) + 4)) + 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 maximum with the smallest y-value of the function f(x) = (-3(2(-2(2|((2x - 1)/(1x + 1)) + 2| + 3)^2 + 4(2|((2x - 1)/(1x + 1)) + 2| + 3) + 3) - 1) - 3)/(-2(2(-2(2|((2x - 1)/(1x + 1)) + 2| + 3)^2 + 4(2|((2x - 1)/(1x + 1)) + 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 x-coordinate of the local maximum of the function f(x) = -1((1((1((1(-3x - 3) - 1)/(1(-3x - 3) - 2)) - 3)/(-1((1(-3x - 3) - 1)/(1(-3x - 3) - 2)) - 1)) + 1)/(3((1((1(-3x - 3) - 1)/(1(-3x - 3) - 2)) - 3)/(-1((1(-3x - 3) - 1)/(1(-3x - 3) - 2)) - 1)) + 2))^2 + 3((1((1((1(-3x - 3) - 1)/(1(-3x - 3) - 2)) - 3)/(-1((1(-3x - 3) - 1)/(1(-3x - 3) - 2)) - 1)) + 1)/(3((1((1(-3x - 3) - 1)/(1(-3x - 3) - 2)) - 3)/(-1((1(-3x - 3) - 1)/(1(-3x - 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": "-2", "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((2((-1(2(-2x^2 - 3x)^2 - 2(-2x^2 - 3x) + 2) - 1)/(-2(2(-2x^2 - 3x)^2 - 2(-2x^2 - 3x) + 2) + 3)) - 1)/(-1((-1(2(-2x^2 - 3x)^2 - 2(-2x^2 - 3x) + 2) - 1)/(-2(2(-2x^2 - 3x)^2 - 2(-2x^2 - 3x) + 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": "-2", "dataset": "MATH"}
{"messages": [{"content": "Find the average of all x-coordinates of local minima of the function f(x) = (-3((1(3(4(1|x + 1| - 3)^2 + 1(1|x + 1| - 3) - 5)^2 + 3) + 1)/(-1(3(4(1|x + 1| - 3)^2 + 1(1|x + 1| - 3) - 5)^2 + 3) + 2)) + 2)/(-3((1(3(4(1|x + 1| - 3)^2 + 1(1|x + 1| - 3) - 5)^2 + 3) + 1)/(-1(3(4(1|x + 1| - 3)^2 + 1(1|x + 1| - 3) - 5)^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 average of all x-coordinates of local maxima of the function f(x) = (3(1(-2((1(4x^2 - 1x - 5) + 3)/(-2(4x^2 - 1x - 5) - 3)))^2 - 3(-2((1(4x^2 - 1x - 5) + 3)/(-2(4x^2 - 1x - 5) - 3))) - 1) - 2)/(1(1(-2((1(4x^2 - 1x - 5) + 3)/(-2(4x^2 - 1x - 5) - 3)))^2 - 3(-2((1(4x^2 - 1x - 5) + 3)/(-2(4x^2 - 1x - 5) - 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 minimum of the function f(x) = -1(-5((-3((-2(-2x - 3) - 1)/(-2(-2x - 3) - 3)) + 1)/(1((-2(-2x - 3) - 1)/(-2(-2x - 3) - 3)) + 3))^2 - 3((-3((-2(-2x - 3) - 1)/(-2(-2x - 3) - 3)) + 1)/(1((-2(-2x - 3) - 1)/(-2(-2x - 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": "-2", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local extremum of the function f(x) = -2|(-3|((1(-4(1x + 4)^2 - 4(1x + 4) - 3) + 1)/(2(-4(1x + 4)^2 - 4(1x + 4) - 3) + 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": "How many local maxima does the function f(x) = (3(1(-3|((1((-3x + 3)/(1x)) + 1)/(-3((-3x + 3)/(1x)))) + 3|) + 1) - 3)/(-1(1(-3|((1((-3x + 3)/(1x)) + 1)/(-3((-3x + 3)/(1x)))) + 3|) + 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": "Find the x-coordinate of the rightmost local minimum of the function f(x) = -2|(-3|(5(2cos(1\u03c0(2|x - 2| + 3) - 1) + 2)) + 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 rightmost local maximum of the function f(x) = (-3(2sin(3\u03c0((-1(1(5x - 1) - 3) - 2)/(1(1(5x - 1) - 3) - 2)) - 2) - 1) + 3)/(-2(2sin(3\u03c0((-1(1(5x - 1) - 3) - 2)/(1(1(5x - 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": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the average of all x-coordinates of local maxima of the function f(x) = -2cos(2\u03c0(2(5(-3(1x^2 + 3x + 2) + 4)^2 - 5(-3(1x^2 + 3x + 2) + 4) - 1)^2 + 2(5(-3(1x^2 + 3x + 2) + 4)^2 - 5(-3(1x^2 + 3x + 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": "-1", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the rightmost local maximum of the function f(x) = -3|(1(-3cos(3\u03c0(-3(1|x + 2| + 3)^2 - 2(1|x + 2| + 3) + 5) - 3) + 2)^2 - 1(-3cos(3\u03c0(-3(1|x + 2| + 3)^2 - 2(1|x + 2| + 3) + 5) - 3) + 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": "Find the average of all x-coordinates of local maxima of the function f(x) = 2sin(1\u03c0(-2(2((1((3x + 3)/(-2x - 2)) - 3)/(1((3x + 3)/(-2x - 2)))))^2 + 5(2((1((3x + 3)/(-2x - 2)) - 3)/(1((3x + 3)/(-2x - 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": "5", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the leftmost local extremum of the function f(x) = -1((-1(-3|(2(-4x - 2) - 4) - 1| + 2) - 2)/(3(-3|(2(-4x - 2) - 4) - 1| + 2) - 1))^2 + 2((-1(-3|(2(-4x - 2) - 4) - 1| + 2) - 2)/(3(-3|(2(-4x - 2) - 4) - 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 average of all x-coordinates of local minima of the function f(x) = (3(1|(1cos(1\u03c0(2|((3x - 3)/(-2x + 3)) + 1| + 1) + 1) + 3) - 1| - 3) + 1)/(-1(1|(1cos(1\u03c0(2|((3x - 3)/(-2x + 3)) + 1| + 1) + 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": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local maximum with the largest y-value of the function f(x) = (3(-2cos(3\u03c0(3|(4(2|x - 2| + 3) - 2) - 3| + 2) + 1)) - 2)/(-1(-2cos(3\u03c0(3|(4(2|x - 2| + 3) - 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": "How many local maxima does the function f(x) = -4(-2((2(-5((-1x - 2)/(2x - 1))^2 - 4((-1x - 2)/(2x - 1)) - 1) + 1)/(2(-5((-1x - 2)/(2x - 1))^2 - 4((-1x - 2)/(2x - 1)) - 1) - 1))^2 + 4((2(-5((-1x - 2)/(2x - 1))^2 - 4((-1x - 2)/(2x - 1)) - 1) + 1)/(2(-5((-1x - 2)/(2x - 1))^2 - 4((-1x - 2)/(2x - 1)) - 1) - 1)) + 4) - 5 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) = -4(-1|(-2sin(2\u03c0(1(-3x^2 + 5x + 1)^2 + 4(-3x^2 + 5x + 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": "7", "dataset": "MATH"}
{"messages": [{"content": "Find the average of all x-coordinates of local extrema of the function f(x) = -1(-2|(5(-1cos(3\u03c0(5x^2 - 4x + 3) - 3) + 3)^2 + 4(-1cos(3\u03c0(5x^2 - 4x + 3) - 3) + 3) + 2) - 2|)^2 - 4(-2|(5(-1cos(3\u03c0(5x^2 - 4x + 3) - 3) + 3)^2 + 4(-1cos(3\u03c0(5x^2 - 4x + 3) - 3) + 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": "0", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the leftmost local extremum of the function f(x) = -1(4(5(3|(-1|x + 3|) + 1| - 3)^2 + 2(3|(-1|x + 3|) + 1| - 3) + 1)^2 - 3(5(3|(-1|x + 3|) + 1| - 3)^2 + 2(3|(-1|x + 3|) + 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": "-5", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the leftmost local maximum of the function f(x) = 5((2(3e^(1(2|((3x + 2)/(2x - 3)) + 3| + 3)) - 1) + 1)/(-1(3e^(1(2|((3x + 2)/(2x - 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": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the average of all x-coordinates of local minima of the function f(x) = 2|((1(3|(-1|(-2sin(3\u03c0x) + 2) + 3| + 3) - 2|) + 1)/(3(3|(-1|(-2sin(3\u03c0x) + 2) + 3| + 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": "0", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local extremum of the function f(x) = 3e^(1(5((2(1(4x^2 + 5x + 4) + 1) + 2)/(-3(1(4x^2 + 5x + 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": "-1", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local minimum with the largest y-value of the function f(x) = -2(-1cos(3\u03c0(-5(-1((-3x + 2)/(-1x - 3)) + 1)^2 + 2(-1((-3x + 2)/(-1x - 3)) + 1) - 1) - 1) - 1)^2 - 1(-1cos(3\u03c0(-5(-1((-3x + 2)/(-1x - 3)) + 1)^2 + 2(-1((-3x + 2)/(-1x - 3)) + 1) - 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 leftmost local maximum of the function f(x) = 3e^(-1(3|((2(-2|((2x - 2)/(3x)) + 1| + 3))/(-1(-2|((2x - 2)/(3x)) + 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": "-3", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local extremum with the largest y-value of the function f(x) = 3|(4((-2(1(3sin(3\u03c0x + 1) - 2)^2 + 4(3sin(3\u03c0x + 1) - 2) - 4) - 3)/(-3(1(3sin(3\u03c0x + 1) - 2)^2 + 4(3sin(3\u03c0x + 1) - 2) - 4) + 2))^2 + 5((-2(1(3sin(3\u03c0x + 1) - 2)^2 + 4(3sin(3\u03c0x + 1) - 2) - 4) - 3)/(-3(1(3sin(3\u03c0x + 1) - 2)^2 + 4(3sin(3\u03c0x + 1) - 2) - 4) + 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": "-10", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local minimum with the smallest y-value of the function f(x) = -2|(-5(-2|(4(-1x + 4)^2 - 4(-1x + 4))| + 3)^2 - 2(-2|(4(-1x + 4)^2 - 4(-1x + 4))| + 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": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the average of all x-coordinates of local extrema of the function f(x) = -3((1((-1(1(2cos(2\u03c0x + 2) + 3) + 1) - 1)/(-2(1(2cos(2\u03c0x + 2) + 3) + 1) - 1)) - 1)/(-3((-1(1(2cos(2\u03c0x + 2) + 3) + 1) - 1)/(-2(1(2cos(2\u03c0x + 2) + 3) + 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": "0", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local extremum with the smallest y-value of the function f(x) = -2|(2|(-1(-1(-3sin(3\u03c0x - 2) + 2) + 2)^2 + 4(-1(-3sin(3\u03c0x - 2) + 2) + 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": "-10", "dataset": "MATH"}
{"messages": [{"content": "How many local extrema (both minima and maxima) does the function f(x) = (-2(3|(1cos(2\u03c0((-1((-3x + 2)/(-1x + 2)) + 2)/(-3((-3x + 2)/(-1x + 2)) + 2))) + 2) + 2|) + 2)/(1(3|(1cos(2\u03c0((-1((-3x + 2)/(-1x + 2)) + 2)/(-3((-3x + 2)/(-1x + 2)) + 2))) + 2) + 2|) + 1) have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "16", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the rightmost local extremum of the function f(x) = 4(5(-2((2((3x - 3)/(-2x - 2)) + 1)/(-1((3x - 3)/(-2x - 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": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the rightmost local maximum of the function f(x) = 3((-1(-1(1|(4x - 5) - 3| - 3)^2 - 1(1|(4x - 5) - 3| - 3) - 4) + 2)/(-2(-1(1|(4x - 5) - 3| - 3)^2 - 1(1|(4x - 5) - 3| - 3) - 4) + 1))^2 - 3((-1(-1(1|(4x - 5) - 3| - 3)^2 - 1(1|(4x - 5) - 3| - 3) - 4) + 2)/(-2(-1(1|(4x - 5) - 3| - 3)^2 - 1(1|(4x - 5) - 3| - 3) - 4) + 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": "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(-1(5(3e^(1x) - 3)^2 + 3(3e^(1x) - 3) - 4)^2 - 3) + 2) + 3)/(-2(-2(-1(5(3e^(1x) - 3)^2 + 3(3e^(1x) - 3) - 4)^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": "How many local maxima does the function f(x) = -2e^(1(2|((-1(-1|(3x^2 + 5x - 2) + 1| - 2) - 1)/(2(-1|(3x^2 + 5x - 2) + 1| - 2)))| - 3)) - 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) = 2sin(1\u03c0(-5(4(-1|(-1x - 2) - 1| + 2) - 5)^2 + 1(4(-1|(-1x - 2) - 1| + 2) - 5) - 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) = -2(5((2(1cos(3\u03c0((-2x - 2)/(1x - 2)) - 1)) + 1)/(2(1cos(3\u03c0((-2x - 2)/(1x - 2)) - 1)) + 3)) - 1)^2 + 5(5((2(1cos(3\u03c0((-2x - 2)/(1x - 2)) - 1)) + 1)/(2(1cos(3\u03c0((-2x - 2)/(1x - 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": "-7", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local extremum with the largest y-value of the function f(x) = -2(2|(-2|(-2(2|x + 3| - 3)^2 - 5(2|x + 3| - 3) + 1) + 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": "-4", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local maximum of the function f(x) = (3(-5(-5(-2(5x^2 + 3x - 2)) + 4)^2 - 3(-5(-2(5x^2 + 3x - 2)) + 4)) - 1)/(-2(-5(-5(-2(5x^2 + 3x - 2)) + 4)^2 - 3(-5(-2(5x^2 + 3x - 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 minimum of the function f(x) = -2e^(1(-1|(-2|(-4(-1x + 3) - 2) - 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": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the leftmost local minimum of the function f(x) = -2|((2(-5((-3(-5x^2 - 4x + 5))/(1(-5x^2 - 4x + 5) + 1))^2 + 4((-3(-5x^2 - 4x + 5))/(1(-5x^2 - 4x + 5) + 1)) - 3) - 1)/(-1(-5((-3(-5x^2 - 4x + 5))/(1(-5x^2 - 4x + 5) + 1))^2 + 4((-3(-5x^2 - 4x + 5))/(1(-5x^2 - 4x + 5) + 1)) - 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": "-2", "dataset": "MATH"}
{"messages": [{"content": "Find the average of all x-coordinates of local extrema of the function f(x) = -2|(-2(-2|(-3(5x + 1)^2 + 3(5x + 1) - 2) + 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": "0", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local minimum of the function f(x) = (2(-3(1(-2|(1|x| - 2) - 2| - 2)^2 + 4(-2|(1|x| - 2) - 2| - 2) + 5) - 1) + 2)/(1(-3(1(-2|(1|x| - 2) - 2| - 2)^2 + 4(-2|(1|x| - 2) - 2| - 2) + 5) - 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 of the function f(x) = 3sin(2\u03c0((-1(-1|((-2(-1x^2) + 2)/(-2(-1x^2) - 2)) - 3| - 3) + 1)/(-1(-1|((-2(-1x^2) + 2)/(-2(-1x^2) - 2)) - 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 leftmost local maximum of the function f(x) = -3|(1cos(3\u03c0(1|(1|((-2x - 2)/(-2x + 1))| - 2) - 1| + 2) + 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": "-4", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the rightmost local minimum of the function f(x) = -1|(5((1(1(-2sin(1\u03c0x + 1) + 2) + 4) - 2)/(-2(1(-2sin(1\u03c0x + 1) + 2) + 4)))^2 + 4((1(1(-2sin(1\u03c0x + 1) + 2) + 4) - 2)/(-2(1(-2sin(1\u03c0x + 1) + 2) + 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": "8", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local maximum of the function f(x) = 1|((1(3e^(-2((-1(5x^2 - 2x + 5) - 1)/(2(5x^2 - 2x + 5) + 3))) - 1) + 3)/(-2(3e^(-2((-1(5x^2 - 2x + 5) - 1)/(2(5x^2 - 2x + 5) + 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": "0", "dataset": "MATH"}
{"messages": [{"content": "How many local maxima does the function f(x) = 2|(1|((2(-3|(2x^2 - 3) - 2| - 2) - 1)/(-1(-3|(2x^2 - 3) - 2| - 2))) + 3| - 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 local extremum with the smallest y-value of the function f(x) = 1(-3cos(3\u03c0(2(-1|(2|x - 1| - 3)| - 2)^2 + 1(-1|(2|x - 1| - 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 leftmost local minimum of the function f(x) = -3|(-1|(5(-4((1x - 2)/(1x)) + 2)^2 - 4(-4((1x - 2)/(1x)) + 2) + 5) - 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": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the leftmost local extremum of the function f(x) = (2(-1(-3sin(3\u03c0(-4(4x - 2) - 4) - 3) + 2)^2 - 3(-3sin(3\u03c0(-4(4x - 2) - 4) - 3) + 2) + 4) + 3)/(1(-1(-3sin(3\u03c0(-4(4x - 2) - 4) - 3) + 2)^2 - 3(-3sin(3\u03c0(-4(4x - 2) - 4) - 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 extremum with the smallest y-value of the function f(x) = -1(2|(-2(-3sin(2\u03c0((-2x - 3)/(2x - 3)) + 3) + 2)^2 - 2(-3sin(2\u03c0((-2x - 3)/(2x - 3)) + 3) + 2) - 5) + 3|)^2 + 2(2|(-2(-3sin(2\u03c0((-2x - 3)/(2x - 3)) + 3) + 2)^2 - 2(-3sin(2\u03c0((-2x - 3)/(2x - 3)) + 3) + 2) - 5) + 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 rightmost local minimum of the function f(x) = 2|(1cos(1\u03c0(-1(-3(1|x + 3| - 3) - 2)^2 - 3(-3(1|x + 3| - 3) - 2) + 3) + 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": "10", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the leftmost local extremum of the function f(x) = -1sin(3\u03c0((-3(2(1((2x - 3)/(1x + 3))^2 - 4((2x - 3)/(1x + 3)) + 5)^2 - 5(1((2x - 3)/(1x + 3))^2 - 4((2x - 3)/(1x + 3)) + 5) + 5) - 1)/(1(2(1((2x - 3)/(1x + 3))^2 - 4((2x - 3)/(1x + 3)) + 5)^2 - 5(1((2x - 3)/(1x + 3))^2 - 4((2x - 3)/(1x + 3)) + 5) + 5) + 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": "-9", "dataset": "MATH"}
{"messages": [{"content": "How many local maxima does the function f(x) = 1((1(2|((3(1x - 1))/(-1(1x - 1) + 2)) + 2| - 2) - 2)/(-3(2|((3(1x - 1))/(-1(1x - 1) + 2)) + 2| - 2) + 2))^2 + 2((1(2|((3(1x - 1))/(-1(1x - 1) + 2)) + 2| - 2) - 2)/(-3(2|((3(1x - 1))/(-1(1x - 1) + 2)) + 2| - 2) + 2)) + 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 rightmost local minimum of the function f(x) = -5(1(1(1((-2x + 2)/(3x))^2 - 5((-2x + 2)/(3x)) - 3)^2 + 5(1((-2x + 2)/(3x))^2 - 5((-2x + 2)/(3x)) - 3) - 3))^2 + 1(1(1(1((-2x + 2)/(3x))^2 - 5((-2x + 2)/(3x)) - 3)^2 + 5(1((-2x + 2)/(3x))^2 - 5((-2x + 2)/(3x)) - 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": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local maximum with the smallest y-value of the function f(x) = -2sin(2\u03c0(-1(-1((-2(-2|x + 1| - 1) - 3)/(2(-2|x + 1| - 1) - 1)) + 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": "-2", "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|(1(-1|x + 3| - 3)^2 + 4(-1|x + 3| - 3) - 1) + 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": "-3", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the rightmost local maximum of the function f(x) = -5(4(-3((-1((1x - 2)/(1x)) + 2)/(-1((1x - 2)/(1x)) + 3)))^2 + 2(-3((-1((1x - 2)/(1x)) + 2)/(-1((1x - 2)/(1x)) + 3))) - 4)^2 + 2(4(-3((-1((1x - 2)/(1x)) + 2)/(-1((1x - 2)/(1x)) + 3)))^2 + 2(-3((-1((1x - 2)/(1x)) + 2)/(-1((1x - 2)/(1x)) + 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": "-2", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the rightmost local minimum of the function f(x) = (-2(5((2(1|(3cos(2\u03c0x + 1) - 1) - 3| - 1) - 2)/(-2(1|(3cos(2\u03c0x + 1) - 1) - 3| - 1) - 1)) + 4) + 2)/(1(5((2(1|(3cos(2\u03c0x + 1) - 1) - 3| - 1) - 2)/(-2(1|(3cos(2\u03c0x + 1) - 1) - 3| - 1) - 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": "How many local minima does the function f(x) = (-1(2|(-4(-3(1|x + 3|)^2 + 4(1|x + 3|)) + 3) - 1| + 2) - 3)/(2(2|(-4(-3(1|x + 3|)^2 + 4(1|x + 3|)) + 3) - 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 local maximum of the function f(x) = -1|(3e^(-2((-2(3|(2|x + 2| + 1) - 1| - 1) + 3)/(2(3|(2|x + 2| + 1) - 1| - 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": "-2", "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(-3(2|(-3x + 2)| + 1) + 4) - 1))^2 - 2(1sin(1\u03c0(-3(2|(-3x + 2)| + 1) + 4) - 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 minimum of the function f(x) = 2|(-3|(-2e^(1(1|(-5x)| - 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 leftmost local minimum of the function f(x) = -2(1|(2|(2sin(3\u03c0(1|x - 3| - 3) - 3) + 1) - 2| - 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": "-9", "dataset": "MATH"}
{"messages": [{"content": "How many local maxima does the function f(x) = 1|(-3((-3(2(-5x^2 + 5x - 2) - 5) - 2)/(3(2(-5x^2 + 5x - 2) - 5) - 2)) - 3) + 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": "Find the x-coordinate of the local maximum of the function f(x) = -1|(-2(1|(-1cos(2\u03c0(2|x - 2| + 1) + 1) - 1)| - 2)^2 + 4(1|(-1cos(2\u03c0(2|x - 2| + 1) + 1) - 1)| - 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": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local maximum with the largest y-value of the function f(x) = -2(4(-2((-3(2|x + 2| - 2) - 3)/(-2(2|x + 2| - 2) + 3)) - 2)^2 - 1(-2((-3(2|x + 2| - 2) - 3)/(-2(2|x + 2| - 2) + 3)) - 2) + 5) + 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": "-3", "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|(-3cos(1\u03c0(-4x + 4) + 3) - 3) + 3| + 3) + 1| - 3))/(-1(-3|(1|(-3cos(1\u03c0(-4x + 4) + 3) - 3) + 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": "Find the x-coordinate of the local extremum with the smallest y-value of the function f(x) = -2|(-2cos(3\u03c0(-1(2|(-2x^2 + 2x + 4) - 1| - 1)^2 - 5(2|(-2x^2 + 2x + 4) - 1| - 1) + 4) + 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": "-6", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the rightmost local minimum of the function f(x) = (-3(2(-1(5(-2sin(1\u03c0x + 1) - 3) - 4) - 1)^2 - 2(-1(5(-2sin(1\u03c0x + 1) - 3) - 4) - 1) - 1) + 2)/(-1(2(-1(5(-2sin(1\u03c0x + 1) - 3) - 4) - 1)^2 - 2(-1(5(-2sin(1\u03c0x + 1) - 3) - 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": "8", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local minimum of the function f(x) = 2|(1((3(-3|(5x^2 + 2) + 1| + 2) + 3)/(-1(-3|(5x^2 + 2) + 1| + 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": "How many local maxima does the function f(x) = -2|(-4(2((3(-3x^2 - 2x - 5) + 1)/(3(-3x^2 - 2x - 5) - 2)) - 3) - 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": "How many local maxima does the function f(x) = 1e^(1((-1((-3(-3((-3x - 1)/(-3x - 2))^2 + 5((-3x - 1)/(-3x - 2)) - 4) - 1)/(-2(-3((-3x - 1)/(-3x - 2))^2 + 5((-3x - 1)/(-3x - 2)) - 4))) + 2)/(-2((-3(-3((-3x - 1)/(-3x - 2))^2 + 5((-3x - 1)/(-3x - 2)) - 4) - 1)/(-2(-3((-3x - 1)/(-3x - 2))^2 + 5((-3x - 1)/(-3x - 2)) - 4))) + 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) = (3(1(2|(1cos(2\u03c0(2|x| - 3) - 3) - 1)| + 3) + 3) - 3)/(1(1(2|(1cos(2\u03c0(2|x| - 3) - 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": "-10", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the leftmost local maximum of the function f(x) = -2(1(5(-2|((-1x + 1)/(-3x - 3)) - 2| + 3)^2 - 4(-2|((-1x + 1)/(-3x - 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": "-3", "dataset": "MATH"}
{"messages": [{"content": "Find the average of all x-coordinates of local extrema of the function f(x) = -2|(-4((3(-3(-3|x + 3| + 2)^2 + 4(-3|x + 3| + 2) + 5) - 3)/(1(-3(-3|x + 3| + 2)^2 + 4(-3|x + 3| + 2) + 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": "-3", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local minimum of the function f(x) = 5(1((-3(-1|((2x + 1)/(-1x)) - 3| - 2) - 1)/(1(-1|((2x + 1)/(-1x)) - 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": "0", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the leftmost local extremum of the function f(x) = -2(1|(-2cos(2\u03c0(-3|(5x^2 - 3x + 1) + 1| - 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": "-10", "dataset": "MATH"}
{"messages": [{"content": "How many local extrema (both minima and maxima) does the function f(x) = -5(-3|(-1|(-2sin(3\u03c0((2x - 1)/(3x + 2)) + 1) + 2) - 2| + 1)|)^2 - 1(-3|(-1|(-2sin(3\u03c0((2x - 1)/(3x + 2)) + 1) + 2) - 2| + 1)|) + 1 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "60", "dataset": "MATH"}
{"messages": [{"content": "How many local maxima does the function f(x) = -2(-1((-3(4((-3x + 1)/(2x - 1)) + 3) - 1)/(3(4((-3x + 1)/(2x - 1)) + 3) - 2))^2 + 2((-3(4((-3x + 1)/(2x - 1)) + 3) - 1)/(3(4((-3x + 1)/(2x - 1)) + 3) - 2)) - 2) + 5 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 minimum of the function f(x) = (3(-5(-1(5(-2x^2 + 5x + 1)^2 - 2) + 1)^2 + 1(-1(5(-2x^2 + 5x + 1)^2 - 2) + 1) - 5) - 1)/(3(-5(-1(5(-2x^2 + 5x + 1)^2 - 2) + 1)^2 + 1(-1(5(-2x^2 + 5x + 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": "10", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the leftmost local extremum of the function f(x) = -4(-1|(4(5((2x - 2)/(2x + 2))^2 - 3((2x - 2)/(2x + 2)) - 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": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local minimum with the smallest y-value of the function f(x) = 5((-2(-1cos(3\u03c0((2(-2x - 1) + 1)/(1(-2x - 1) + 3)) + 1)) - 1)/(-3(-1cos(3\u03c0((2(-2x - 1) + 1)/(1(-2x - 1) + 3)) + 1))))^2 + 2((-2(-1cos(3\u03c0((2(-2x - 1) + 1)/(1(-2x - 1) + 3)) + 1)) - 1)/(-3(-1cos(3\u03c0((2(-2x - 1) + 1)/(1(-2x - 1) + 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 average of all x-coordinates of local minima of the function f(x) = 5(-1((-1(-1(-3x - 4)^2 - 5(-3x - 4) - 4) - 3)/(1(-1(-3x - 4)^2 - 5(-3x - 4) - 4) + 1))^2 - 3((-1(-1(-3x - 4)^2 - 5(-3x - 4) - 4) - 3)/(1(-1(-3x - 4)^2 - 5(-3x - 4) - 4) + 1)) - 4)^2 + 1(-1((-1(-1(-3x - 4)^2 - 5(-3x - 4) - 4) - 3)/(1(-1(-3x - 4)^2 - 5(-3x - 4) - 4) + 1))^2 - 3((-1(-1(-3x - 4)^2 - 5(-3x - 4) - 4) - 3)/(1(-1(-3x - 4)^2 - 5(-3x - 4) - 4) + 1)) - 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": "0", "dataset": "MATH"}
{"messages": [{"content": "Find the average of all x-coordinates of local extrema of the function f(x) = -1sin(1\u03c0(3|(1|(-2(-1x^2 + 1x - 2) - 2) - 1| + 1) + 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": "0", "dataset": "MATH"}
{"messages": [{"content": "How many local minima does the function f(x) = (-3(2(4(-2|(1|x - 1| - 3) + 3| + 1) - 1) - 4) - 2)/(3(2(4(-2|(1|x - 1| - 3) + 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 local minimum with the smallest y-value of the function f(x) = 2|(-4(2cos(2\u03c0(5((-1x - 3)/(-3x - 2)) - 1) - 2) - 2)^2 - 4(2cos(2\u03c0(5((-1x - 3)/(-3x - 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": "-4", "dataset": "MATH"}
{"messages": [{"content": "How many local extrema (both minima and maxima) does the function f(x) = -3(-1(-2((2(-3cos(2\u03c0x) + 2) - 3)/(1(-3cos(2\u03c0x) + 2)))^2 - 1((2(-3cos(2\u03c0x) + 2) - 3)/(1(-3cos(2\u03c0x) + 2))))^2 + 2(-2((2(-3cos(2\u03c0x) + 2) - 3)/(1(-3cos(2\u03c0x) + 2)))^2 - 1((2(-3cos(2\u03c0x) + 2) - 3)/(1(-3cos(2\u03c0x) + 2)))) - 3) - 2 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "117", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the rightmost local maximum of the function f(x) = -3((-1(-3sin(2\u03c0(1|(-4x^2 - 3x - 4) - 2| + 1) - 3) + 1))/(-2(-3sin(2\u03c0(1|(-4x^2 - 3x - 4) - 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": "10", "dataset": "MATH"}
{"messages": [{"content": "How many local extrema (both minima and maxima) does the function f(x) = (-2(2(-3(-3cos(3\u03c0(-2x^2 - 4x + 4) + 2) + 3)^2 - 1(-3cos(3\u03c0(-2x^2 - 4x + 4) + 2) + 3) + 3)^2 + 1(-3(-3cos(3\u03c0(-2x^2 - 4x + 4) + 2) + 3)^2 - 1(-3cos(3\u03c0(-2x^2 - 4x + 4) + 2) + 3) + 3) - 3) - 3)/(3(2(-3(-3cos(3\u03c0(-2x^2 - 4x + 4) + 2) + 3)^2 - 1(-3cos(3\u03c0(-2x^2 - 4x + 4) + 2) + 3) + 3)^2 + 1(-3(-3cos(3\u03c0(-2x^2 - 4x + 4) + 2) + 3)^2 - 1(-3cos(3\u03c0(-2x^2 - 4x + 4) + 2) + 3) + 3) - 3) - 2) have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "463", "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(1|(-3(3|(2x + 3) + 1| + 2) - 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 local extremum with the largest y-value of the function f(x) = 3(1sin(3\u03c0(2|(2(-3x^2 - 5x - 1)^2 + 3(-3x^2 - 5x - 1) + 2) - 3|) + 2))^2 + 2(1sin(3\u03c0(2|(2(-3x^2 - 5x - 1)^2 + 3(-3x^2 - 5x - 1) + 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": "-4", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local maximum with the smallest y-value of the function f(x) = 1|(-2|(3cos(2\u03c0(-3((-1x)/(3x + 1)) + 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 average of all x-coordinates of local minima of the function f(x) = (2(3(-1e^(-1(-1|((1x + 3)/(1x)) - 1| - 1)) + 3)^2 + 4(-1e^(-1(-1|((1x + 3)/(1x)) - 1| - 1)) + 3) - 4))/(3(3(-1e^(-1(-1|((1x + 3)/(1x)) - 1| - 1)) + 3)^2 + 4(-1e^(-1(-1|((1x + 3)/(1x)) - 1| - 1)) + 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": "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((-2(-2|(2sin(3\u03c0x + 2) - 1) + 2| + 3) - 3)/(1(-2|(2sin(3\u03c0x + 2) - 1) + 2| + 3))) + 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": "-9", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the rightmost local maximum of the function f(x) = -4(-5(-3|(1sin(2\u03c0(-1|x| + 1) - 2) - 3) + 2| + 3)^2 - 1(-3|(1sin(2\u03c0(-1|x| + 1) - 2) - 3) + 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 rightmost local extremum of the function f(x) = (-1((1(2|((-1(1x^2 + 2x - 1) + 1)/(-1(1x^2 + 2x - 1)))| - 3) - 1)/(3(2|((-1(1x^2 + 2x - 1) + 1)/(-1(1x^2 + 2x - 1)))| - 3) + 3)) - 3)/(3((1(2|((-1(1x^2 + 2x - 1) + 1)/(-1(1x^2 + 2x - 1)))| - 3) - 1)/(3(2|((-1(1x^2 + 2x - 1) + 1)/(-1(1x^2 + 2x - 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": "-1", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the rightmost local extremum of the function f(x) = (3(1(2|(-1((-2x - 1)/(-1x - 3))^2 - 2((-2x - 1)/(-1x - 3)) + 2) - 1| - 2) + 1) - 2)/(-1(1(2|(-1((-2x - 1)/(-1x - 3))^2 - 2((-2x - 1)/(-1x - 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": "-1", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local minimum with the smallest y-value of the function f(x) = (2((2(-3|(-3|((3x - 3)/(-3x - 3)) - 3| + 2) + 2| + 1) - 3)/(3(-3|(-3|((3x - 3)/(-3x - 3)) - 3| + 2) + 2| + 1) + 3)) + 2)/(-2((2(-3|(-3|((3x - 3)/(-3x - 3)) - 3| + 2) + 2| + 1) - 3)/(3(-3|(-3|((3x - 3)/(-3x - 3)) - 3| + 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": "-1", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the rightmost local minimum of the function f(x) = -5(4(-4(-2|(2sin(3\u03c0x - 3) - 3) + 1| - 1) - 5) - 4) + 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 local minimum with the smallest y-value of the function f(x) = 3|(3cos(2\u03c0(-4((3((1x + 3)/(1x - 3)) + 1)/(-1((1x + 3)/(1x - 3)) - 2))^2 + 2((3((1x + 3)/(1x - 3)) + 1)/(-1((1x + 3)/(1x - 3)) - 2)) + 4) - 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": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local maximum of the function f(x) = (3(-1e^(1(3(2(5x^2 - 3x + 2)) - 1))) - 2)/(3(-1e^(1(3(2(5x^2 - 3x + 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": "How many local maxima does the function f(x) = (-2(-3|(-4(-3|(-3x - 5) + 3| + 1) - 3)| - 2) + 2)/(-3(-3|(-4(-3|(-3x - 5) + 3| + 1) - 3)| - 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 local minimum of the function f(x) = 3|(2|(-2|(-5(-4x - 5)^2 - 1(-4x - 5) + 1) - 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": "-1", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local minimum of the function f(x) = 1|(-2((1(1(-5x^2 - 3x - 1) - 4) - 2)/(-3(1(-5x^2 - 3x - 1) - 4) - 2))^2 + 3((1(1(-5x^2 - 3x - 1) - 4) - 2)/(-3(1(-5x^2 - 3x - 1) - 4) - 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": "0", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the rightmost local minimum of the function f(x) = (-1(4(-5(1cos(2\u03c0((-1x + 3)/(1x - 2)) + 2) + 3)^2 - 2(1cos(2\u03c0((-1x + 3)/(1x - 2)) + 2) + 3) + 5)^2 - 1(-5(1cos(2\u03c0((-1x + 3)/(1x - 2)) + 2) + 3)^2 - 2(1cos(2\u03c0((-1x + 3)/(1x - 2)) + 2) + 3) + 5) + 1) - 3)/(1(4(-5(1cos(2\u03c0((-1x + 3)/(1x - 2)) + 2) + 3)^2 - 2(1cos(2\u03c0((-1x + 3)/(1x - 2)) + 2) + 3) + 5)^2 - 1(-5(1cos(2\u03c0((-1x + 3)/(1x - 2)) + 2) + 3)^2 - 2(1cos(2\u03c0((-1x + 3)/(1x - 2)) + 2) + 3) + 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": "8", "dataset": "MATH"}
{"messages": [{"content": "Find the average of all x-coordinates of local maxima of the function f(x) = 4(5(1(-1(-3|x + 3| + 3)^2 + 3(-3|x + 3| + 3) + 3)^2 - 5(-1(-3|x + 3| + 3)^2 + 3(-3|x + 3| + 3) + 3) + 3) - 1)^2 + 5(5(1(-1(-3|x + 3| + 3)^2 + 3(-3|x + 3| + 3) + 3)^2 - 5(-1(-3|x + 3| + 3)^2 + 3(-3|x + 3| + 3) + 3) + 3) - 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": "Find the x-coordinate of the local extremum with the largest y-value of the function f(x) = (-3((-1(2e^(1(5(1|x + 2| + 1)^2 - 2(1|x + 2| + 1) - 5)) - 3) + 2)/(-2(2e^(1(5(1|x + 2| + 1)^2 - 2(1|x + 2| + 1) - 5)) - 3))) - 3)/(-2((-1(2e^(1(5(1|x + 2| + 1)^2 - 2(1|x + 2| + 1) - 5)) - 3) + 2)/(-2(2e^(1(5(1|x + 2| + 1)^2 - 2(1|x + 2| + 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": "0", "dataset": "MATH"}
{"messages": [{"content": "How many local minima does the function f(x) = (3(-4(2|(-3e^(1((-1x + 2)/(-2x - 1))) + 1) - 1| + 2)^2 - 4(2|(-3e^(1((-1x + 2)/(-2x - 1))) + 1) - 1| + 2) - 3) - 3)/(3(-4(2|(-3e^(1((-1x + 2)/(-2x - 1))) + 1) - 1| + 2)^2 - 4(2|(-3e^(1((-1x + 2)/(-2x - 1))) + 1) - 1| + 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 rightmost local maximum of the function f(x) = (-3(2cos(3\u03c0(3(3|((-3x + 1)/(3x + 3)) - 1|)^2 - 4(3|((-3x + 1)/(3x + 3)) - 1|) + 2) - 1) + 3) - 1)/(3(2cos(3\u03c0(3(3|((-3x + 1)/(3x + 3)) - 1|)^2 - 4(3|((-3x + 1)/(3x + 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": "9", "dataset": "MATH"}
{"messages": [{"content": "How many local maxima does the function f(x) = (-2(3|(-1|(-3(4x^2 - 4x - 4) - 3) + 2| + 1) - 2| + 1))/(3(3|(-1|(-3(4x^2 - 4x - 4) - 3) + 2| + 1) - 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 x-coordinate of the local maximum with the smallest y-value of the function f(x) = 5(-4(3cos(3\u03c0(1|(-2|x + 2| - 2) - 2|) + 2) + 2) - 2)^2 + 2(-4(3cos(3\u03c0(1|(-2|x + 2| - 2) - 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": "-10", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local maximum of the function f(x) = -1|((1(1(1((2x - 2)/(2x - 1))^2 - 3((2x - 2)/(2x - 1)) - 1) - 4) - 1)/(-3(1(1((2x - 2)/(2x - 1))^2 - 3((2x - 2)/(2x - 1)) - 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": "0", "dataset": "MATH"}
{"messages": [{"content": "Find the average of all x-coordinates of local minima of the function f(x) = -4(3|(-1sin(1\u03c0(1|(-3x^2 + 3x + 4) - 3| - 3) - 3) - 1) + 1| - 1)^2 - 3(3|(-1sin(1\u03c0(1|(-3x^2 + 3x + 4) - 3| - 3) - 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 local maximum with the largest y-value of the function f(x) = -1sin(2\u03c0((-3(1|(3((3x + 2)/(1x + 1)) - 1) - 2| - 1))/(3(1|(3((3x + 2)/(1x + 1)) - 1) - 2| - 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": "-1", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local minimum of the function f(x) = -2e^(-2(-2((2(-2|(-3x^2 + 5x + 3)| - 3) + 1)/(-1(-2|(-3x^2 + 5x + 3)| - 3) + 2))^2 + 2((2(-2|(-3x^2 + 5x + 3)| - 3) + 1)/(-1(-2|(-3x^2 + 5x + 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": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local extremum of the function f(x) = -3|(2|(1(-2((2x + 1)/(-1x - 1))^2 + 4((2x + 1)/(-1x - 1)) - 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": "-1", "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|(-3e^(-1(5x + 4)) - 2) + 3| - 2)^2 - 5(2|(-3e^(-1(5x + 4)) - 2) + 3| - 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": "-1", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local maximum of the function f(x) = 3e^(1(5(-1|(-2|(3|x - 2| - 3) + 1| - 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": "6", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local maximum of the function f(x) = -2|(2(5((-2(-2x^2 + 1x) + 3)/(2(-2x^2 + 1x) + 3)) - 2)^2 + 2(5((-2(-2x^2 + 1x) + 3)/(2(-2x^2 + 1x) + 3)) - 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": "0", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local minimum of the function f(x) = -5(-2|((-1(-2(3x - 1)^2 + 1(3x - 1) - 4) - 2)/(-1(-2(3x - 1)^2 + 1(3x - 1) - 4) - 1))| + 3)^2 + 2(-2|((-1(-2(3x - 1)^2 + 1(3x - 1) - 4) - 2)/(-1(-2(3x - 1)^2 + 1(3x - 1) - 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": "0", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the rightmost local maximum of the function f(x) = -2((-2(-3e^(1(1|(-4x^2 - 1x) + 1| + 2)) + 2) - 3)/(1(-3e^(1(1|(-4x^2 - 1x) + 1| + 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": "3", "dataset": "MATH"}
{"messages": [{"content": "How many local minima does the function f(x) = (2(2e^(1(-2(-5(1x^2 + 4x) + 2)^2 - 3(-5(1x^2 + 4x) + 2) - 4)) - 1) + 3)/(-1(2e^(1(-2(-5(1x^2 + 4x) + 2)^2 - 3(-5(1x^2 + 4x) + 2) - 4)) - 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 leftmost local minimum of the function f(x) = 1|(1(2(3|((-1x - 2)/(-1x - 3)) + 1| - 1)^2 - 2(3|((-1x - 2)/(-1x - 3)) + 1| - 1) + 3)^2 - 2(2(3|((-1x - 2)/(-1x - 3)) + 1| - 1)^2 - 2(3|((-1x - 2)/(-1x - 3)) + 1| - 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": "-3", "dataset": "MATH"}
{"messages": [{"content": "How many local maxima does the function f(x) = -1|(-2sin(2\u03c0(-2|((1(-2|x + 3| + 2))/(2(-2|x + 3| + 2) - 1)) - 2| - 2) - 3) - 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 extremum of the function f(x) = -3(3|(2|(1cos(2\u03c0((-3x + 1)/(1x - 2)) - 3)) + 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": "-8", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the leftmost local maximum of the function f(x) = (-3(-3e^(-1(-3(1(1x + 5)^2 - 3(1x + 5) - 4)^2 + 2(1(1x + 5)^2 - 3(1x + 5) - 4) + 1)) - 1) + 1)/(-2(-3e^(-1(-3(1(1x + 5)^2 - 3(1x + 5) - 4)^2 + 2(1(1x + 5)^2 - 3(1x + 5) - 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": "-7", "dataset": "MATH"}
{"messages": [{"content": "Find the average of all x-coordinates of local minima of the function f(x) = (1(2sin(3\u03c0(-1|(-2(-4x + 1) - 3) - 2| + 1) + 2) + 1) + 1)/(-1(2sin(3\u03c0(-1|(-2(-4x + 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": "0", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the rightmost local minimum of the function f(x) = -4(1(-2|(-2(-1cos(2\u03c0x - 1) + 1) - 5)| - 1)^2 + 3(-2|(-2(-1cos(2\u03c0x - 1) + 1) - 5)| - 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 average of all x-coordinates of local extrema of the function f(x) = (-2(1sin(1\u03c0(3(4(1x + 5)^2 - 3(1x + 5) - 5) - 3) + 3) - 2) - 3)/(1(1sin(1\u03c0(3(4(1x + 5)^2 - 3(1x + 5) - 5) - 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": "0", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local extremum of the function f(x) = (3(-5(-2e^(1(-4(2|x - 2| + 1)^2 + 2)) - 3) - 5) - 3)/(3(-5(-2e^(1(-4(2|x - 2| + 1)^2 + 2)) - 3) - 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": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the leftmost local maximum of the function f(x) = 3e^(2(-4(-2((2(3|x - 2| + 3) + 1)/(-3(3|x - 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": "8", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local minimum with the largest y-value of the function f(x) = -5((-2((3(-1((-2x - 2)/(3x + 3))^2 + 3((-2x - 2)/(3x + 3)) + 4) - 3)/(-1(-1((-2x - 2)/(3x + 3))^2 + 3((-2x - 2)/(3x + 3)) + 4))) + 1)/(2((3(-1((-2x - 2)/(3x + 3))^2 + 3((-2x - 2)/(3x + 3)) + 4) - 3)/(-1(-1((-2x - 2)/(3x + 3))^2 + 3((-2x - 2)/(3x + 3)) + 4))) - 3))^2 + 4((-2((3(-1((-2x - 2)/(3x + 3))^2 + 3((-2x - 2)/(3x + 3)) + 4) - 3)/(-1(-1((-2x - 2)/(3x + 3))^2 + 3((-2x - 2)/(3x + 3)) + 4))) + 1)/(2((3(-1((-2x - 2)/(3x + 3))^2 + 3((-2x - 2)/(3x + 3)) + 4) - 3)/(-1(-1((-2x - 2)/(3x + 3))^2 + 3((-2x - 2)/(3x + 3)) + 4))) - 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": "-2", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local minimum with the largest y-value of the function f(x) = -1|(-1(-2cos(1\u03c0(1|(3x - 1) + 2|)) - 2)^2 + 3(-2cos(1\u03c0(1|(3x - 1) + 2|)) - 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 of the function f(x) = -1(3(1|((-3(-5x^2 - 1x - 5) + 3)/(1(-5x^2 - 1x - 5) + 3)) + 3| + 1) - 5) + 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 leftmost local maximum of the function f(x) = 3|(-4(1(-3((-2x - 3)/(-2x))^2 + 3) - 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": "How many local maxima does the function f(x) = -2|(-2(-3|(-3cos(2\u03c0(2|x - 2| - 1) + 2) + 2) - 3| - 1) - 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": "How many local minima does the function f(x) = 4(-4((2(-3e^(-2((-1x + 3)/(-2x + 3))) - 3) + 1)/(2(-3e^(-2((-1x + 3)/(-2x + 3))) - 3) + 2))^2 + 3((2(-3e^(-2((-1x + 3)/(-2x + 3))) - 3) + 1)/(2(-3e^(-2((-1x + 3)/(-2x + 3))) - 3) + 2)) - 5) - 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(3(-3e^(2((3((1x - 2)/(-3x)) - 3)/(2((1x - 2)/(-3x)) - 3))) + 3) + 2)^2 - 4(3(-3e^(2((3((1x - 2)/(-3x)) - 3)/(2((1x - 2)/(-3x)) - 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 maximum with the largest y-value of the function f(x) = 1(-2|(-2sin(3\u03c0((-1(4x - 4) + 3)/(-2(4x - 4) + 1)) + 1) - 3) - 2|)^2 + 5(-2|(-2sin(3\u03c0((-1(4x - 4) + 3)/(-2(4x - 4) + 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 leftmost local maximum of the function f(x) = 3(-1((2(-1(-1sin(2\u03c0x - 3) - 3) - 5) + 2)/(3(-1(-1sin(2\u03c0x - 3) - 3) - 5) + 2))^2 - 3((2(-1(-1sin(2\u03c0x - 3) - 3) - 5) + 2)/(3(-1(-1sin(2\u03c0x - 3) - 3) - 5) + 2)) + 3)^2 + 1(-1((2(-1(-1sin(2\u03c0x - 3) - 3) - 5) + 2)/(3(-1(-1sin(2\u03c0x - 3) - 3) - 5) + 2))^2 - 3((2(-1(-1sin(2\u03c0x - 3) - 3) - 5) + 2)/(3(-1(-1sin(2\u03c0x - 3) - 3) - 5) + 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": "-9", "dataset": "MATH"}
{"messages": [{"content": "How many local maxima does the function f(x) = (2(-1(-2((3(-2|x| + 2))/(-1(-2|x| + 2) + 2)) + 3) - 1) - 3)/(-3(-1(-2((3(-2|x| + 2))/(-1(-2|x| + 2) + 2)) + 3) - 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": "How many local minima does the function f(x) = (-1(-2((-2(5(-2e^(1x) + 3)^2 + 3(-2e^(1x) + 3) + 3))/(-3(5(-2e^(1x) + 3)^2 + 3(-2e^(1x) + 3) + 3) - 2)) + 5) + 1)/(2(-2((-2(5(-2e^(1x) + 3)^2 + 3(-2e^(1x) + 3) + 3))/(-3(5(-2e^(1x) + 3)^2 + 3(-2e^(1x) + 3) + 3) - 2)) + 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 maxima of the function f(x) = -3(-1(-4(-1e^(2((1x + 3)/(-3x + 1))) + 1) - 1) + 4)^2 - 5(-1(-4(-1e^(2((1x + 3)/(-3x + 1))) + 1) - 1) + 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": "0", "dataset": "MATH"}
{"messages": [{"content": "Find the average of all x-coordinates of local minima of the function f(x) = -4((2(4((1(3cos(3\u03c0x - 1) + 3) + 2)/(1(3cos(3\u03c0x - 1) + 3) + 3)) + 5) + 3)/(3(4((1(3cos(3\u03c0x - 1) + 3) + 2)/(1(3cos(3\u03c0x - 1) + 3) + 3)) + 5)))^2 + 3((2(4((1(3cos(3\u03c0x - 1) + 3) + 2)/(1(3cos(3\u03c0x - 1) + 3) + 3)) + 5) + 3)/(3(4((1(3cos(3\u03c0x - 1) + 3) + 2)/(1(3cos(3\u03c0x - 1) + 3) + 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": "0", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the rightmost local minimum of the function f(x) = -2|((1(3((-3(-3x^2 + 4) - 1)/(-3(-3x^2 + 4) + 4))^2 - 1((-3(-3x^2 + 4) - 1)/(-3(-3x^2 + 4) + 4)) + 4) + 3)/(3(3((-3(-3x^2 + 4) - 1)/(-3(-3x^2 + 4) + 4))^2 - 1((-3(-3x^2 + 4) - 1)/(-3(-3x^2 + 4) + 4)) + 4) - 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 minimum of the function f(x) = (2(1(2(2|(1x + 4) + 3| + 1) - 3)^2 + 5(2(2|(1x + 4) + 3| + 1) - 3) - 4) - 3)/(2(1(2(2|(1x + 4) + 3| + 1) - 3)^2 + 5(2(2|(1x + 4) + 3| + 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": "-7", "dataset": "MATH"}
{"messages": [{"content": "Find the average of all x-coordinates of local extrema of the function f(x) = -2|(-1(3|(1cos(1\u03c0(1x^2 + 5x - 2) + 2) + 1) + 3| + 3)^2 - 5(3|(1cos(1\u03c0(1x^2 + 5x - 2) + 2) + 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": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the rightmost local minimum of the function f(x) = 1|(1((1(1|(1x^2 + 4x) - 2| - 2) - 3)/(3(1|(1x^2 + 4x) - 2| - 2) + 1)) + 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": "0", "dataset": "MATH"}
{"messages": [{"content": "How many local minima does the function f(x) = 1(-2(1e^(-1(3(3|x + 2| + 3))) - 1) - 1)^2 + 3(-2(1e^(-1(3(3|x + 2| + 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 maximum of the function f(x) = -3|((2(-5(-2(-5x^2 - 3x + 2) - 5)^2 + 5(-2(-5x^2 - 3x + 2) - 5) + 3))/(-3(-5(-2(-5x^2 - 3x + 2) - 5)^2 + 5(-2(-5x^2 - 3x + 2) - 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": "0", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local extremum with the largest y-value of the function f(x) = -1sin(3\u03c0(2|(1|((-3(3|x - 3| + 3) - 3)/(-3(3|x - 3| + 3))) + 3| + 1) + 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": "-7", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local extremum with the largest y-value of the function f(x) = 2(-1|(-2|(-1cos(1\u03c0(4x^2 + 2x + 5) + 2) - 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 maximum with the smallest y-value of the function f(x) = -3(-2sin(2\u03c0(-2(-2(1|x + 3| - 2)^2 - 2(1|x + 3| - 2) + 2) - 4) - 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": "How many local extrema (both minima and maxima) does the function f(x) = 1(-3cos(2\u03c0(-3|(5(-2|x - 3| - 2) - 4) - 1| - 2) - 3) - 2) - 2 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "799", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local maximum of the function f(x) = (2(2(-1(-4(3x - 5)^2 + 1(3x - 5) - 1)^2 - 5(-4(3x - 5)^2 + 1(3x - 5) - 1) - 2) - 2) - 1)/(3(2(-1(-4(3x - 5)^2 + 1(3x - 5) - 1)^2 - 5(-4(3x - 5)^2 + 1(3x - 5) - 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": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local extremum with the largest y-value of the function f(x) = (3(3(3cos(1\u03c0(2(2x^2 + 5x + 4)^2 - 2(2x^2 + 5x + 4) + 1) + 3) + 3)^2 - 2(3cos(1\u03c0(2(2x^2 + 5x + 4)^2 - 2(2x^2 + 5x + 4) + 1) + 3) + 3) - 4) + 1)/(-2(3(3cos(1\u03c0(2(2x^2 + 5x + 4)^2 - 2(2x^2 + 5x + 4) + 1) + 3) + 3)^2 - 2(3cos(1\u03c0(2(2x^2 + 5x + 4)^2 - 2(2x^2 + 5x + 4) + 1) + 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": "-6", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the rightmost local extremum of the function f(x) = 2|(-3(-3(3cos(1\u03c0((3x + 3)/(-3x - 1))) + 1)^2 - 4(3cos(1\u03c0((3x + 3)/(-3x - 1))) + 1) + 5)^2 - 3(-3(3cos(1\u03c0((3x + 3)/(-3x - 1))) + 1)^2 - 4(3cos(1\u03c0((3x + 3)/(-3x - 1))) + 1) + 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": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local maximum with the smallest y-value of the function f(x) = -2|(2cos(1\u03c0(-4((-1(-4x + 5))/(1(-4x + 5) - 2)) + 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": "How many local extrema (both minima and maxima) does the function f(x) = -1|(-2|(3e^(-2(-1(4x^2 + 4x + 3) + 3)) - 2) + 3| + 3) - 3| - 3 have in the interval [-10, 10]?\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 of the function f(x) = -5(3|((2(-2(-4x^2 - 3)^2 + 3(-4x^2 - 3) + 1))/(-2(-2(-4x^2 - 3)^2 + 3(-4x^2 - 3) + 1) + 1)) - 2| - 2)^2 + 4(3|((2(-2(-4x^2 - 3)^2 + 3(-4x^2 - 3) + 1))/(-2(-2(-4x^2 - 3)^2 + 3(-4x^2 - 3) + 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": "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(4(2|(2x^2 + 4x + 3) - 1| - 2) + 4)^2 + 3(4(2|(2x^2 + 4x + 3) - 1| - 2) + 4) + 2) + 3)/(-2(1(4(2|(2x^2 + 4x + 3) - 1| - 2) + 4)^2 + 3(4(2|(2x^2 + 4x + 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": "-1", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local maximum of the function f(x) = 2cos(2\u03c0(-1((-2(2|(1x^2 + 5x - 3) - 2| + 3) - 1)/(-3(2|(1x^2 + 5x - 3) - 2| + 3) + 2)) - 5) + 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 largest y-value of the function f(x) = 4(3(-1|(-3(-3x^2 - 1x + 3)^2) + 1| - 2)^2 + 1(-1|(-3(-3x^2 - 1x + 3)^2) + 1| - 2) + 2)^2 + 1(3(-1|(-3(-3x^2 - 1x + 3)^2) + 1| - 2)^2 + 1(-1|(-3(-3x^2 - 1x + 3)^2) + 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": "-1", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local extremum with the largest y-value of the function f(x) = (1(3(1|((-1(3x^2 + 1x) - 3)/(2(3x^2 + 1x))) + 1|)^2 - 5) - 1)/(3(3(1|((-1(3x^2 + 1x) - 3)/(2(3x^2 + 1x))) + 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": "-1", "dataset": "MATH"}
{"messages": [{"content": "How many local minima does the function f(x) = -3(2(-3|((2(2|x - 1| - 3) + 1)/(3(2|x - 1| - 3) + 1)) - 3| - 3)^2 + 4(-3|((2(2|x - 1| - 3) + 1)/(3(2|x - 1| - 3) + 1)) - 3| - 3) + 2) - 5 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) = -4(1(-1(1|(-4x^2 - 2) + 3| - 1)^2 + 2(1|(-4x^2 - 2) + 3| - 1) - 4) - 2)^2 - 2(1(-1(1|(-4x^2 - 2) + 3| - 1)^2 + 2(1|(-4x^2 - 2) + 3| - 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": "0", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local minimum with the largest y-value of the function f(x) = (-1(3cos(3\u03c0(3|(-3|(2x^2 - 5) - 1| - 1) + 2| + 2) + 3) - 3) + 3)/(3(3cos(3\u03c0(3|(-3|(2x^2 - 5) - 1| - 1) + 2| + 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": "Find the x-coordinate of the local maximum with the smallest y-value of the function f(x) = (1(-1cos(1\u03c0(2(2|(1|x + 3| + 1) - 3| - 2)^2 - 5(2|(1|x + 3| + 1) - 3| - 2) - 1) - 2) + 3) + 1)/(1(-1cos(1\u03c0(2(2|(1|x + 3| + 1) - 3| - 2)^2 - 5(2|(1|x + 3| + 1) - 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": "-7", "dataset": "MATH"}
{"messages": [{"content": "Find the average of all x-coordinates of local maxima of the function f(x) = -1|(1(-2|(1sin(2\u03c0(1x^2 + 2x + 3) + 3) - 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": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local maximum of the function f(x) = -5((-2((2((1((-2x + 1)/(-2x - 1)) - 3)/(-3((-2x + 1)/(-2x - 1)) + 4)))/(-1((1((-2x + 1)/(-2x - 1)) - 3)/(-3((-2x + 1)/(-2x - 1)) + 4)) - 3)) + 3)/(-3((2((1((-2x + 1)/(-2x - 1)) - 3)/(-3((-2x + 1)/(-2x - 1)) + 4)))/(-1((1((-2x + 1)/(-2x - 1)) - 3)/(-3((-2x + 1)/(-2x - 1)) + 4)) - 3)) - 3))^2 - 3((-2((2((1((-2x + 1)/(-2x - 1)) - 3)/(-3((-2x + 1)/(-2x - 1)) + 4)))/(-1((1((-2x + 1)/(-2x - 1)) - 3)/(-3((-2x + 1)/(-2x - 1)) + 4)) - 3)) + 3)/(-3((2((1((-2x + 1)/(-2x - 1)) - 3)/(-3((-2x + 1)/(-2x - 1)) + 4)))/(-1((1((-2x + 1)/(-2x - 1)) - 3)/(-3((-2x + 1)/(-2x - 1)) + 4)) - 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 of the function f(x) = (2(-2e^(2(-3|(-1(5x^2 - 4x) - 2) + 1| - 1)) - 2) + 2)/(-1(-2e^(2(-3|(-1(5x^2 - 4x) - 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": "Find the x-coordinate of the leftmost local extremum of the function f(x) = 2|((3(2(-2(2|x + 2|) + 1) + 5))/(2(2(-2(2|x + 2|) + 1) + 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": "-2", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the rightmost local minimum of the function f(x) = -3(3|(2|(3|(-2cos(1\u03c0x + 1) - 2) - 3| - 2) - 1| + 3) + 3| + 2)^2 - 2(3|(2|(3|(-2cos(1\u03c0x + 1) - 2) - 3| - 2) - 1| + 3) + 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 minimum with the largest y-value of the function f(x) = 1(1((2(3e^(-1(2|x| - 2)) - 1) - 1)/(-1(3e^(-1(2|x| - 2)) - 1) + 2))^2 + 2((2(3e^(-1(2|x| - 2)) - 1) - 1)/(-1(3e^(-1(2|x| - 2)) - 1) + 2)) - 3)^2 - 3(1((2(3e^(-1(2|x| - 2)) - 1) - 1)/(-1(3e^(-1(2|x| - 2)) - 1) + 2))^2 + 2((2(3e^(-1(2|x| - 2)) - 1) - 1)/(-1(3e^(-1(2|x| - 2)) - 1) + 2)) - 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 rightmost local extremum of the function f(x) = -1e^(-2(-4(-3(-3|(2|x + 3|) - 1| + 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 extremum of the function f(x) = 1(-2|(1cos(1\u03c0(4(-3x^2 - 3x - 3) + 4) + 2)) + 3| + 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 average of all x-coordinates of local extrema of the function f(x) = 2((2(-2(-3(2x - 4)^2 - 5(2x - 4))^2 + 5(-3(2x - 4)^2 - 5(2x - 4)) + 4) + 2)/(-3(-2(-3(2x - 4)^2 - 5(2x - 4))^2 + 5(-3(2x - 4)^2 - 5(2x - 4)) + 4) - 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 extremum with the smallest y-value of the function f(x) = 3(-3sin(1\u03c0(-2(-5((-2x + 3)/(-1x)) + 3) - 3) - 1) + 3)^2 + 2(-3sin(1\u03c0(-2(-5((-2x + 3)/(-1x)) + 3) - 3) - 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": "-8", "dataset": "MATH"}
{"messages": [{"content": "How many local maxima does the function f(x) = -5(-5(-2|((-2(5x^2 + 3x) - 2)/(2(5x^2 + 3x) + 1)) - 3| + 3) - 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": "How many local extrema (both minima and maxima) does the function f(x) = 1cos(1\u03c0(3|(-4(-3(-3|x + 1| + 3)^2 - 2(-3|x + 1| + 3) + 4) - 5) + 2| + 2) + 3) + 2 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "382", "dataset": "MATH"}
{"messages": [{"content": "How many local minima does the function f(x) = 1((3(-2(3|(2x^2 - 1x + 5) - 2| + 1)^2 - 5(3|(2x^2 - 1x + 5) - 2| + 1) + 4) - 2)/(-3(-2(3|(2x^2 - 1x + 5) - 2| + 1)^2 - 5(3|(2x^2 - 1x + 5) - 2| + 1) + 4) + 1))^2 + 2((3(-2(3|(2x^2 - 1x + 5) - 2| + 1)^2 - 5(3|(2x^2 - 1x + 5) - 2| + 1) + 4) - 2)/(-3(-2(3|(2x^2 - 1x + 5) - 2| + 1)^2 - 5(3|(2x^2 - 1x + 5) - 2| + 1) + 4) + 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": "How many local minima does the function f(x) = 3|(2((-2(-3((-3x + 2)/(-2x + 3))^2 - 4((-3x + 2)/(-2x + 3)) - 2) - 3)/(3(-3((-3x + 2)/(-2x + 3))^2 - 4((-3x + 2)/(-2x + 3)) - 2) + 2))^2 + 1((-2(-3((-3x + 2)/(-2x + 3))^2 - 4((-3x + 2)/(-2x + 3)) - 2) - 3)/(3(-3((-3x + 2)/(-2x + 3))^2 - 4((-3x + 2)/(-2x + 3)) - 2) + 2)) + 2) - 2| - 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 of the function f(x) = 2e^(2(-2|((1(-2|(1x^2 - 4x - 3) + 3| - 3) + 2)/(-3(-2|(1x^2 - 4x - 3) + 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 leftmost local extremum of the function f(x) = 5(2(1sin(1\u03c0(1(1|x + 2|)^2 - 2) + 2) - 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 rightmost local maximum of the function f(x) = -3(1cos(3\u03c0((-2(1((-3x + 3)/(1x + 2))^2 + 5((-3x + 3)/(1x + 2)) + 3) - 1)/(3(1((-3x + 3)/(1x + 2))^2 + 5((-3x + 3)/(1x + 2)) + 3) - 2)) - 1) - 2)^2 + 4(1cos(3\u03c0((-2(1((-3x + 3)/(1x + 2))^2 + 5((-3x + 3)/(1x + 2)) + 3) - 1)/(3(1((-3x + 3)/(1x + 2))^2 + 5((-3x + 3)/(1x + 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": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local extremum with the largest y-value of the function f(x) = -3|(-2cos(3\u03c0(-1|((1(-3x^2 - 3x - 1) + 2)/(-3(-3x^2 - 3x - 1) - 1)) + 1| + 3) + 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": "-1", "dataset": "MATH"}
{"messages": [{"content": "How many local maxima does the function f(x) = 2sin(2\u03c0(2((1(5(1x^2 + 2x + 4)^2 + 2(1x^2 + 2x + 4)) + 1)/(-3(5(1x^2 + 2x + 4)^2 + 2(1x^2 + 2x + 4)) - 1)) + 4) - 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": "Find the x-coordinate of the local extremum with the smallest y-value of the function f(x) = (-3(3(1sin(1\u03c0((2(3|x - 3| - 1) - 3)/(-3(3|x - 3| - 1) - 3)) + 3) - 3) - 4) - 2)/(-3(3(1sin(1\u03c0((2(3|x - 3| - 1) - 3)/(-3(3|x - 3| - 1) - 3)) + 3) - 3) - 4) + 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 minimum of the function f(x) = -3(1(3(1sin(1\u03c0(2x^2 - 3x + 1) + 1) - 3)^2 - 4(1sin(1\u03c0(2x^2 - 3x + 1) + 1) - 3) + 5) - 4) + 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 average of all x-coordinates of local maxima of the function f(x) = (-3((2(-2(2(3x^2 - 5x + 1) - 4)^2 - 5(2(3x^2 - 5x + 1) - 4) + 2) - 2)/(-1(-2(2(3x^2 - 5x + 1) - 4)^2 - 5(2(3x^2 - 5x + 1) - 4) + 2) - 3)) + 3)/(3((2(-2(2(3x^2 - 5x + 1) - 4)^2 - 5(2(3x^2 - 5x + 1) - 4) + 2) - 2)/(-1(-2(2(3x^2 - 5x + 1) - 4)^2 - 5(2(3x^2 - 5x + 1) - 4) + 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 local extremum with the largest y-value of the function f(x) = 2|((3(-1|(-3|(-3x^2 - 4x - 2) + 3| + 1) + 1| + 1) + 1)/(2(-1|(-3|(-3x^2 - 4x - 2) + 3| + 1) + 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": "How many local maxima does the function f(x) = 1(-1(3|(1|(-1x^2 + 5x - 2)| - 2) - 3|)^2 + 1(3|(1|(-1x^2 + 5x - 2)| - 2) - 3|) + 1)^2 - 3(-1(3|(1|(-1x^2 + 5x - 2)| - 2) - 3|)^2 + 1(3|(1|(-1x^2 + 5x - 2)| - 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 local extremum of the function f(x) = (1(2|(-2|(3|(-2x^2 - 2x - 3) + 1|) + 2| + 2) - 1| + 2) + 1)/(-1(2|(-2|(3|(-2x^2 - 2x - 3) + 1|) + 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 minima does the function f(x) = 3(1e^(1(-2((3(-3x + 1) + 2)/(-2(-3x + 1) - 3))^2 + 2((3(-3x + 1) + 2)/(-2(-3x + 1) - 3)) - 5)) + 3) - 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) = -3cos(2\u03c0(1(3(2|(2|x - 3| + 2) + 1| - 3)^2 - 4(2|(2|x - 3| + 2) + 1| - 3) - 2)^2 - 3(3(2|(2|x - 3| + 2) + 1| - 3)^2 - 4(2|(2|x - 3| + 2) + 1| - 3) - 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": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local extremum with the largest y-value of the function f(x) = 4(1|(2((-2(-1x^2 - 1x + 3) - 2)/(3(-1x^2 - 1x + 3) - 2))^2 + 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((3(2(2((-1x + 1)/(-3x)))^2 + 5(2((-1x + 1)/(-3x))) - 4) + 3)/(-2(2(2((-1x + 1)/(-3x)))^2 + 5(2((-1x + 1)/(-3x))) - 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": "0", "dataset": "MATH"}
{"messages": [{"content": "How many local extrema (both minima and maxima) does the function f(x) = 3|(2(2cos(2\u03c0(3(-1x^2 + 5x + 3)^2 - 2(-1x^2 + 5x + 3)) - 1) - 3) + 4) - 3| + 3 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "323", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local maximum of the function f(x) = 1|(-1|(3|(2|(4x + 1) - 2| - 1) - 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 average of all x-coordinates of local maxima of the function f(x) = 5((-1(1(3(2x^2 - 5x - 3)^2 - 4)^2 - 3(3(2x^2 - 5x - 3)^2 - 4) - 3) + 1)/(3(1(3(2x^2 - 5x - 3)^2 - 4)^2 - 3(3(2x^2 - 5x - 3)^2 - 4) - 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 smallest y-value of the function f(x) = 2(2(-3(1|(1sin(3\u03c0x + 1) - 2) + 3|)^2 - 1(1|(1sin(3\u03c0x + 1) - 2) + 3|) + 1)^2 - 3(-3(1|(1sin(3\u03c0x + 1) - 2) + 3|)^2 - 1(1|(1sin(3\u03c0x + 1) - 2) + 3|) + 1) + 3)^2 + 4(2(-3(1|(1sin(3\u03c0x + 1) - 2) + 3|)^2 - 1(1|(1sin(3\u03c0x + 1) - 2) + 3|) + 1)^2 - 3(-3(1|(1sin(3\u03c0x + 1) - 2) + 3|)^2 - 1(1|(1sin(3\u03c0x + 1) - 2) + 3|) + 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 minimum of the function f(x) = 2e^(1(5((-1(4(-2x - 4) - 2) + 2)/(3(4(-2x - 4) - 2) + 1))^2 - 3((-1(4(-2x - 4) - 2) + 2)/(3(4(-2x - 4) - 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": "-2", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local minimum with the largest y-value of the function f(x) = -1(-3cos(1\u03c0((1((-1(-2|x + 3| - 1) + 1)/(1(-2|x + 3| - 1) - 3)) + 3)/(3((-1(-2|x + 3| - 1) + 1)/(1(-2|x + 3| - 1) - 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": "-7", "dataset": "MATH"}
{"messages": [{"content": "How many local maxima does the function f(x) = 1e^(-1((3(1((-3(-2x^2 - 1x - 1) + 3)/(1(-2x^2 - 1x - 1)))^2 - 4((-3(-2x^2 - 1x - 1) + 3)/(1(-2x^2 - 1x - 1))) + 2) + 2)/(-2(1((-3(-2x^2 - 1x - 1) + 3)/(1(-2x^2 - 1x - 1)))^2 - 4((-3(-2x^2 - 1x - 1) + 3)/(1(-2x^2 - 1x - 1))) + 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 rightmost local extremum of the function f(x) = -2|(3e^(-2(-1|((-3(3|x - 1| - 2) - 1)/(-3(3|x - 1| - 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 extremum with the largest y-value of the function f(x) = -1|(4(1|((1(4x^2 + 5x + 3) + 3)/(-2(4x^2 + 5x + 3) + 3))| + 2)^2 + 3(1|((1(4x^2 + 5x + 3) + 3)/(-2(4x^2 + 5x + 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": "-1", "dataset": "MATH"}
{"messages": [{"content": "How many local minima does the function f(x) = 3|(-5(5(1cos(1\u03c0(-4x - 4) + 2) + 1) - 3) + 5)| - 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 local extremum with the largest y-value of the function f(x) = (-3(-5(-3|((-1(-3|x - 1| + 1) - 1)/(-1(-3|x - 1| + 1) + 2))|) - 5) + 1)/(2(-5(-3|((-1(-3|x - 1| + 1) - 1)/(-1(-3|x - 1| + 1) + 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": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local maximum of the function f(x) = -2|(1(2cos(2\u03c0(3((-1x)/(1x + 3))^2 + 4((-1x)/(1x + 3)) + 1) - 3) - 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": "-5", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local maximum with the largest y-value of the function f(x) = -2|(4(-2(1|((-1x + 1)/(-3x + 1)) - 3| - 1)^2 - 2(1|((-1x + 1)/(-3x + 1)) - 3| - 1) + 3)^2 - 5(-2(1|((-1x + 1)/(-3x + 1)) - 3| - 1)^2 - 2(1|((-1x + 1)/(-3x + 1)) - 3| - 1) + 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": "How many local minima does the function f(x) = -1(-1(2|(2(-2|x + 1| - 2)^2 + 1(-2|x + 1| - 2) + 2) - 2|)^2 + 1(2|(2(-2|x + 1| - 2)^2 + 1(-2|x + 1| - 2) + 2) - 2|) - 3)^2 + 1(-1(2|(2(-2|x + 1| - 2)^2 + 1(-2|x + 1| - 2) + 2) - 2|)^2 + 1(2|(2(-2|x + 1| - 2)^2 + 1(-2|x + 1| - 2) + 2) - 2|) - 3) - 5 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) = 2(3sin(3\u03c0(1(3(3x - 1)^2 + 3(3x - 1) + 5)^2 - 5(3(3x - 1)^2 + 3(3x - 1) + 5) - 5) - 3) - 3)^2 + 4(3sin(3\u03c0(1(3(3x - 1)^2 + 3(3x - 1) + 5)^2 - 5(3(3x - 1)^2 + 3(3x - 1) + 5) - 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": "-1", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local maximum of the function f(x) = (-1(-2(3|(-1|((-2x - 3)/(-2x + 1)) + 2| + 2)| - 1) + 1) + 2)/(1(-2(3|(-1|((-2x - 3)/(-2x + 1)) + 2| + 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": "0", "dataset": "MATH"}
{"messages": [{"content": "How many local maxima does the function f(x) = -1|(3(3(-1cos(1\u03c0(1x^2 + 3x - 3) - 3) + 2) - 2)^2 - 1) - 3| + 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": "How many local extrema (both minima and maxima) does the function f(x) = -1|(-2|(-4(-3(-1sin(3\u03c0x) - 1)^2 - 2(-1sin(3\u03c0x) - 1) - 4)^2 - 3(-3(-1sin(3\u03c0x) - 1)^2 - 2(-1sin(3\u03c0x) - 1) - 4) - 2) - 2|) - 3| + 1 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "120", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local extremum with the smallest y-value of the function f(x) = (-2((2(2|(-2(1x - 2)^2 + 5(1x - 2) - 1) - 2| + 2) - 2)/(-1(2|(-2(1x - 2)^2 + 5(1x - 2) - 1) - 2| + 2) - 3)) + 3)/(3((2(2|(-2(1x - 2)^2 + 5(1x - 2) - 1) - 2| + 2) - 2)/(-1(2|(-2(1x - 2)^2 + 5(1x - 2) - 1) - 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": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local minimum with the smallest y-value of the function f(x) = 5((3(1(3sin(1\u03c0((2x + 1)/(-3x + 4)) + 1) + 3) - 2) - 3)/(-1(1(3sin(1\u03c0((2x + 1)/(-3x + 4)) + 1) + 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 leftmost local extremum of the function f(x) = 3((2(-4(-3cos(3\u03c0(-1x^2 - 1x - 5) + 3) + 2)^2 + 3(-3cos(3\u03c0(-1x^2 - 1x - 5) + 3) + 2) - 4) + 3)/(2(-4(-3cos(3\u03c0(-1x^2 - 1x - 5) + 3) + 2)^2 + 3(-3cos(3\u03c0(-1x^2 - 1x - 5) + 3) + 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": "-10", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local minimum with the smallest y-value of the function f(x) = 2(3((-3(-1((-1x + 2)/(-1x - 1)) + 1) + 3)/(1(-1((-1x + 2)/(-1x - 1)) + 1) - 2))^2 - 4)^2 + 4(3((-3(-1((-1x + 2)/(-1x - 1)) + 1) + 3)/(1(-1((-1x + 2)/(-1x - 1)) + 1) - 2))^2 - 4) + 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 average of all x-coordinates of local extrema of the function f(x) = 1|(3|((3(1sin(3\u03c0(-3x^2 + 3x + 2) + 2) - 1) + 1)/(2(1sin(3\u03c0(-3x^2 + 3x + 2) + 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": "0", "dataset": "MATH"}
{"messages": [{"content": "How many local extrema (both minima and maxima) does the function f(x) = (-3(-1e^(-2(-3(2((-1x + 3)/(-2x - 1)) + 5) - 1)) + 3) + 3)/(2(-1e^(-2(-3(2((-1x + 3)/(-2x - 1)) + 5) - 1)) + 3) + 1) have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "205", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the rightmost local minimum of the function f(x) = -4((-2(1|(-3|((-2x + 1)/(3x + 1)) - 2| + 1) + 2| - 2) - 3)/(-3(1|(-3|((-2x + 1)/(3x + 1)) - 2| + 1) + 2| - 2) + 4)) - 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 minimum with the smallest y-value of the function f(x) = -3|(-1sin(3\u03c0(-2(-3|(-1|x| + 3) + 1| - 3)^2 + 3(-3|(-1|x| + 3) + 1| - 3) - 1) - 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 local maximum with the largest y-value of the function f(x) = -3|(-1((-3((-2((-1x + 2)/(1x)) - 1)/(-3((-1x + 2)/(1x)) + 2)))/(2((-2((-1x + 2)/(1x)) - 1)/(-3((-1x + 2)/(1x)) + 2))))^2 - 4((-3((-2((-1x + 2)/(1x)) - 1)/(-3((-1x + 2)/(1x)) + 2)))/(2((-2((-1x + 2)/(1x)) - 1)/(-3((-1x + 2)/(1x)) + 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": "How many local minima does the function f(x) = -4(-5(1e^(-1(5((-3x - 2)/(1x))^2 + 3((-3x - 2)/(1x)) + 4))) - 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": "How many local extrema (both minima and maxima) does the function f(x) = (-1(-2|(-3|((2(1x - 4))/(-1(1x - 4) + 2)) - 2| + 2)| - 1) + 3)/(-3(-2|(-3|((2(1x - 4))/(-1(1x - 4) + 2)) - 2| + 2)| - 1) - 3) have in the interval [-10, 10]?\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) = -1cos(1\u03c0(-1(-1(-2|(-1x^2 - 3x - 3) - 1|)^2 + 2(-2|(-1x^2 - 3x - 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 local extremum with the largest y-value of the function f(x) = 2|(-5((-2(-3((-1x - 3)/(3x + 1))^2 - 3((-1x - 3)/(3x + 1))) + 2)/(1(-3((-1x - 3)/(3x + 1))^2 - 3((-1x - 3)/(3x + 1))) - 3)) - 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": "0", "dataset": "MATH"}
{"messages": [{"content": "Find the average of all x-coordinates of local maxima of the function f(x) = 2(3|(-3cos(2\u03c0(-4(2|x| - 2)^2 - 3(2|x| - 2) + 1) + 1) + 3) + 1| - 3)^2 - 4(3|(-3cos(2\u03c0(-4(2|x| - 2)^2 - 3(2|x| - 2) + 1) + 1) + 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": "0", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the leftmost local maximum of the function f(x) = 2sin(2\u03c0(-4(-1(3|((3x)/(3x - 2)) - 2| - 3) + 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": "-4", "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((-1(-1(1x + 4)^2 - 5(1x + 4) + 2) + 2)/(3(-1(1x + 4)^2 - 5(1x + 4) + 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": "-10", "dataset": "MATH"}
{"messages": [{"content": "Find the average of all x-coordinates of local extrema of the function f(x) = -2((2((-1(-3e^(1(-1x^2 + 1x + 3)) + 3) + 1)/(-2(-3e^(1(-1x^2 + 1x + 3)) + 3) + 3)) - 2)/(1((-1(-3e^(1(-1x^2 + 1x + 3)) + 3) + 1)/(-2(-3e^(1(-1x^2 + 1x + 3)) + 3) + 3)) + 1))^2 - 1((2((-1(-3e^(1(-1x^2 + 1x + 3)) + 3) + 1)/(-2(-3e^(1(-1x^2 + 1x + 3)) + 3) + 3)) - 2)/(1((-1(-3e^(1(-1x^2 + 1x + 3)) + 3) + 1)/(-2(-3e^(1(-1x^2 + 1x + 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": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local maximum of the function f(x) = -2|(4(3(-3|(-2|x + 3| - 3)| + 3)^2 + 1(-3|(-2|x + 3| - 3)| + 3) - 4)^2 + 5(3(-3|(-2|x + 3| - 3)| + 3)^2 + 1(-3|(-2|x + 3| - 3)| + 3) - 4) - 5) + 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 maxima does the function f(x) = 2|(-3(1((2((-2x + 2)/(-3x)) + 1)/(-1((-2x + 2)/(-3x)) - 2))^2 - 4((2((-2x + 2)/(-3x)) + 1)/(-1((-2x + 2)/(-3x)) - 2)) + 5)^2 - 5(1((2((-2x + 2)/(-3x)) + 1)/(-1((-2x + 2)/(-3x)) - 2))^2 - 4((2((-2x + 2)/(-3x)) + 1)/(-1((-2x + 2)/(-3x)) - 2)) + 5) - 4) + 2| - 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 extrema of the function f(x) = (-1(3|(-3|(-5(-3x + 1)^2 - 4(-3x + 1)) + 1| - 2) - 2| - 2) + 3)/(2(3|(-3|(-5(-3x + 1)^2 - 4(-3x + 1)) + 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": "0", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local maximum of the function f(x) = 4((1(-3(-4((-1x - 3)/(3x))^2 + 2((-1x - 3)/(3x)) - 2) + 2) + 1)/(-3(-3(-4((-1x - 3)/(3x))^2 + 2((-1x - 3)/(3x)) - 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": "0", "dataset": "MATH"}
{"messages": [{"content": "Find the average of all x-coordinates of local extrema of the function f(x) = -3sin(1\u03c0((-3(-2(-2(-1x^2 + 5x + 4)^2 - 1(-1x^2 + 5x + 4) - 5)^2 + 4(-2(-1x^2 + 5x + 4)^2 - 1(-1x^2 + 5x + 4) - 5) - 4) - 1)/(-1(-2(-2(-1x^2 + 5x + 4)^2 - 1(-1x^2 + 5x + 4) - 5)^2 + 4(-2(-1x^2 + 5x + 4)^2 - 1(-1x^2 + 5x + 4) - 5) - 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": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local minimum of the function f(x) = 1((-1((1((-2(5x^2 + 4x - 4) + 2)/(-1(5x^2 + 4x - 4) + 2)) - 2)/(1((-2(5x^2 + 4x - 4) + 2)/(-1(5x^2 + 4x - 4) + 2)))) + 3)/(3((1((-2(5x^2 + 4x - 4) + 2)/(-1(5x^2 + 4x - 4) + 2)) - 2)/(1((-2(5x^2 + 4x - 4) + 2)/(-1(5x^2 + 4x - 4) + 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": "How many local maxima does the function f(x) = -1|(-2(-1(-2(-1|x + 1| - 3)^2 - 3(-1|x + 1| - 3) + 5)^2 - 4(-2(-1|x + 1| - 3)^2 - 3(-1|x + 1| - 3) + 5) + 2) + 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 leftmost local minimum of the function f(x) = -2cos(2\u03c0(-2|(1|(-3((-2x + 1)/(-3x + 2)) + 5) - 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": "0", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local maximum of the function f(x) = -2e^(-2(1|(5(-2((3x + 2)/(-3x - 1)) - 5)^2 + 3(-2((3x + 2)/(-3x - 1)) - 5) + 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": "9", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local extremum of the function f(x) = (3(1|(1|(-1|((-1x + 2)/(-1x)) - 3| + 1) - 3| + 1) - 3| + 1) - 2)/(-3(1|(1|(-1|((-1x + 2)/(-1x)) - 3| + 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 leftmost local maximum of the function f(x) = -4((1(-5(1(-2|x - 3| - 2)^2 + 5(-2|x - 3| - 2) - 3) - 3) - 1)/(1(-5(1(-2|x - 3| - 2)^2 + 5(-2|x - 3| - 2) - 3) - 3) - 2))^2 - 1((1(-5(1(-2|x - 3| - 2)^2 + 5(-2|x - 3| - 2) - 3) - 3) - 1)/(1(-5(1(-2|x - 3| - 2)^2 + 5(-2|x - 3| - 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 leftmost local extremum of the function f(x) = -2|(2sin(3\u03c0((-2(3((3x - 2)/(-2x + 3)) - 5) - 2)/(-1(3((3x - 2)/(-2x + 3)) - 5) - 3)) + 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": "0", "dataset": "MATH"}
{"messages": [{"content": "How many local extrema (both minima and maxima) does the function f(x) = (1((-3(1(1((-2x + 3)/(-3x + 1))^2 - 2((-2x + 3)/(-3x + 1)) + 3)^2 + 3(1((-2x + 3)/(-3x + 1))^2 - 2((-2x + 3)/(-3x + 1)) + 3) + 3) + 2)/(1(1(1((-2x + 3)/(-3x + 1))^2 - 2((-2x + 3)/(-3x + 1)) + 3)^2 + 3(1((-2x + 3)/(-3x + 1))^2 - 2((-2x + 3)/(-3x + 1)) + 3) + 3))) + 2)/(2((-3(1(1((-2x + 3)/(-3x + 1))^2 - 2((-2x + 3)/(-3x + 1)) + 3)^2 + 3(1((-2x + 3)/(-3x + 1))^2 - 2((-2x + 3)/(-3x + 1)) + 3) + 3) + 2)/(1(1(1((-2x + 3)/(-3x + 1))^2 - 2((-2x + 3)/(-3x + 1)) + 3)^2 + 3(1((-2x + 3)/(-3x + 1))^2 - 2((-2x + 3)/(-3x + 1)) + 3) + 3))) - 1) have in the interval [-10, 10]?\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 of the function f(x) = -2|(-3cos(3\u03c0(1|(3|(-1x^2 + 2x + 3) - 3| + 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": "-7", "dataset": "MATH"}
{"messages": [{"content": "Find the average of all x-coordinates of local maxima of the function f(x) = -2(-5((3(-2e^(-1(2|x + 3| + 1)) + 2))/(-2(-2e^(-1(2|x + 3| + 1)) + 2) - 3))^2 - 3((3(-2e^(-1(2|x + 3| + 1)) + 2))/(-2(-2e^(-1(2|x + 3| + 1)) + 2) - 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 extremum with the smallest y-value of the function f(x) = (-2(-5((-2(2|(2|x + 2| + 2) - 2| - 3) - 3)/(2(2|(2|x + 2| + 2) - 2| - 3) - 1))^2 - 1((-2(2|(2|x + 2| + 2) - 2| - 3) - 3)/(2(2|(2|x + 2| + 2) - 2| - 3) - 1)) - 3) + 3)/(-2(-5((-2(2|(2|x + 2| + 2) - 2| - 3) - 3)/(2(2|(2|x + 2| + 2) - 2| - 3) - 1))^2 - 1((-2(2|(2|x + 2| + 2) - 2| - 3) - 3)/(2(2|(2|x + 2| + 2) - 2| - 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": "-3", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the leftmost local minimum of the function f(x) = (-3(1((3(-2|(-2|x + 1| + 2) + 3| + 3) - 2)/(1(-2|(-2|x + 1| + 2) + 3| + 3) - 3))))/(-1(1((3(-2|(-2|x + 1| + 2) + 3| + 3) - 2)/(1(-2|(-2|x + 1| + 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": "-10", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the leftmost local extremum of the function f(x) = 5(-4(-2|(4(1cos(2\u03c0x + 1) - 3) + 3) + 2| + 3)^2 + 5(-2|(4(1cos(2\u03c0x + 1) - 3) + 3) + 2| + 3) - 5) - 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|(1(3(-1|((-2x)/(-2x + 3)) + 3| + 1) + 1)^2 - 5(3(-1|((-2x)/(-2x + 3)) + 3| + 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": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local minimum with the smallest y-value of the function f(x) = (-2(-3(-1cos(3\u03c0((1(4x^2 - 2x - 2))/(-1(4x^2 - 2x - 2) - 3)) + 1))^2 + 2(-1cos(3\u03c0((1(4x^2 - 2x - 2))/(-1(4x^2 - 2x - 2) - 3)) + 1)) - 2) + 3)/(-2(-3(-1cos(3\u03c0((1(4x^2 - 2x - 2))/(-1(4x^2 - 2x - 2) - 3)) + 1))^2 + 2(-1cos(3\u03c0((1(4x^2 - 2x - 2))/(-1(4x^2 - 2x - 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": "-2", "dataset": "MATH"}
{"messages": [{"content": "How many local extrema (both minima and maxima) does the function f(x) = -4(-1|(3(-2sin(3\u03c0(1x + 5) - 1) + 2)) - 2| - 2)^2 + 5(-1|(3(-2sin(3\u03c0(1x + 5) - 1) + 2)) - 2| - 2) + 3 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "111", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local extremum with the largest y-value of the function f(x) = -2(2e^(1(5(-1(-2|x - 2| - 2) - 4)^2 + 4(-1(-2|x - 2| - 2) - 4) + 4)) - 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) = -3|((-3(-2sin(2\u03c0((-1(5x - 5) + 1)/(-2(5x - 5) - 2)) - 2) + 3) + 3)/(2(-2sin(2\u03c0((-1(5x - 5) + 1)/(-2(5x - 5) - 2)) - 2) + 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 local maximum of the function f(x) = -1(4(1((1((-1x + 3)/(2x + 2)) + 2)/(-1((-1x + 3)/(2x + 2)))) + 1)^2 - 1(1((1((-1x + 3)/(2x + 2)) + 2)/(-1((-1x + 3)/(2x + 2)))) + 1) + 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": "-1", "dataset": "MATH"}
{"messages": [{"content": "How many local minima does the function f(x) = -3(-1(1(-1e^(1((3x - 1)/(-2x + 3))) + 1) + 1) + 2)^2 - 4(-1(1(-1e^(1((3x - 1)/(-2x + 3))) + 1) + 1) + 2) - 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": "How many local minima does the function f(x) = 1|(-1(-1|((-1(4x - 4) - 2)/(-2(4x - 4) + 3)) + 3| + 2)^2 + 5(-1|((-1(4x - 4) - 2)/(-2(4x - 4) + 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": "0", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local extremum of the function f(x) = -3|(-2(-2((-3(-2|x - 2| + 3))/(1(-2|x - 2| + 3)))^2 + 5((-3(-2|x - 2| + 3))/(1(-2|x - 2| + 3))) + 2)^2 - 4(-2((-3(-2|x - 2| + 3))/(1(-2|x - 2| + 3)))^2 + 5((-3(-2|x - 2| + 3))/(1(-2|x - 2| + 3))) + 2) + 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": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the rightmost local extremum of the function f(x) = 5((-2(-2cos(3\u03c0(-1|(-4x - 4) - 2| + 1) - 1) - 1) - 2)/(-1(-2cos(3\u03c0(-1|(-4x - 4) - 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": "10", "dataset": "MATH"}
{"messages": [{"content": "How many local minima does the function f(x) = 1(5((-2((-2(5x^2 + 5x + 5) - 3)/(-1(5x^2 + 5x + 5) + 2)) + 3)/(2((-2(5x^2 + 5x + 5) - 3)/(-1(5x^2 + 5x + 5) + 2)) + 3))^2 - 5((-2((-2(5x^2 + 5x + 5) - 3)/(-1(5x^2 + 5x + 5) + 2)) + 3)/(2((-2(5x^2 + 5x + 5) - 3)/(-1(5x^2 + 5x + 5) + 2)) + 3)) + 3)^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 rightmost local maximum of the function f(x) = (-3(5((-1(-1sin(3\u03c0(-5x^2 - 5x - 3) - 2) - 3) - 2)/(-1(-1sin(3\u03c0(-5x^2 - 5x - 3) - 2) - 3))) - 2))/(-3(5((-1(-1sin(3\u03c0(-5x^2 - 5x - 3) - 2) - 3) - 2)/(-1(-1sin(3\u03c0(-5x^2 - 5x - 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 of the function f(x) = -1|(2|(-3(-2e^(-1(1x^2 + 5x + 5)) - 2)^2 - 3(-2e^(-1(1x^2 + 5x + 5)) - 2) + 5) - 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": "-2", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local extremum with the smallest y-value of the function f(x) = (-2(-4(-3|(2sin(1\u03c0(-1x^2 - 3x - 2) + 1) - 1)|)^2 - 5(-3|(2sin(1\u03c0(-1x^2 - 3x - 2) + 1) - 1)|) + 3) + 1)/(-2(-4(-3|(2sin(1\u03c0(-1x^2 - 3x - 2) + 1) - 1)|)^2 - 5(-3|(2sin(1\u03c0(-1x^2 - 3x - 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": "-10", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the rightmost local extremum of the function f(x) = -2e^(-1(3|(-1|((3((2x + 3)/(-1x + 2)) - 1)/(3((2x + 3)/(-1x + 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": "-1", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the rightmost local minimum of the function f(x) = 5(3sin(3\u03c0(-1|(-1(3|x - 1| - 1) - 3) - 1| + 2) + 1) - 2)^2 + 5(3sin(3\u03c0(-1|(-1(3|x - 1| - 1) - 3) - 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": "How many local minima does the function f(x) = -2e^(2(2(3|(-1(2|x - 3|) - 4) + 2| - 3)^2 + 5(3|(-1(2|x - 3|) - 4) + 2| - 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": "How many local maxima does the function f(x) = 2((2(1|((-2(-2|x - 3|))/(2(-2|x - 3|) - 3)) - 3| - 1))/(-2(1|((-2(-2|x - 3|))/(2(-2|x - 3|) - 3)) - 3| - 1) + 1))^2 + 5((2(1|((-2(-2|x - 3|))/(2(-2|x - 3|) - 3)) - 3| - 1))/(-2(1|((-2(-2|x - 3|))/(2(-2|x - 3|) - 3)) - 3| - 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": "Find the x-coordinate of the local extremum with the largest y-value of the function f(x) = -4(1(2cos(1\u03c0((-3(-1|x + 1| + 1) + 3)/(-2(-1|x + 1| + 1) + 3)) - 1) - 3) - 1)^2 - 4(1(2cos(1\u03c0((-3(-1|x + 1| + 1) + 3)/(-2(-1|x + 1| + 1) + 3)) - 1) - 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 rightmost local extremum of the function f(x) = -2sin(2\u03c0(-3(2|(-3|(-3x^2 + 5x - 5) - 1| + 3)| - 3)^2 + 5(2|(-3|(-3x^2 + 5x - 5) - 1| + 3)| - 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": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local maximum with the largest y-value of the function f(x) = (-3(-1(5(-2(-1cos(1\u03c0x + 3) + 2) + 5) + 4) - 2) + 1)/(-3(-1(5(-2(-1cos(1\u03c0x + 3) + 2) + 5) + 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": "-9", "dataset": "MATH"}
{"messages": [{"content": "Find the average of all x-coordinates of local maxima of the function f(x) = 1((-1(3(-3((-3x + 2)/(-3x - 3)) + 1)^2 + 2(-3((-3x + 2)/(-3x - 3)) + 1) + 1) - 1)/(1(3(-3((-3x + 2)/(-3x - 3)) + 1)^2 + 2(-3((-3x + 2)/(-3x - 3)) + 1) + 1) + 2))^2 + 2((-1(3(-3((-3x + 2)/(-3x - 3)) + 1)^2 + 2(-3((-3x + 2)/(-3x - 3)) + 1) + 1) - 1)/(1(3(-3((-3x + 2)/(-3x - 3)) + 1)^2 + 2(-3((-3x + 2)/(-3x - 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": "How many local minima does the function f(x) = -2((1(1(2|(4x + 2) + 3| - 2)^2 - 4(2|(4x + 2) + 3| - 2) - 3) - 2)/(2(1(2|(4x + 2) + 3| - 2)^2 - 4(2|(4x + 2) + 3| - 2) - 3) + 2))^2 + 1((1(1(2|(4x + 2) + 3| - 2)^2 - 4(2|(4x + 2) + 3| - 2) - 3) - 2)/(2(1(2|(4x + 2) + 3| - 2)^2 - 4(2|(4x + 2) + 3| - 2) - 3) + 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 maxima of the function f(x) = -1(-1((-2(1(1cos(2\u03c0x - 1) - 1)^2 + 5(1cos(2\u03c0x - 1) - 1) + 1) - 1)/(-1(1(1cos(2\u03c0x - 1) - 1)^2 + 5(1cos(2\u03c0x - 1) - 1) + 1) + 3))^2 - 1((-2(1(1cos(2\u03c0x - 1) - 1)^2 + 5(1cos(2\u03c0x - 1) - 1) + 1) - 1)/(-1(1(1cos(2\u03c0x - 1) - 1)^2 + 5(1cos(2\u03c0x - 1) - 1) + 1) + 3)) - 2)^2 - 1(-1((-2(1(1cos(2\u03c0x - 1) - 1)^2 + 5(1cos(2\u03c0x - 1) - 1) + 1) - 1)/(-1(1(1cos(2\u03c0x - 1) - 1)^2 + 5(1cos(2\u03c0x - 1) - 1) + 1) + 3))^2 - 1((-2(1(1cos(2\u03c0x - 1) - 1)^2 + 5(1cos(2\u03c0x - 1) - 1) + 1) - 1)/(-1(1(1cos(2\u03c0x - 1) - 1)^2 + 5(1cos(2\u03c0x - 1) - 1) + 1) + 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": "0", "dataset": "MATH"}
{"messages": [{"content": "How many local extrema (both minima and maxima) does the function f(x) = (-3(-1(-1(-1cos(2\u03c0(3|x - 2| + 3) + 1))^2 - 2(-1cos(2\u03c0(3|x - 2| + 3) + 1)) + 4)^2 + 1(-1(-1cos(2\u03c0(3|x - 2| + 3) + 1))^2 - 2(-1cos(2\u03c0(3|x - 2| + 3) + 1)) + 4) - 1) + 1)/(3(-1(-1(-1cos(2\u03c0(3|x - 2| + 3) + 1))^2 - 2(-1cos(2\u03c0(3|x - 2| + 3) + 1)) + 4)^2 + 1(-1(-1cos(2\u03c0(3|x - 2| + 3) + 1))^2 - 2(-1cos(2\u03c0(3|x - 2| + 3) + 1)) + 4) - 1) + 2) have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "121", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the leftmost local maximum of the function f(x) = 1|(3sin(3\u03c0((2(1|(3x^2 + 1x - 3) - 2|) - 2)/(1(1|(3x^2 + 1x - 3) - 2|) + 2)) + 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": "-7", "dataset": "MATH"}
{"messages": [{"content": "How many local extrema (both minima and maxima) does the function f(x) = 1sin(2\u03c0(1|(2((2(-3x - 5) - 2)/(-3(-3x - 5) + 4)) - 5) + 1| + 3) - 2) - 1 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local extremum with the largest y-value of the function f(x) = 1(2(-3|(-3e^(-1(-5x^2 - 3x)) + 3) + 2| + 2)^2 + 1)^2 - 2(2(-3|(-3e^(-1(-5x^2 - 3x)) + 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": "-5", "dataset": "MATH"}
{"messages": [{"content": "Find the average of all x-coordinates of local extrema of the function f(x) = -3|(1(-1|(1|((-3x - 1)/(2x - 1)) + 1| - 2) - 2| - 1)^2 + 1(-1|(1|((-3x - 1)/(2x - 1)) + 1| - 2) - 2| - 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": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the rightmost local maximum of the function f(x) = 3((3((1(2|(-2x^2 + 5x + 2) - 1|) + 2)/(2(2|(-2x^2 + 5x + 2) - 1|) + 2)) + 2)/(-2((1(2|(-2x^2 + 5x + 2) - 1|) + 2)/(2(2|(-2x^2 + 5x + 2) - 1|) + 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": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local minimum of the function f(x) = -2(1e^(-1(1(-1(3|x - 1| + 1) + 1)^2 - 3)) - 2)^2 - 3(1e^(-1(1(-1(3|x - 1| + 1) + 1)^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": "1", "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(-2|(-5(-2|x + 2| - 2)^2 - 2(-2|x + 2| - 2) - 5) + 2| - 1) - 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 average of all x-coordinates of local minima of the function f(x) = -4(-1(-2|(1((3x)/(1x + 1))^2 - 2((3x)/(1x + 1)) - 5) + 1| + 2) - 5) - 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) = 3|(-4(1|(-3((-2x - 1)/(2x + 3))^2 - 5((-2x - 1)/(2x + 3)) - 3) + 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": "4", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local extremum of the function f(x) = (3((-2(-1(-1(-1x - 5)^2 + 2(-1x - 5) + 1)^2 + 5(-1(-1x - 5)^2 + 2(-1x - 5) + 1) + 3) + 3)/(2(-1(-1(-1x - 5)^2 + 2(-1x - 5) + 1)^2 + 5(-1(-1x - 5)^2 + 2(-1x - 5) + 1) + 3) - 1)) - 1)/(-2((-2(-1(-1(-1x - 5)^2 + 2(-1x - 5) + 1)^2 + 5(-1(-1x - 5)^2 + 2(-1x - 5) + 1) + 3) + 3)/(2(-1(-1(-1x - 5)^2 + 2(-1x - 5) + 1)^2 + 5(-1(-1x - 5)^2 + 2(-1x - 5) + 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": "-6", "dataset": "MATH"}
{"messages": [{"content": "How many local extrema (both minima and maxima) does the function f(x) = -2cos(2\u03c0(-4(-1|(-2|(3x + 2) - 3| + 2) + 1| + 1) - 3) + 1) - 3 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "957", "dataset": "MATH"}
{"messages": [{"content": "How many local minima does the function f(x) = 3|(-2|(-2(-3(-1x + 3)^2 - 2(-1x + 3) + 2) + 5)| + 1) + 3| + 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 rightmost local minimum of the function f(x) = -2sin(2\u03c0(-3|(3((-3(3x^2 + 2x + 3) - 2)/(2(3x^2 + 2x + 3) - 1))^2 + 1((-3(3x^2 + 2x + 3) - 2)/(2(3x^2 + 2x + 3) - 1)) + 4) - 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": "4", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local minimum of the function f(x) = 1(1(-2|(-2|(3|x + 1| - 2) + 3|)| + 2)^2 + 4(-2|(-2|(3|x + 1| - 2) + 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": "-1", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the leftmost local maximum of the function f(x) = -1|(3(1e^(2(-5(-1|x + 1|) - 1)))^2 + 4(1e^(2(-5(-1|x + 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 rightmost local extremum of the function f(x) = 1((1(2(-1(-3sin(3\u03c0x + 3) + 3) + 5)^2 + 2(-1(-3sin(3\u03c0x + 3) + 3) + 5) - 1) + 2)/(-2(2(-1(-3sin(3\u03c0x + 3) + 3) + 5)^2 + 2(-1(-3sin(3\u03c0x + 3) + 3) + 5) - 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": "10", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the leftmost local extremum of the function f(x) = 1(-5(-1e^(2((1(-2|x|) + 3)/(-2(-2|x|) - 2))) - 2)^2 + 1(-1e^(2((1(-2|x|) + 3)/(-2(-2|x|) - 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 leftmost local maximum of the function f(x) = -3(-1|((-1((2(-2|x| + 2) + 3)/(-2(-2|x| + 2) + 3)) + 3)/(1((2(-2|x| + 2) + 3)/(-2(-2|x| + 2) + 3)) + 2)) - 2| + 3)^2 - 5(-1|((-1((2(-2|x| + 2) + 3)/(-2(-2|x| + 2) + 3)) + 3)/(1((2(-2|x| + 2) + 3)/(-2(-2|x| + 2) + 3)) + 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": "0", "dataset": "MATH"}
{"messages": [{"content": "Find the average of all x-coordinates of local minima of the function f(x) = 2sin(2\u03c0(-3(-4(-1(-3x^2 - 4x)^2 + 3(-3x^2 - 4x) + 5)^2 + 3)^2 + 1(-4(-1(-3x^2 - 4x)^2 + 3(-3x^2 - 4x) + 5)^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 x-coordinate of the local maximum of the function f(x) = -3(-3|(3|(-1e^(-1(1x - 1)) + 3) - 2| - 3) - 3|)^2 + 4(-3|(3|(-1e^(-1(1x - 1)) + 3) - 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": "0", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local minimum with the largest y-value of the function f(x) = 4(3|((3(2|(3x^2 + 1)| - 1))/(2(2|(3x^2 + 1)| - 1) - 1)) - 2| - 3)^2 + 1(3|((3(2|(3x^2 + 1)| - 1))/(2(2|(3x^2 + 1)| - 1) - 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": "0", "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(-2(3sin(1\u03c0x - 2) - 3)^2 - 3(3sin(1\u03c0x - 2) - 3) - 5) + 2)/(-3(-2(3sin(1\u03c0x - 2) - 3)^2 - 3(3sin(1\u03c0x - 2) - 3) - 5) - 3)) - 2)/(1((-1(-2(3sin(1\u03c0x - 2) - 3)^2 - 3(3sin(1\u03c0x - 2) - 3) - 5) + 2)/(-3(-2(3sin(1\u03c0x - 2) - 3)^2 - 3(3sin(1\u03c0x - 2) - 3) - 5) - 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 local extremum with the smallest y-value of the function f(x) = (-2(-3sin(2\u03c0(-3(1(1x + 1) - 5)^2 - 5(1(1x + 1) - 5) - 5) - 2) + 2) + 1)/(-1(-3sin(2\u03c0(-3(1(1x + 1) - 5)^2 - 5(1(1x + 1) - 5) - 5) - 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 average of all x-coordinates of local extrema of the function f(x) = 3sin(3\u03c0(-1(1|((-1(-1|x - 3| - 2) - 2)/(1(-1|x - 3| - 2) - 2)) - 2| - 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": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the leftmost local maximum of the function f(x) = (-2((1(3(-2(-2sin(2\u03c0x + 3))^2 - 2(-2sin(2\u03c0x + 3)) - 3)^2 - 2(-2(-2sin(2\u03c0x + 3))^2 - 2(-2sin(2\u03c0x + 3)) - 3) + 3))/(2(3(-2(-2sin(2\u03c0x + 3))^2 - 2(-2sin(2\u03c0x + 3)) - 3)^2 - 2(-2(-2sin(2\u03c0x + 3))^2 - 2(-2sin(2\u03c0x + 3)) - 3) + 3) + 3)) - 2)/(3((1(3(-2(-2sin(2\u03c0x + 3))^2 - 2(-2sin(2\u03c0x + 3)) - 3)^2 - 2(-2(-2sin(2\u03c0x + 3))^2 - 2(-2sin(2\u03c0x + 3)) - 3) + 3))/(2(3(-2(-2sin(2\u03c0x + 3))^2 - 2(-2sin(2\u03c0x + 3)) - 3)^2 - 2(-2(-2sin(2\u03c0x + 3))^2 - 2(-2sin(2\u03c0x + 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 local maximum with the smallest y-value of the function f(x) = 2|(-1|(3sin(1\u03c0(2|(-1x + 2) - 1| + 2) + 1)) - 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": "-10", "dataset": "MATH"}
{"messages": [{"content": "How many local extrema (both minima and maxima) does the function f(x) = 5(3(3(1(-2|x + 1| + 1) + 4)^2 + 5(1(-2|x + 1| + 1) + 4) - 2)^2 - 1(3(1(-2|x + 1| + 1) + 4)^2 + 5(1(-2|x + 1| + 1) + 4) - 2))^2 + 2(3(3(1(-2|x + 1| + 1) + 4)^2 + 5(1(-2|x + 1| + 1) + 4) - 2)^2 - 1(3(1(-2|x + 1| + 1) + 4)^2 + 5(1(-2|x + 1| + 1) + 4) - 2)) - 3 have in the interval [-10, 10]?\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(-1|(-1(-1|(2e^(1x) + 1) - 1| + 3)^2 - 3(-1|(2e^(1x) + 1) - 1| + 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": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local extremum of the function f(x) = 2((1(-1((2(2|x| + 2) - 3)/(3(2|x| + 2))) - 3) + 3)/(1(-1((2(2|x| + 2) - 3)/(3(2|x| + 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": "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(-2|(1|(-4x + 2) - 1|) - 1| - 3)^2 + 4(-2|(1|(-4x + 2) - 1|) - 1| - 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": "0", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local extremum of the function f(x) = 1|(-1|(-5(3|(1x - 1) - 1| + 1)^2 - 1(3|(1x - 1) - 1| + 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": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local extremum of the function f(x) = 1|((1((2(1|(3x^2 + 3x + 4) + 2| + 3) + 3)/(-3(1|(3x^2 + 3x + 4) + 2| + 3) - 1)) + 2)/(3((2(1|(3x^2 + 3x + 4) + 2| + 3) + 3)/(-3(1|(3x^2 + 3x + 4) + 2| + 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 local minimum of the function f(x) = 5((2(-5(-1((-1x - 3)/(-2x)) - 5)^2 - 2(-1((-1x - 3)/(-2x)) - 5) - 5) - 1)/(2(-5(-1((-1x - 3)/(-2x)) - 5)^2 - 2(-1((-1x - 3)/(-2x)) - 5) - 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": "0", "dataset": "MATH"}
{"messages": [{"content": "How many local minima does the function f(x) = 2(3|((3(-1(-1|x + 3| + 1)^2 + 4(-1|x + 3| + 1) - 2))/(1(-1(-1|x + 3| + 1)^2 + 4(-1|x + 3| + 1) - 2) + 2)) + 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(-2(1(-1|(2|x + 1| + 1) - 2| + 3) + 4)^2 + 4(1(-1|(2|x + 1| + 1) - 2| + 3) + 4) + 1)^2 - 4(-2(1(-1|(2|x + 1| + 1) - 2| + 3) + 4)^2 + 4(1(-1|(2|x + 1| + 1) - 2| + 3) + 4) + 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": "How many local minima does the function f(x) = -3(2|(4(-2|((-1x - 1)/(2x - 1)) + 3| - 2)^2 - 5(-2|((-1x - 1)/(2x - 1)) + 3| - 2) - 5) + 2|)^2 + 5(2|(4(-2|((-1x - 1)/(2x - 1)) + 3| - 2)^2 - 5(-2|((-1x - 1)/(2x - 1)) + 3| - 2) - 5) + 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 local maximum of the function f(x) = 1|((2(-1(-2e^(1(5x^2 + 2x + 2)) + 3) + 3) + 1)/(2(-1(-2e^(1(5x^2 + 2x + 2)) + 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 local maximum of the function f(x) = (-3(-1((-1(-2|(1|x - 2| - 1) - 2| + 3) - 2)/(2(-2|(1|x - 2| - 1) - 2| + 3) + 3)) + 1) + 1)/(-1(-1((-1(-2|(1|x - 2| - 1) - 2| + 3) - 2)/(2(-2|(1|x - 2| - 1) - 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": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the rightmost local maximum of the function f(x) = -2cos(2\u03c0(-1|(-1(1(3x^2 + 5x - 5)^2 + 4(3x^2 + 5x - 5) - 4)^2 + 2(1(3x^2 + 5x - 5)^2 + 4(3x^2 + 5x - 5) - 4) + 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": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local maximum of the function f(x) = -5(4(-1|((-1(-4x^2 + 4) + 2)/(3(-4x^2 + 4) + 1)) + 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": "0", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local extremum with the largest y-value of the function f(x) = -3(-4(-2|(3|(-2x^2 - 5x - 1) - 1|) + 1| + 2))^2 - 4(-4(-2|(3|(-2x^2 - 5x - 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": "-2", "dataset": "MATH"}
{"messages": [{"content": "How many local extrema (both minima and maxima) does the function f(x) = (1(3(1(-3((1x + 1)/(1x))^2 + 5((1x + 1)/(1x)) - 1)^2 - 1(-3((1x + 1)/(1x))^2 + 5((1x + 1)/(1x)) - 1) + 3) - 1) + 3)/(3(3(1(-3((1x + 1)/(1x))^2 + 5((1x + 1)/(1x)) - 1)^2 - 1(-3((1x + 1)/(1x))^2 + 5((1x + 1)/(1x)) - 1) + 3) - 1) + 2) have in the interval [-10, 10]?\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) = (-1(4(-2|(4((1x + 1)/(-2x + 3))^2 + 2((1x + 1)/(-2x + 3)) - 4) + 1| + 3)^2 + 3(-2|(4((1x + 1)/(-2x + 3))^2 + 2((1x + 1)/(-2x + 3)) - 4) + 1| + 3) - 1) - 1)/(3(4(-2|(4((1x + 1)/(-2x + 3))^2 + 2((1x + 1)/(-2x + 3)) - 4) + 1| + 3)^2 + 3(-2|(4((1x + 1)/(-2x + 3))^2 + 2((1x + 1)/(-2x + 3)) - 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": "3", "dataset": "MATH"}
{"messages": [{"content": "How many local minima does the function f(x) = 3(-1|(-2|(-2((1x - 3)/(-3x - 2))^2 + 5((1x - 3)/(-3x - 2)) - 5) - 1| + 1) - 3|) - 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 average of all x-coordinates of local extrema of the function f(x) = (3(-4(-2(1((-2x + 1)/(3x)) + 4)^2 - 2(1((-2x + 1)/(3x)) + 4)) + 5) + 2)/(-1(-4(-2(1((-2x + 1)/(3x)) + 4)^2 - 2(1((-2x + 1)/(3x)) + 4)) + 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 minima of the function f(x) = 4(-3e^(2(2|(5(-2x - 3)^2 + 1(-2x - 3) - 5) - 2| - 3)) - 2)^2 - 4(-3e^(2(2|(5(-2x - 3)^2 + 1(-2x - 3) - 5) - 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": "-2", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local maximum of the function f(x) = (2(3(-3e^(2((2(-1x - 2))/(-3(-1x - 2) + 1))) - 1)^2 - 4(-3e^(2((2(-1x - 2))/(-3(-1x - 2) + 1))) - 1) + 3) - 3)/(-3(3(-3e^(2((2(-1x - 2))/(-3(-1x - 2) + 1))) - 1)^2 - 4(-3e^(2((2(-1x - 2))/(-3(-1x - 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": "-2", "dataset": "MATH"}
{"messages": [{"content": "Find the average of all x-coordinates of local extrema of the function f(x) = 2|((-2((-2(3(-2sin(2\u03c0x - 3) - 1) + 2))/(3(3(-2sin(2\u03c0x - 3) - 1) + 2))))/(-3((-2(3(-2sin(2\u03c0x - 3) - 1) + 2))/(3(3(-2sin(2\u03c0x - 3) - 1) + 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": "0", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local minimum of the function f(x) = (1(-2((2(1e^(1((-2x + 3)/(-2x + 1))) + 3))/(-2(1e^(1((-2x + 3)/(-2x + 1))) + 3) - 1))^2 - 1((2(1e^(1((-2x + 3)/(-2x + 1))) + 3))/(-2(1e^(1((-2x + 3)/(-2x + 1))) + 3) - 1)) - 3) - 3)/(1(-2((2(1e^(1((-2x + 3)/(-2x + 1))) + 3))/(-2(1e^(1((-2x + 3)/(-2x + 1))) + 3) - 1))^2 - 1((2(1e^(1((-2x + 3)/(-2x + 1))) + 3))/(-2(1e^(1((-2x + 3)/(-2x + 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 average of all x-coordinates of local extrema of the function f(x) = -3|(-1|(-1|(3|(-1x^2 + 3) - 3| + 2)| + 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": "0", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the rightmost local extremum of the function f(x) = -2|(-1(1sin(1\u03c0((-2(-3x^2 + 2x + 1))/(-2(-3x^2 + 2x + 1) + 3)) - 1) + 2)^2 + 5(1sin(1\u03c0((-2(-3x^2 + 2x + 1))/(-2(-3x^2 + 2x + 1) + 3)) - 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": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local extremum with the largest y-value of the function f(x) = -3(-5(5(2|(1|x - 3| - 3)| - 1)^2 + 4(2|(1|x - 3| - 3)| - 1) + 5) + 4)^2 - 3(-5(5(2|(1|x - 3| - 3)| - 1)^2 + 4(2|(1|x - 3| - 3)| - 1) + 5) + 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": "0", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local extremum of the function f(x) = 5(-1|(2((1(-2x) + 2)/(-1(-2x) + 3))^2 - 4((1(-2x) + 2)/(-1(-2x) + 3)) + 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": "0", "dataset": "MATH"}
{"messages": [{"content": "How many local extrema (both minima and maxima) does the function f(x) = 3(2(-4(1sin(3\u03c0(-2|x + 1| - 2) + 3) + 1) + 3) - 2)^2 + 2(2(-4(1sin(3\u03c0(-2|x + 1| - 2) + 3) + 1) + 3) - 2) + 2 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 local minimum with the largest y-value of the function f(x) = 1|(-2(-5(2(-2|x| - 1) + 2)^2 - 1(2(-2|x| - 1) + 2) - 4) - 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 local extremum of the function f(x) = 3|(3e^(-1((-3(-1(1x^2 - 3x) - 3) - 1)/(-3(-1(1x^2 - 3x) - 3) + 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 minimum of the function f(x) = -1(2|((-3(-1e^(-2(-3|x + 1| + 3)) - 3) + 2)/(2(-1e^(-2(-3|x + 1| + 3)) - 3))) - 1| + 3)^2 - 4(2|((-3(-1e^(-2(-3|x + 1| + 3)) - 3) + 2)/(2(-1e^(-2(-3|x + 1| + 3)) - 3))) - 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": "How many local minima does the function f(x) = 2|((-3(-3(2(-3x^2 - 4)^2 - 1(-3x^2 - 4) - 3) - 1) - 1)/(3(-3(2(-3x^2 - 4)^2 - 1(-3x^2 - 4) - 3) - 1) + 2)) - 2| - 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 largest y-value of the function f(x) = 1((1(1sin(2\u03c0(-3(3|x| + 2) - 4) - 2)) + 1)/(-3(1sin(2\u03c0(-3(3|x| + 2) - 4) - 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) = -3sin(1\u03c0((2(3|((-2(-1x^2 - 5x + 2) + 1)/(-2(-1x^2 - 5x + 2) - 2)) - 3| - 3))/(-2(3|((-2(-1x^2 - 5x + 2) + 1)/(-2(-1x^2 - 5x + 2) - 2)) - 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": "-3", "dataset": "MATH"}
{"messages": [{"content": "How many local minima does the function f(x) = 4(-3|(2e^(1(-1((-1x - 2)/(-3x - 3))^2 - 1)) + 3)| - 3)^2 - 3(-3|(2e^(1(-1((-1x - 2)/(-3x - 3))^2 - 1)) + 3)| - 3) + 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": "How many local minima does the function f(x) = 2|(-1|(-1(-2((-2x)/(-3x - 2)) - 1)^2 - 3(-2((-2x)/(-3x - 2)) - 1) - 3) + 2| - 3)| - 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 maxima of the function f(x) = 2(2|(4((2(3|x + 3| - 2) + 2)/(2(3|x + 3| - 2) - 3))^2 - 1((2(3|x + 3| - 2) + 2)/(2(3|x + 3| - 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": "-3", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the rightmost local extremum of the function f(x) = 3(3|(2|(2(-1sin(1\u03c0x - 2) - 2)^2 + 1(-1sin(1\u03c0x - 2) - 2) - 4)| + 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": "9", "dataset": "MATH"}
{"messages": [{"content": "How many local maxima does the function f(x) = -3|((-1((-3(-3(-3|x| - 3) - 4) + 1)/(2(-3(-3|x| - 3) - 4) - 3)) + 1)/(1((-3(-3(-3|x| - 3) - 4) + 1)/(2(-3(-3|x| - 3) - 4) - 3)) + 3)) + 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": "How many local extrema (both minima and maxima) does the function f(x) = -5(1(4((1(-2|x - 1| - 3) - 3)/(1(-2|x - 1| - 3) + 1))^2 - 3((1(-2|x - 1| - 3) - 3)/(1(-2|x - 1| - 3) + 1)) - 4) - 1)^2 - 5(1(4((1(-2|x - 1| - 3) - 3)/(1(-2|x - 1| - 3) + 1))^2 - 3((1(-2|x - 1| - 3) - 3)/(1(-2|x - 1| - 3) + 1)) - 4) - 1) + 1 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 maximum with the smallest y-value of the function f(x) = 1|(-2(-2cos(3\u03c0(1|((-2x - 1)/(1x))| - 1) - 2) - 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": "0", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local extremum with the smallest y-value of the function f(x) = -3sin(1\u03c0(-2((-1(-3(-2x^2 + 2x + 5)^2 - 5(-2x^2 + 2x + 5)) - 3)/(-2(-3(-2x^2 + 2x + 5)^2 - 5(-2x^2 + 2x + 5)) + 3)) - 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": "-1", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local minimum with the smallest y-value of the function f(x) = (3(-1(3cos(3\u03c0(1|(4x^2 - 5x - 5) - 1| + 1) - 3) - 3)^2 - 4(3cos(3\u03c0(1|(4x^2 - 5x - 5) - 1| + 1) - 3) - 3) + 1) - 3)/(-3(-1(3cos(3\u03c0(1|(4x^2 - 5x - 5) - 1| + 1) - 3) - 3)^2 - 4(3cos(3\u03c0(1|(4x^2 - 5x - 5) - 1| + 1) - 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 minima of the function f(x) = 1(1(2sin(3\u03c0(3((2x + 3)/(1x + 2))^2 + 4((2x + 3)/(1x + 2)) + 2) + 1) - 3)^2 - 5(2sin(3\u03c0(3((2x + 3)/(1x + 2))^2 + 4((2x + 3)/(1x + 2)) + 2) + 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": "-2", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the rightmost local extremum of the function f(x) = 1(5(1|((-3(-5x - 5) + 1)/(3(-5x - 5) + 3)) - 1| - 1)^2 - 2(1|((-3(-5x - 5) + 1)/(3(-5x - 5) + 3)) - 1| - 1) - 2)^2 - 4(5(1|((-3(-5x - 5) + 1)/(3(-5x - 5) + 3)) - 1| - 1)^2 - 2(1|((-3(-5x - 5) + 1)/(3(-5x - 5) + 3)) - 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": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the average of all x-coordinates of local extrema of the function f(x) = -1|(-5(-1|(-2sin(2\u03c0(-4x) + 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": "0", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the rightmost local extremum of the function f(x) = (3((-3(-1|((-3(2x^2 - 3x - 5) - 3)/(1(2x^2 - 3x - 5) - 2)) - 2| + 2) + 3)/(-2(-1|((-3(2x^2 - 3x - 5) - 3)/(1(2x^2 - 3x - 5) - 2)) - 2| + 2) + 3)) + 1)/(-3((-3(-1|((-3(2x^2 - 3x - 5) - 3)/(1(2x^2 - 3x - 5) - 2)) - 2| + 2) + 3)/(-2(-1|((-3(2x^2 - 3x - 5) - 3)/(1(2x^2 - 3x - 5) - 2)) - 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 x-coordinate of the leftmost local maximum of the function f(x) = -4(-1(-3cos(3\u03c0(-4(-2|x + 3| - 1)^2 - 3(-2|x + 3| - 1) + 4) - 2) + 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": "-10", "dataset": "MATH"}
{"messages": [{"content": "How many local minima does the function f(x) = -1|(-3(2(-2e^(-2(-1|x - 2| + 3)) - 3) + 4)^2 - 2(2(-2e^(-2(-1|x - 2| + 3)) - 3) + 4) - 5)| 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((2(-2|(-3sin(3\u03c0(2x^2 - 4x - 5) + 2) - 2) + 2| + 1) + 2)/(-2(-2|(-3sin(3\u03c0(2x^2 - 4x - 5) + 2) - 2) + 2| + 1) - 1)) - 2)/(-3((2(-2|(-3sin(3\u03c0(2x^2 - 4x - 5) + 2) - 2) + 2| + 1) + 2)/(-2(-2|(-3sin(3\u03c0(2x^2 - 4x - 5) + 2) - 2) + 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": "-1", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the leftmost local maximum of the function f(x) = 5(-2|(-1(3(-4x^2 + 2x + 1)^2 - 3(-4x^2 + 2x + 1) - 3) + 5) - 3|)^2 - 3(-2|(-1(3(-4x^2 + 2x + 1)^2 - 3(-4x^2 + 2x + 1) - 3) + 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 rightmost local minimum of the function f(x) = -1|(1|(1(-4((-2x + 3)/(-2x - 1))^2 + 4((-2x + 3)/(-2x - 1)) + 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": "4", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local extremum with the smallest y-value of the function f(x) = (-2(-4((3(2sin(3\u03c0(3|x + 3| - 3) + 1)) - 2)/(1(2sin(3\u03c0(3|x + 3| - 3) + 1)) + 1)) + 3))/(-2(-4((3(2sin(3\u03c0(3|x + 3| - 3) + 1)) - 2)/(1(2sin(3\u03c0(3|x + 3| - 3) + 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 minimum with the largest y-value of the function f(x) = 1(1|((-1((2(1cos(3\u03c0x + 3) - 2) - 3)/(1(1cos(3\u03c0x + 3) - 2) + 1)) + 1)/(3((2(1cos(3\u03c0x + 3) - 2) - 3)/(1(1cos(3\u03c0x + 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 average of all x-coordinates of local maxima of the function f(x) = -3sin(3\u03c0(-2((-3(2|(1x - 2) - 2| - 1) + 3)/(2(2|(1x - 2) - 2| - 1) - 1)) - 5)) - 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((-2(1(5(-3|x - 2| + 2) + 3)^2 - 5(5(-3|x - 2| + 2) + 3) - 5) - 2)/(-3(1(5(-3|x - 2| + 2) + 3)^2 - 5(5(-3|x - 2| + 2) + 3) - 5) + 2))^2 - 4((-2(1(5(-3|x - 2| + 2) + 3)^2 - 5(5(-3|x - 2| + 2) + 3) - 5) - 2)/(-3(1(5(-3|x - 2| + 2) + 3)^2 - 5(5(-3|x - 2| + 2) + 3) - 5) + 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": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local extremum with the smallest y-value of the function f(x) = 3sin(2\u03c0(2|((-3(3|(-2x^2 - 1x + 2) + 3| - 2) + 3)/(2(3|(-2x^2 - 1x + 2) + 3| - 2))) + 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": "-2", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local minimum with the smallest y-value of the function f(x) = -5(5(-3(2sin(1\u03c0(-1|x - 1| - 2) - 3))^2 + 3(2sin(1\u03c0(-1|x - 1| - 2) - 3)) + 3)^2 + 2(-3(2sin(1\u03c0(-1|x - 1| - 2) - 3))^2 + 3(2sin(1\u03c0(-1|x - 1| - 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": "-9", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local extremum of the function f(x) = -2(-3(3e^(2((1(-4x^2 + 1x - 5) + 2)/(1(-4x^2 + 1x - 5) - 3)))) - 3)^2 + 5(-3(3e^(2((1(-4x^2 + 1x - 5) + 2)/(1(-4x^2 + 1x - 5) - 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": "How many local maxima does the function f(x) = -3(-2(-2((-1(-3|x + 2| + 2) + 2)/(3(-3|x + 2| + 2) - 1)) - 3)^2 + 1(-2((-1(-3|x + 2| + 2) + 2)/(3(-3|x + 2| + 2) - 1)) - 3) - 3) - 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": "How many local extrema (both minima and maxima) does the function f(x) = (2(3|(-5(5(3cos(2\u03c0x - 1)) + 2) + 1)| + 2) - 1)/(-3(3|(-5(5(3cos(2\u03c0x - 1)) + 2) + 1)| + 2)) 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 average of all x-coordinates of local extrema of the function f(x) = (-2(-5(-2|(-3sin(2\u03c0((-3x - 1)/(-3x + 2)) - 1) + 3)| - 3)^2 + 2(-2|(-3sin(2\u03c0((-3x - 1)/(-3x + 2)) - 1) + 3)| - 3) - 5) - 2)/(-1(-5(-2|(-3sin(2\u03c0((-3x - 1)/(-3x + 2)) - 1) + 3)| - 3)^2 + 2(-2|(-3sin(2\u03c0((-3x - 1)/(-3x + 2)) - 1) + 3)| - 3) - 5) - 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) = 2cos(2\u03c0(1(-3|(-5(-5x^2 - 2) - 3) + 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": "0", "dataset": "MATH"}
{"messages": [{"content": "How many local maxima does the function f(x) = -3|(-3|(-1|(3|(-2x^2 + 5x + 4) + 1| - 2) - 1| - 3) + 3| - 1) - 3| - 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 maximum with the smallest y-value of the function f(x) = (-2(1(2(1((1x + 3)/(3x + 1))^2 - 4((1x + 3)/(3x + 1)))^2 - 2(1((1x + 3)/(3x + 1))^2 - 4((1x + 3)/(3x + 1))) + 3) - 4) + 1)/(3(1(2(1((1x + 3)/(3x + 1))^2 - 4((1x + 3)/(3x + 1)))^2 - 2(1((1x + 3)/(3x + 1))^2 - 4((1x + 3)/(3x + 1))) + 3) - 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": "0", "dataset": "MATH"}
{"messages": [{"content": "How many local minima does the function f(x) = (2((3(-1((1(3|x - 1|) - 3)/(-1(3|x - 1|) - 1))^2 - 3((1(3|x - 1|) - 3)/(-1(3|x - 1|) - 1)) + 1) + 2)/(-3(-1((1(3|x - 1|) - 3)/(-1(3|x - 1|) - 1))^2 - 3((1(3|x - 1|) - 3)/(-1(3|x - 1|) - 1)) + 1) + 4)) + 3)/(1((3(-1((1(3|x - 1|) - 3)/(-1(3|x - 1|) - 1))^2 - 3((1(3|x - 1|) - 3)/(-1(3|x - 1|) - 1)) + 1) + 2)/(-3(-1((1(3|x - 1|) - 3)/(-1(3|x - 1|) - 1))^2 - 3((1(3|x - 1|) - 3)/(-1(3|x - 1|) - 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": "How many local minima does the function f(x) = (-3(2|(2((1(3|x - 2|) + 2)/(3(3|x - 2|) - 2)) + 5) + 3| - 2))/(-1(2|(2((1(3|x - 2|) + 2)/(3(3|x - 2|) - 2)) + 5) + 3| - 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 maxima of the function f(x) = (-1(4(-2sin(2\u03c0(2((1x + 3)/(-1x + 2)) + 5) - 3) - 2) - 3) - 1)/(3(4(-2sin(2\u03c0(2((1x + 3)/(-1x + 2)) + 5) - 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 extremum of the function f(x) = -3((2((-1(1(-5x + 2) + 1) - 2)/(-3(1(-5x + 2) + 1))))/(2((-1(1(-5x + 2) + 1) - 2)/(-3(1(-5x + 2) + 1))) - 1))^2 + 2((2((-1(1(-5x + 2) + 1) - 2)/(-3(1(-5x + 2) + 1))))/(2((-1(1(-5x + 2) + 1) - 2)/(-3(1(-5x + 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": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the average of all x-coordinates of local maxima of the function f(x) = (3(1(2|(-2|(2cos(1\u03c0x - 1) + 1) + 2| + 1) - 1| - 3)^2 + 5(2|(-2|(2cos(1\u03c0x - 1) + 1) + 2| + 1) - 1| - 3) - 5) - 1)/(1(1(2|(-2|(2cos(1\u03c0x - 1) + 1) + 2| + 1) - 1| - 3)^2 + 5(2|(-2|(2cos(1\u03c0x - 1) + 1) + 2| + 1) - 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": "-1", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local minimum with the largest y-value of the function f(x) = -2sin(3\u03c0(-3(5(-1|(-1x - 5) - 3| - 3)^2 + 3(-1|(-1x - 5) - 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": "-10", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the rightmost local minimum of the function f(x) = (3(-5(-4(-3|(1|x - 1| - 2) + 1| - 2)^2 + 1(-3|(1|x - 1| - 2) + 1| - 2) + 4)^2 - 2(-4(-3|(1|x - 1| - 2) + 1| - 2)^2 + 1(-3|(1|x - 1| - 2) + 1| - 2) + 4) + 4) + 3)/(-2(-5(-4(-3|(1|x - 1| - 2) + 1| - 2)^2 + 1(-3|(1|x - 1| - 2) + 1| - 2) + 4)^2 - 2(-4(-3|(1|x - 1| - 2) + 1| - 2)^2 + 1(-3|(1|x - 1| - 2) + 1| - 2) + 4) + 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": "9", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local minimum with the largest y-value of the function f(x) = (3((-3(1|(-4((-2x + 2)/(1x))^2 - 5((-2x + 2)/(1x)) + 1) + 3| + 3))/(-2(1|(-4((-2x + 2)/(1x))^2 - 5((-2x + 2)/(1x)) + 1) + 3| + 3) - 2)) - 3)/(-1((-3(1|(-4((-2x + 2)/(1x))^2 - 5((-2x + 2)/(1x)) + 1) + 3| + 3))/(-2(1|(-4((-2x + 2)/(1x))^2 - 5((-2x + 2)/(1x)) + 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": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the rightmost local maximum of the function f(x) = -1(2(-2sin(1\u03c0(-1|(2|x + 2| - 1)| + 1) + 3) + 3)^2 - 3(-2sin(1\u03c0(-1|(2|x + 2| - 1)| + 1) + 3) + 3) + 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": "9", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local maximum with the smallest y-value of the function f(x) = -5(-1((-2(1sin(1\u03c0(3x^2 - 4x - 3) + 3)) - 1)/(2(1sin(1\u03c0(3x^2 - 4x - 3) + 3)) - 3))^2 + 4((-2(1sin(1\u03c0(3x^2 - 4x - 3) + 3)) - 1)/(2(1sin(1\u03c0(3x^2 - 4x - 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": "1", "dataset": "MATH"}
{"messages": [{"content": "How many local minima does the function f(x) = 1|((-3(-2|(3|((2x - 1)/(3x)) - 3| - 3) + 3| + 1) + 2)/(2(-2|(3|((2x - 1)/(3x)) - 3| - 3) + 3| + 1) - 3)) - 3| + 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 rightmost local minimum of the function f(x) = -3(-3sin(3\u03c0(-1(-5(-2x + 4) - 1)^2 + 3(-5(-2x + 4) - 1) + 4) - 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": "9", "dataset": "MATH"}
{"messages": [{"content": "How many local extrema (both minima and maxima) does the function f(x) = 1(1|(-5(2sin(2\u03c0(-5x^2 - 3x) - 1) + 3) - 4) - 2| - 2) have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "502", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the leftmost local extremum of the function f(x) = -2|(-2|(-2(-2sin(1\u03c0(4x^2 - 2x - 2) - 1) + 3) + 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 leftmost local extremum of the function f(x) = (1(-5(1(-1(-2sin(1\u03c0x)) + 4)^2 - 3(-1(-2sin(1\u03c0x)) + 4) - 4)^2 + 1(1(-1(-2sin(1\u03c0x)) + 4)^2 - 3(-1(-2sin(1\u03c0x)) + 4) - 4) - 3) + 3)/(3(-5(1(-1(-2sin(1\u03c0x)) + 4)^2 - 3(-1(-2sin(1\u03c0x)) + 4) - 4)^2 + 1(1(-1(-2sin(1\u03c0x)) + 4)^2 - 3(-1(-2sin(1\u03c0x)) + 4) - 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": "-10", "dataset": "MATH"}
{"messages": [{"content": "Find the average of all x-coordinates of local extrema of the function f(x) = 2(-2cos(2\u03c0((1((-3(-3x^2 + 1x + 2) + 2)/(-2(-3x^2 + 1x + 2) - 3)) - 2)/(2((-3(-3x^2 + 1x + 2) + 2)/(-2(-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": "0", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the rightmost local maximum of the function f(x) = 3((1(-2(-3|((2x - 3)/(1x))| + 3)^2 - 5(-3|((2x - 3)/(1x))| + 3) - 5) + 1)/(-2(-2(-3|((2x - 3)/(1x))| + 3)^2 - 5(-3|((2x - 3)/(1x))| + 3) - 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": "5", "dataset": "MATH"}
{"messages": [{"content": "Find the average of all x-coordinates of local minima of the function f(x) = -2(2|(2(3|(2|x + 3| - 1) - 1|)^2 - 5(3|(2|x + 3| - 1) - 1|) + 1) - 3| + 1)^2 - 2(2|(2(3|(2|x + 3| - 1) - 1|)^2 - 5(3|(2|x + 3| - 1) - 1|) + 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": "-3", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local maximum with the largest y-value of the function f(x) = (-2(-3(2cos(1\u03c0(3(-3x - 5) - 1) + 2) + 1)^2 - 1) + 3)/(3(-3(2cos(1\u03c0(3(-3x - 5) - 1) + 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 minimum with the largest y-value of the function f(x) = 5(-2|(-4(-1e^(-2(-2|x + 2| + 3)) + 3) + 3) + 1| + 2)^2 + 5(-2|(-4(-1e^(-2(-2|x + 2| + 3)) + 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": "-4", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the leftmost local minimum of the function f(x) = -1|(-5(-5(-3sin(1\u03c0(3|x - 2|)))^2 - 1(-3sin(1\u03c0(3|x - 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": "-10", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local minimum of the function f(x) = 4(-2((-2((2(1|x + 3| - 3) + 3)/(-3(1|x + 3| - 3) + 1)) - 2)/(-1((2(1|x + 3| - 3) + 3)/(-3(1|x + 3| - 3) + 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": "-3", "dataset": "MATH"}
{"messages": [{"content": "How many local extrema (both minima and maxima) does the function f(x) = 1(-3cos(2\u03c0(2(-2|(-2|x - 2| - 3) - 1| - 2)^2 + 2(-2|(-2|x - 2| - 3) - 1| - 2) + 5)) - 1) - 4 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "439", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local maximum of the function f(x) = (-2(-1((-1(2|(1x^2 - 1x - 2) - 1| + 2) - 3)/(-3(2|(1x^2 - 1x - 2) - 1| + 2) + 1))^2 + 2((-1(2|(1x^2 - 1x - 2) - 1| + 2) - 3)/(-3(2|(1x^2 - 1x - 2) - 1| + 2) + 1)) - 3) - 1)/(-2(-1((-1(2|(1x^2 - 1x - 2) - 1| + 2) - 3)/(-3(2|(1x^2 - 1x - 2) - 1| + 2) + 1))^2 + 2((-1(2|(1x^2 - 1x - 2) - 1| + 2) - 3)/(-3(2|(1x^2 - 1x - 2) - 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 leftmost local maximum of the function f(x) = -3sin(2\u03c0(-2|(-4(1|((-3x - 3)/(2x + 3)) + 1| - 1)^2 + 1(1|((-3x - 3)/(2x + 3)) + 1| - 1) - 1) + 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": "-9", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the leftmost local maximum of the function f(x) = -3|(-3((3(-5(1cos(2\u03c0x))^2 + 1(1cos(2\u03c0x)) - 2) - 1)/(1(-5(1cos(2\u03c0x))^2 + 1(1cos(2\u03c0x)) - 2))) + 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": "-10", "dataset": "MATH"}
{"messages": [{"content": "Find the average of all x-coordinates of local maxima of the function f(x) = (-2((3(-2(1(-2|x + 1| - 1)) + 3))/(1(-2(1(-2|x + 1| - 1)) + 3))) - 2)/(-1((3(-2(1(-2|x + 1| - 1)) + 3))/(1(-2(1(-2|x + 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 leftmost local extremum of the function f(x) = (1(4((-2(1(1|x + 2| - 3) - 1) - 1)/(3(1(1|x + 2| - 3) - 1) + 1))^2 - 5((-2(1(1|x + 2| - 3) - 1) - 1)/(3(1(1|x + 2| - 3) - 1) + 1)) - 5) + 3)/(-2(4((-2(1(1|x + 2| - 3) - 1) - 1)/(3(1(1|x + 2| - 3) - 1) + 1))^2 - 5((-2(1(1|x + 2| - 3) - 1) - 1)/(3(1(1|x + 2| - 3) - 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": "-6", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local maximum with the smallest y-value of the function f(x) = -2(1(5(-1cos(1\u03c0((-3x + 3)/(1x)) + 2)) + 3)^2 - 5(5(-1cos(1\u03c0((-3x + 3)/(1x)) + 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": "-3", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local maximum with the smallest y-value of the function f(x) = 2cos(1\u03c0(5(1(-2|((1x)/(1x + 1)) + 2| - 3) + 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": "-6", "dataset": "MATH"}
{"messages": [{"content": "Find the average of all x-coordinates of local extrema of the function f(x) = -1(1(3|(-5((2x + 1)/(3x + 3))^2 + 1((2x + 1)/(3x + 3)) + 2) + 2| + 1) - 2)^2 + 5(1(3|(-5((2x + 1)/(3x + 3))^2 + 1((2x + 1)/(3x + 3)) + 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": "-2", "dataset": "MATH"}
{"messages": [{"content": "How many local maxima does the function f(x) = -3|(-2|(1(2cos(3\u03c0(3x + 1)) - 3) + 1) + 2| + 3) - 3| - 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": "How many local extrema (both minima and maxima) does the function f(x) = -2cos(3\u03c0((1(-1|(-1((1x)/(3x + 3)) + 4) + 2|) - 1)/(-2(-1|(-1((1x)/(3x + 3)) + 4) + 2|) - 3)) + 2) + 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 minimum with the largest y-value of the function f(x) = 1((1(-5(1sin(3\u03c0((-3x - 1)/(-1x + 3)))) + 1) - 2)/(-3(-5(1sin(3\u03c0((-3x - 1)/(-1x + 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": "-6", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the leftmost local maximum of the function f(x) = 2|(2|(3|(2|(-1x^2 - 4x + 1) - 3| - 1) - 1| + 2) + 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": "How many local extrema (both minima and maxima) does the function f(x) = 1cos(3\u03c0(-3|(-1|(1(4x - 3) + 5) + 3|) + 2| - 3) + 1) - 3 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "719", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the rightmost local maximum of the function f(x) = 2|(3(3cos(2\u03c0(-3(4x^2 + 1x + 3) + 5) + 3) - 1)^2 - 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": "How many local minima does the function f(x) = (3((-3(-2(-3(3x^2 - 5x + 3) - 5) + 4))/(-3(-2(-3(3x^2 - 5x + 3) - 5) + 4) + 2)) + 3)/(-2((-3(-2(-3(3x^2 - 5x + 3) - 5) + 4))/(-3(-2(-3(3x^2 - 5x + 3) - 5) + 4) + 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 of the function f(x) = -3|(3|((-1(5(4x^2 + 1x + 5)^2 - 3(4x^2 + 1x + 5) + 5) - 1)/(1(5(4x^2 + 1x + 5)^2 - 3(4x^2 + 1x + 5) + 5) + 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": "0", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local extremum of the function f(x) = -3(1|(-3|(4(-2x + 1)^2 - 5(-2x + 1) + 4) + 2| - 2) + 2| - 3)^2 + 3(1|(-3|(4(-2x + 1)^2 - 5(-2x + 1) + 4) + 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": "0", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local extremum with the largest y-value of the function f(x) = -2(-1((3(-4(-1|x - 1| + 3) + 3))/(3(-4(-1|x - 1| + 3) + 3) - 1))^2 + 5((3(-4(-1|x - 1| + 3) + 3))/(3(-4(-1|x - 1| + 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": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the leftmost local extremum of the function f(x) = (2(-2(-2(2sin(2\u03c0(1|x + 1| - 1)) - 2) - 3)^2 + 1(-2(2sin(2\u03c0(1|x + 1| - 1)) - 2) - 3) - 5) + 3)/(2(-2(-2(2sin(2\u03c0(1|x + 1| - 1)) - 2) - 3)^2 + 1(-2(2sin(2\u03c0(1|x + 1| - 1)) - 2) - 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 rightmost local extremum of the function f(x) = -2|(1|(-3(2|(3cos(3\u03c0x - 2) - 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": "10", "dataset": "MATH"}
{"messages": [{"content": "How many local extrema (both minima and maxima) does the function f(x) = -2|((3(-1cos(3\u03c0(-1|(4x + 4) + 2| - 1) + 2) + 1) + 2)/(1(-1cos(3\u03c0(-1|(4x + 4) + 2| - 1) + 2) + 1) - 2)) + 1| + 3 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "239", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local minimum of the function f(x) = 1|(-5(-1((-3((-1x - 1)/(3x)) - 1)/(-3((-1x - 1)/(3x)) - 2))^2 + 3((-3((-1x - 1)/(3x)) - 1)/(-3((-1x - 1)/(3x)) - 2)) - 3)^2 + 3(-1((-3((-1x - 1)/(3x)) - 1)/(-3((-1x - 1)/(3x)) - 2))^2 + 3((-3((-1x - 1)/(3x)) - 1)/(-3((-1x - 1)/(3x)) - 2)) - 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": "0", "dataset": "MATH"}
{"messages": [{"content": "How many local extrema (both minima and maxima) does the function f(x) = 2|(2|(-1((-2(-3x - 3) - 3)/(-3(-3x - 3) - 3))^2 - 1((-2(-3x - 3) - 3)/(-3(-3x - 3) - 3)) - 5) - 2| + 2) + 2| + 3 have in the interval [-10, 10]?\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 maximum of the function f(x) = 2|(1cos(2\u03c0(-2|(-4(-2x - 1) - 5) - 1| + 3) - 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": "How many local minima does the function f(x) = 5(-3|((2(-2|(3e^(1x) - 1) - 2| + 3) + 2)/(-2(-2|(3e^(1x) - 1) - 2| + 3) - 1)) + 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": "How many local maxima does the function f(x) = 2|(1|(-1sin(3\u03c0((1((2x + 1)/(3x - 2)) - 1)/(1((2x + 1)/(3x - 2)) + 1)) + 3) + 3) - 3| - 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 local maximum with the smallest y-value of the function f(x) = -5(1(2((-2(-3cos(3\u03c0x - 2) - 1) - 3)/(2(-3cos(3\u03c0x - 2) - 1) - 1))^2 + 5((-2(-3cos(3\u03c0x - 2) - 1) - 3)/(2(-3cos(3\u03c0x - 2) - 1) - 1)) + 4) - 4)^2 - 5(1(2((-2(-3cos(3\u03c0x - 2) - 1) - 3)/(2(-3cos(3\u03c0x - 2) - 1) - 1))^2 + 5((-2(-3cos(3\u03c0x - 2) - 1) - 3)/(2(-3cos(3\u03c0x - 2) - 1) - 1)) + 4) - 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": "-10", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local minimum with the smallest y-value of the function f(x) = -5(2(-3cos(3\u03c0(2((-1x - 3)/(-3x + 2))^2 + 1((-1x - 3)/(-3x + 2))) - 3) + 3) + 5)^2 + 3(2(-3cos(3\u03c0(2((-1x - 3)/(-3x + 2))^2 + 1((-1x - 3)/(-3x + 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 extremum with the largest y-value of the function f(x) = 4(-3|((-2(4(2|x + 1| - 2)^2 + 5(2|x + 1| - 2) - 4) + 2)/(2(4(2|x + 1| - 2)^2 + 5(2|x + 1| - 2) - 4) - 3)) + 1| - 3)^2 - 2(-3|((-2(4(2|x + 1| - 2)^2 + 5(2|x + 1| - 2) - 4) + 2)/(2(4(2|x + 1| - 2)^2 + 5(2|x + 1| - 2) - 4) - 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": "-1", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local maximum with the largest y-value of the function f(x) = -2(-1|((2(4(-1|x - 2|)^2 - 2(-1|x - 2|) - 2) - 2)/(-1(4(-1|x - 2|)^2 - 2(-1|x - 2|) - 2) + 2)) + 2| - 3)^2 + 4(-1|((2(4(-1|x - 2|)^2 - 2(-1|x - 2|) - 2) - 2)/(-1(4(-1|x - 2|)^2 - 2(-1|x - 2|) - 2) + 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": "2", "dataset": "MATH"}
{"messages": [{"content": "How many local extrema (both minima and maxima) does the function f(x) = (2(-3e^(-2(4(3((-3x + 1)/(2x + 1))^2 + 2((-3x + 1)/(2x + 1)) - 5) - 3)) + 1) + 1)/(-3(-3e^(-2(4(3((-3x + 1)/(2x + 1))^2 + 2((-3x + 1)/(2x + 1)) - 5) - 3)) + 1) + 1) 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 local minimum of the function f(x) = (-1(3(-4(1((2x + 3)/(-2x + 3)) + 1)^2 - 4(1((2x + 3)/(-2x + 3)) + 1))^2 - 1(-4(1((2x + 3)/(-2x + 3)) + 1)^2 - 4(1((2x + 3)/(-2x + 3)) + 1)) + 3) + 1)/(-3(3(-4(1((2x + 3)/(-2x + 3)) + 1)^2 - 4(1((2x + 3)/(-2x + 3)) + 1))^2 - 1(-4(1((2x + 3)/(-2x + 3)) + 1)^2 - 4(1((2x + 3)/(-2x + 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": "5", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the leftmost local extremum of the function f(x) = (-1(-3(3|(-2|(-4x^2 + 4x + 5) + 1|) - 2| + 2)^2 - 3(3|(-2|(-4x^2 + 4x + 5) + 1|) - 2| + 2) - 5) - 2)/(1(-3(3|(-2|(-4x^2 + 4x + 5) + 1|) - 2| + 2)^2 - 3(3|(-2|(-4x^2 + 4x + 5) + 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": "0", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local maximum of the function f(x) = 2(1(-1(1((-2x - 3)/(-2x + 3))^2 - 4((-2x - 3)/(-2x + 3)) + 3)^2 - 5(1((-2x - 3)/(-2x + 3))^2 - 4((-2x - 3)/(-2x + 3)) + 3) - 3) + 3)^2 - 5(1(-1(1((-2x - 3)/(-2x + 3))^2 - 4((-2x - 3)/(-2x + 3)) + 3)^2 - 5(1((-2x - 3)/(-2x + 3))^2 - 4((-2x - 3)/(-2x + 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": "4", "dataset": "MATH"}
{"messages": [{"content": "How many local minima does the function f(x) = -2|(-3|(1e^(-2(4(-3|x - 3| - 2) - 5)) - 2) - 3| + 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 local minimum of the function f(x) = -3((-3(1|(2((-1x - 2)/(2x - 1))^2 + 4) + 2| + 3) + 1)/(2(1|(2((-1x - 2)/(2x - 1))^2 + 4) + 2| + 3) + 3))^2 + 1((-3(1|(2((-1x - 2)/(2x - 1))^2 + 4) + 2| + 3) + 1)/(2(1|(2((-1x - 2)/(2x - 1))^2 + 4) + 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": "0", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local extremum with the largest y-value of the function f(x) = 3((-2(-1(2|(3|x| - 1) + 1| - 1)^2 + 5(2|(3|x| - 1) + 1| - 1) + 4) - 3)/(-1(-1(2|(3|x| - 1) + 1| - 1)^2 + 5(2|(3|x| - 1) + 1| - 1) + 4) - 1))^2 + 4((-2(-1(2|(3|x| - 1) + 1| - 1)^2 + 5(2|(3|x| - 1) + 1| - 1) + 4) - 3)/(-1(-1(2|(3|x| - 1) + 1| - 1)^2 + 5(2|(3|x| - 1) + 1| - 1) + 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": "-1", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local maximum of the function f(x) = -1((2(1((-3(5x + 3) + 2)/(1(5x + 3) + 1))) - 1)/(1(1((-3(5x + 3) + 2)/(1(5x + 3) + 1))) - 2))^2 - 1((2(1((-3(5x + 3) + 2)/(1(5x + 3) + 1))) - 1)/(1(1((-3(5x + 3) + 2)/(1(5x + 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 average of all x-coordinates of local maxima of the function f(x) = 1(-2(1((1(-2|x + 3|))/(-3(-2|x + 3|) - 1))^2 + 1((1(-2|x + 3|))/(-3(-2|x + 3|) - 1)) - 5)^2 + 1(1((1(-2|x + 3|))/(-3(-2|x + 3|) - 1))^2 + 1((1(-2|x + 3|))/(-3(-2|x + 3|) - 1)) - 5) - 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 leftmost local extremum of the function f(x) = -3|(1|(-4((-2(-1|x - 3|) - 2)/(-2(-1|x - 3|) - 1))) + 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": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the rightmost local minimum of the function f(x) = -1|(-3cos(2\u03c0(1|(-5((3x - 3)/(-1x)))| + 1) - 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 average of all x-coordinates of local extrema of the function f(x) = (2(-2|(1(-2(3e^(1x) + 1)^2 + 1(3e^(1x) + 1))^2 - 4(-2(3e^(1x) + 1)^2 + 1(3e^(1x) + 1)) + 3) + 2| - 1) + 1)/(1(-2|(1(-2(3e^(1x) + 1)^2 + 1(3e^(1x) + 1))^2 - 4(-2(3e^(1x) + 1)^2 + 1(3e^(1x) + 1)) + 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": "6", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the rightmost local extremum of the function f(x) = -5(-1|((3(-2(-5x - 3)^2 + 2(-5x - 3) + 2) + 2)/(-3(-2(-5x - 3)^2 + 2(-5x - 3) + 2) + 1)) + 2| + 3)^2 + 5(-1|((3(-2(-5x - 3)^2 + 2(-5x - 3) + 2) + 2)/(-3(-2(-5x - 3)^2 + 2(-5x - 3) + 2) + 1)) + 2| + 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 x-coordinate of the local maximum with the largest y-value of the function f(x) = 1|(5(2|(-3(-2sin(1\u03c0x - 2) + 3) + 4)| - 2)^2 - 3(2|(-3(-2sin(1\u03c0x - 2) + 3) + 4)| - 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 rightmost local minimum of the function f(x) = (2(-3(4(2sin(2\u03c0(3|x + 2| + 3) + 1) + 3) + 5)^2 - 1(4(2sin(2\u03c0(3|x + 2| + 3) + 1) + 3) + 5) - 3) - 2)/(1(-3(4(2sin(2\u03c0(3|x + 2| + 3) + 1) + 3) + 5)^2 - 1(4(2sin(2\u03c0(3|x + 2| + 3) + 1) + 3) + 5) - 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 largest y-value of the function f(x) = (-3((-2(2cos(3\u03c0(-1|(-5x + 2)| + 1) + 1) - 3) + 1)/(-2(2cos(3\u03c0(-1|(-5x + 2)| + 1) + 1) - 3) - 3)) - 3)/(2((-2(2cos(3\u03c0(-1|(-5x + 2)| + 1) + 1) - 3) + 1)/(-2(2cos(3\u03c0(-1|(-5x + 2)| + 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": "-10", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the leftmost local maximum of the function f(x) = (1((-2((-2(2sin(1\u03c0(-2|x|) - 2) - 3))/(1(2sin(1\u03c0(-2|x|) - 2) - 3) + 2)) + 3)/(-2((-2(2sin(1\u03c0(-2|x|) - 2) - 3))/(1(2sin(1\u03c0(-2|x|) - 2) - 3) + 2)) - 2)) - 1)/(-3((-2((-2(2sin(1\u03c0(-2|x|) - 2) - 3))/(1(2sin(1\u03c0(-2|x|) - 2) - 3) + 2)) + 3)/(-2((-2(2sin(1\u03c0(-2|x|) - 2) - 3))/(1(2sin(1\u03c0(-2|x|) - 2) - 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": "-9", "dataset": "MATH"}
{"messages": [{"content": "How many local maxima does the function f(x) = (3(3|(-5(-2|(1x^2 + 2x + 1) + 1| + 1) + 1) + 2| - 3) - 3)/(-2(3|(-5(-2|(1x^2 + 2x + 1) + 1| + 1) + 1) + 2| - 3) + 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": "How many local extrema (both minima and maxima) does the function f(x) = -3|(5(-1|(4(2e^(-2x) - 1)^2 + 2(2e^(-2x) - 1) - 1) - 1|)^2 + 4(-1|(4(2e^(-2x) - 1)^2 + 2(2e^(-2x) - 1) - 1) - 1|) - 2) - 1| - 2 have in the interval [-10, 10]?\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(1|(1((-2((-1x + 1)/(2x + 1)) + 1)/(2((-1x + 1)/(2x + 1)) + 1))^2 - 5((-2((-1x + 1)/(2x + 1)) + 1)/(2((-1x + 1)/(2x + 1)) + 1)) - 1) - 2| + 3) - 2)/(-2(1|(1((-2((-1x + 1)/(2x + 1)) + 1)/(2((-1x + 1)/(2x + 1)) + 1))^2 - 5((-2((-1x + 1)/(2x + 1)) + 1)/(2((-1x + 1)/(2x + 1)) + 1)) - 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": "Find the average of all x-coordinates of local extrema of the function f(x) = -3(2|(5(2|(-2cos(2\u03c0x - 3) - 3) + 3| - 2)^2 + 2(2|(-2cos(2\u03c0x - 3) - 3) + 3| - 2) + 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": "0", "dataset": "MATH"}
{"messages": [{"content": "How many local minima does the function f(x) = -1|((-1(5(3(5x) + 1)^2 + 2(3(5x) + 1) + 4) + 1)/(3(5(3(5x) + 1)^2 + 2(3(5x) + 1) + 4) + 3)) - 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 local maximum with the largest y-value of the function f(x) = 1(-2|(-2e^(1(-5(-4x^2 - 5x + 3)^2 + 4(-4x^2 - 5x + 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": "-2", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local maximum with the smallest y-value of the function f(x) = -4(-1|(-1|(1(2x^2 + 5x + 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": "-1", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local maximum of the function f(x) = 1(-3|(-1|((-1(1x^2 + 3x + 2) + 1)/(3(1x^2 + 3x + 2) + 3)) + 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": "-2", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local extremum with the smallest y-value of the function f(x) = -2(-5(4(-4((-1x + 3)/(-1x - 1))^2 + 3((-1x + 3)/(-1x - 1)) + 4)^2 + 2(-4((-1x + 3)/(-1x - 1))^2 + 3((-1x + 3)/(-1x - 1)) + 4) - 1)^2 - 3(4(-4((-1x + 3)/(-1x - 1))^2 + 3((-1x + 3)/(-1x - 1)) + 4)^2 + 2(-4((-1x + 3)/(-1x - 1))^2 + 3((-1x + 3)/(-1x - 1)) + 4) - 1) - 2)^2 + 3(-5(4(-4((-1x + 3)/(-1x - 1))^2 + 3((-1x + 3)/(-1x - 1)) + 4)^2 + 2(-4((-1x + 3)/(-1x - 1))^2 + 3((-1x + 3)/(-1x - 1)) + 4) - 1)^2 - 3(4(-4((-1x + 3)/(-1x - 1))^2 + 3((-1x + 3)/(-1x - 1)) + 4)^2 + 2(-4((-1x + 3)/(-1x - 1))^2 + 3((-1x + 3)/(-1x - 1)) + 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": "-9", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local extremum of the function f(x) = -2(-1((-2(-3e^(-1(2|x + 3|))) - 3)/(1(-3e^(-1(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": "-3", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the leftmost local extremum of the function f(x) = -1(-1(-3|(2|((2x - 3)/(1x + 1)) - 1| - 2) - 1| + 3)^2 - 4(-3|(2|((2x - 3)/(1x + 1)) - 1| - 2) - 1| + 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": "-5", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the leftmost local maximum of the function f(x) = -2(-1cos(2\u03c0(3(1(-1|x - 3| + 3)^2 + 2(-1|x - 3| + 3) - 1)^2 - 5(1(-1|x - 3| + 3)^2 + 2(-1|x - 3| + 3) - 1) + 4) + 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 local minimum with the largest y-value of the function f(x) = (-3(-3|((2(-1|(-5x^2 - 3x + 4) + 1| - 2) + 3)/(3(-1|(-5x^2 - 3x + 4) + 1| - 2) + 3)) - 3| - 2) - 1)/(1(-3|((2(-1|(-5x^2 - 3x + 4) + 1| - 2) + 3)/(3(-1|(-5x^2 - 3x + 4) + 1| - 2) + 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 of the function f(x) = (2((-3(-3((2(-4x^2 + 3x + 1) - 1)/(2(-4x^2 + 3x + 1) + 1)) - 2) + 1)/(1(-3((2(-4x^2 + 3x + 1) - 1)/(2(-4x^2 + 3x + 1) + 1)) - 2) + 3)) - 2)/(3((-3(-3((2(-4x^2 + 3x + 1) - 1)/(2(-4x^2 + 3x + 1) + 1)) - 2) + 1)/(1(-3((2(-4x^2 + 3x + 1) - 1)/(2(-4x^2 + 3x + 1) + 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": "0", "dataset": "MATH"}
{"messages": [{"content": "How many local maxima does the function f(x) = 2|(2|((-3((3(-3x^2 - 2x + 5) - 2)/(-2(-3x^2 - 2x + 5))) + 2)/(2((3(-3x^2 - 2x + 5) - 2)/(-2(-3x^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": "0", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the leftmost local extremum of the function f(x) = -4(2|(3|(-3cos(2\u03c0((-3x + 3)/(-1x + 2))) - 2) - 1| - 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": "-4", "dataset": "MATH"}
{"messages": [{"content": "Find the average of all x-coordinates of local extrema of the function f(x) = -4((-1(-2|((1(1|x - 3| - 1) - 1)/(-2(1|x - 3| - 1))) + 2| - 2) - 2)/(2(-2|((1(1|x - 3| - 1) - 1)/(-2(1|x - 3| - 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": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local maximum with the smallest y-value of the function f(x) = -2|((2(-1|(3sin(2\u03c0((-3x + 2)/(3x + 3)) - 1) + 3) - 3| + 3) + 1)/(2(-1|(3sin(2\u03c0((-3x + 2)/(3x + 3)) - 1) + 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": "-6", "dataset": "MATH"}
{"messages": [{"content": "How many local extrema (both minima and maxima) does the function f(x) = 3(-3|(-1(1((-3x + 2)/(3x))^2 + 2((-3x + 2)/(3x)))^2 + 4(1((-3x + 2)/(3x))^2 + 2((-3x + 2)/(3x))) + 3) - 3| + 3) + 3 have in the interval [-10, 10]?\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) = -2|((3(-1|(-2cos(3\u03c0((-1x + 1)/(-3x - 1)) + 1) - 1) - 1| + 1) + 2)/(2(-1|(-2cos(3\u03c0((-1x + 1)/(-3x - 1)) + 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": "4", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the leftmost local extremum of the function f(x) = 1sin(3\u03c0(2|(-3(3|(2|x + 3| + 1) - 1| - 3) + 4) - 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 extrema (both minima and maxima) does the function f(x) = (-1(-1sin(3\u03c0(4((3(4x - 5) - 3)/(-3(4x - 5)))^2 - 3((3(4x - 5) - 3)/(-3(4x - 5))) - 2) + 1) - 2) - 2)/(-1(-1sin(3\u03c0(4((3(4x - 5) - 3)/(-3(4x - 5)))^2 - 3((3(4x - 5) - 3)/(-3(4x - 5))) - 2) + 1) - 2) + 2) 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 maximum of the function f(x) = -1|(-2((2(1(2|x + 1| - 3)^2 + 2(2|x + 1| - 3)) + 3)/(1(1(2|x + 1| - 3)^2 + 2(2|x + 1| - 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": "-2", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the leftmost local maximum of the function f(x) = -5(-1|(-4(5((3x - 2)/(3x + 3)) - 2)) + 1| + 2)^2 + 5(-1|(-4(5((3x - 2)/(3x + 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": "2", "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((3(2|(-3(2|x - 2| - 3) - 2) - 3| - 1) - 3)/(-2(2|(-3(2|x - 2| - 3) - 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": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local extremum with the smallest y-value of the function f(x) = (-2(2((-1(-1|(-1x^2 - 5x - 4) + 2| + 1))/(-2(-1|(-1x^2 - 5x - 4) + 2| + 1) + 3))^2 + 3((-1(-1|(-1x^2 - 5x - 4) + 2| + 1))/(-2(-1|(-1x^2 - 5x - 4) + 2| + 1) + 3)) + 5) + 3)/(-3(2((-1(-1|(-1x^2 - 5x - 4) + 2| + 1))/(-2(-1|(-1x^2 - 5x - 4) + 2| + 1) + 3))^2 + 3((-1(-1|(-1x^2 - 5x - 4) + 2| + 1))/(-2(-1|(-1x^2 - 5x - 4) + 2| + 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": "-5", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the leftmost local maximum of the function f(x) = (-1((2(3(5(-1cos(3\u03c0x - 3) - 1)^2 + 4(-1cos(3\u03c0x - 3) - 1)) - 1) - 3)/(2(3(5(-1cos(3\u03c0x - 3) - 1)^2 + 4(-1cos(3\u03c0x - 3) - 1)) - 1))) + 2)/(1((2(3(5(-1cos(3\u03c0x - 3) - 1)^2 + 4(-1cos(3\u03c0x - 3) - 1)) - 1) - 3)/(2(3(5(-1cos(3\u03c0x - 3) - 1)^2 + 4(-1cos(3\u03c0x - 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": "-10", "dataset": "MATH"}
{"messages": [{"content": "How many local minima does the function f(x) = 1|(-3((2(2(3x^2 - 2x + 2)^2 - 1(3x^2 - 2x + 2) - 5) - 2)/(1(2(3x^2 - 2x + 2)^2 - 1(3x^2 - 2x + 2) - 5) + 3)) + 3) - 2| + 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) = 2|(1(3((2(2sin(1\u03c0x + 1) + 2) + 1)/(-1(2sin(1\u03c0x + 1) + 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": "-9", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the rightmost local extremum of the function f(x) = -3((3((-2(1(-2|x + 1| + 2)^2 - 2(-2|x + 1| + 2) - 1) + 3)/(-3(1(-2|x + 1| + 2)^2 - 2(-2|x + 1| + 2) - 1) - 2)) + 3)/(3((-2(1(-2|x + 1| + 2)^2 - 2(-2|x + 1| + 2) - 1) + 3)/(-3(1(-2|x + 1| + 2)^2 - 2(-2|x + 1| + 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": "0", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local maximum of the function f(x) = -2|(4(5(3e^(1((-1x - 3)/(1x + 1))) + 1)^2)^2 - 3(5(3e^(1((-1x - 3)/(1x + 1))) + 1)^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": "-1", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the leftmost local minimum of the function f(x) = 1(2(-1((-1(-3x - 5) - 3)/(1(-3x - 5)))^2 - 2((-1(-3x - 5) - 3)/(1(-3x - 5))) + 2)^2 + 5(-1((-1(-3x - 5) - 3)/(1(-3x - 5)))^2 - 2((-1(-3x - 5) - 3)/(1(-3x - 5))) + 2) + 1)^2 - 4(2(-1((-1(-3x - 5) - 3)/(1(-3x - 5)))^2 - 2((-1(-3x - 5) - 3)/(1(-3x - 5))) + 2)^2 + 5(-1((-1(-3x - 5) - 3)/(1(-3x - 5)))^2 - 2((-1(-3x - 5) - 3)/(1(-3x - 5))) + 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 maxima does the function f(x) = 1(-3|((1(-3|(3x^2 + 2x - 2) + 1| - 2) - 3)/(-1(-3|(3x^2 + 2x - 2) + 1| - 2) - 3)) + 1| - 2)^2 + 2(-3|((1(-3|(3x^2 + 2x - 2) + 1| - 2) - 3)/(-1(-3|(3x^2 + 2x - 2) + 1| - 2) - 3)) + 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 local minimum of the function f(x) = -2e^(1(1((2(-5(3x^2 + 2x - 4) + 4))/(2(-5(3x^2 + 2x - 4) + 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": "How many local minima does the function f(x) = -2|(-2((-3(-2|((3x + 1)/(2x - 1)) - 3| + 2) - 1)/(-1(-2|((3x + 1)/(2x - 1)) - 3| + 2) - 2)) - 5) + 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) = (-3(-1|((-1(-3(2sin(1\u03c0x + 2) - 1) - 3) + 2)/(-3(-3(2sin(1\u03c0x + 2) - 1) - 3) - 3)) - 3| - 2))/(2(-1|((-1(-3(2sin(1\u03c0x + 2) - 1) - 3) + 2)/(-3(-3(2sin(1\u03c0x + 2) - 1) - 3) - 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": "-8", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the rightmost local extremum of the function f(x) = -3|(-2|(-2cos(1\u03c0((-2(1x^2 + 1x - 2) + 3)/(2(1x^2 + 1x - 2) + 1)) - 2) + 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": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the rightmost local maximum of the function f(x) = -2(3e^(-2(4(-3|(-3x + 5) + 3| + 2) - 5)) - 3)^2 - 1(3e^(-2(4(-3|(-3x + 5) + 3| + 2) - 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": "4", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local maximum with the largest y-value of the function f(x) = 3e^(1(-1|(-3(-2|(-1x + 3) - 3| - 2)^2 - 2(-2|(-1x + 3) - 3| - 2) + 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": "0", "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((-2(-1sin(2\u03c0x + 1)) - 2)/(-1(-1sin(2\u03c0x + 1)) + 2)))/(-1((-2(-1sin(2\u03c0x + 1)) - 2)/(-1(-1sin(2\u03c0x + 1)) + 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) = -1((-2(-2|(-2(-2|x - 1|)) + 1| + 2))/(1(-2|(-2(-2|x - 1|)) + 1| + 2) + 3))^2 - 1((-2(-2|(-2(-2|x - 1|)) + 1| + 2))/(1(-2|(-2(-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": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local maximum with the largest y-value of the function f(x) = -1(1cos(1\u03c0(1|(-4(1x - 1) - 1) + 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 local minimum with the smallest y-value of the function f(x) = 1(-2|(3cos(2\u03c0(-1|(-2x - 3) + 2| + 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": "-10", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local extremum of the function f(x) = -2|(2|(1(1|((-2x + 2)/(-1x)) + 1| + 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": "0", "dataset": "MATH"}
{"messages": [{"content": "Find the average of all x-coordinates of local maxima of the function f(x) = -4(-1(-4(3cos(3\u03c0(4x + 4) + 3) + 2)^2 + 1(3cos(3\u03c0(4x + 4) + 3) + 2) - 4)^2 + 5(-4(3cos(3\u03c0(4x + 4) + 3) + 2)^2 + 1(3cos(3\u03c0(4x + 4) + 3) + 2) - 4) + 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 x-coordinate of the local maximum with the smallest y-value of the function f(x) = 4((-1(-4(2cos(2\u03c0(1|x + 2|) + 1) - 2)^2 - 3(2cos(2\u03c0(1|x + 2|) + 1) - 2) - 4))/(3(-4(2cos(2\u03c0(1|x + 2|) + 1) - 2)^2 - 3(2cos(2\u03c0(1|x + 2|) + 1) - 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 rightmost local minimum of the function f(x) = 1|((2(2(-2cos(1\u03c0((1x - 1)/(3x)) + 1) - 3) - 3) + 1)/(3(2(-2cos(1\u03c0((1x - 1)/(3x)) + 1) - 3) - 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 average of all x-coordinates of local extrema of the function f(x) = 1((3(-3cos(1\u03c0((-3(-2x + 4) - 3)/(-3(-2x + 4))) - 1) + 3) + 1)/(-3(-3cos(1\u03c0((-3(-2x + 4) - 3)/(-3(-2x + 4))) - 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": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local maximum of the function f(x) = -2((3(5(-1|(-2|x + 2| - 1) + 2|) + 1))/(2(5(-1|(-2|x + 2| - 1) + 2|) + 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": "-2", "dataset": "MATH"}
{"messages": [{"content": "Find the average of all x-coordinates of local extrema of the function f(x) = -3cos(2\u03c0(-4(-3|(-2((-3x + 3)/(2x + 1)) - 5) + 1| + 1)^2 - 4(-3|(-2((-3x + 3)/(2x + 1)) - 5) + 1| + 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 rightmost local maximum of the function f(x) = 1sin(3\u03c0(3(-4(3(-3|x + 2| + 1)^2 + 1(-3|x + 2| + 1) + 1) + 1)^2 - 5(-4(3(-3|x + 2| + 1)^2 + 1(-3|x + 2| + 1) + 1) + 1) - 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": "-1", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the leftmost local minimum of the function f(x) = -2|(3|((-2(-2(-2sin(1\u03c0x - 2) - 1) - 4) + 2)/(-2(-2(-2sin(1\u03c0x - 2) - 1) - 4))) - 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 leftmost local maximum of the function f(x) = -4(2(-4((-3(-2x + 4) - 2)/(1(-2x + 4) + 3))^2 - 5((-3(-2x + 4) - 2)/(1(-2x + 4) + 3)) + 5)^2 - 1(-4((-3(-2x + 4) - 2)/(1(-2x + 4) + 3))^2 - 5((-3(-2x + 4) - 2)/(1(-2x + 4) + 3)) + 5) + 4) + 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 of the function f(x) = -3((2(5(-1((1x - 1)/(3x - 1))^2 - 3) + 2) - 1)/(-3(5(-1((1x - 1)/(3x - 1))^2 - 3) + 2) - 3))^2 + 5((2(5(-1((1x - 1)/(3x - 1))^2 - 3) + 2) - 1)/(-3(5(-1((1x - 1)/(3x - 1))^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": "0", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local extremum of the function f(x) = (-3(4(-1|(1(3x + 3)^2 + 1(3x + 3) + 4) - 1| + 1)^2 - 2(-1|(1(3x + 3)^2 + 1(3x + 3) + 4) - 1| + 1) - 5) - 1)/(-3(4(-1|(1(3x + 3)^2 + 1(3x + 3) + 4) - 1| + 1)^2 - 2(-1|(1(3x + 3)^2 + 1(3x + 3) + 4) - 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": "-1", "dataset": "MATH"}
{"messages": [{"content": "How many local maxima does the function f(x) = -3(2|(-3(3(-2|x + 1| - 1)^2 - 1(-2|x + 1| - 1) - 3)^2 + 2(3(-2|x + 1| - 1)^2 - 1(-2|x + 1| - 1) - 3) + 5) + 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 average of all x-coordinates of local minima of the function f(x) = -4((1(2cos(2\u03c0(-4(-5x^2 + 3x + 2)^2 - 5(-5x^2 + 3x + 2) - 5)) + 1) - 3)/(2(2cos(2\u03c0(-4(-5x^2 + 3x + 2)^2 - 5(-5x^2 + 3x + 2) - 5)) + 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 maximum with the smallest y-value of the function f(x) = -1(-2|(-2sin(3\u03c0(-1((1x + 2)/(-3x - 3))^2 - 3((1x + 2)/(-3x - 3)) - 2) - 2) - 2) - 1| - 2)^2 - 5(-2|(-2sin(3\u03c0(-1((1x + 2)/(-3x - 3))^2 - 3((1x + 2)/(-3x - 3)) - 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": "-6", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the leftmost local extremum of the function f(x) = (-2(2(3|((-1(-5x - 5) - 3)/(-3(-5x - 5) + 2)) - 1| - 1)^2 + 4(3|((-1(-5x - 5) - 3)/(-3(-5x - 5) + 2)) - 1| - 1) - 4) - 1)/(3(2(3|((-1(-5x - 5) - 3)/(-3(-5x - 5) + 2)) - 1| - 1)^2 + 4(3|((-1(-5x - 5) - 3)/(-3(-5x - 5) + 2)) - 1| - 1) - 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": "-2", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local extremum with the largest y-value of the function f(x) = 1cos(1\u03c0(3|(4(3|((3x)/(-2x - 2)) - 2| + 1) - 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": "-9", "dataset": "MATH"}
{"messages": [{"content": "How many local maxima does the function f(x) = (3(-3|((3(3((1x - 2)/(-3x - 2)) - 5) - 3)/(-3(3((1x - 2)/(-3x - 2)) - 5) - 1)) - 1| - 1) + 2)/(-1(-3|((3(3((1x - 2)/(-3x - 2)) - 5) - 3)/(-3(3((1x - 2)/(-3x - 2)) - 5) - 1)) - 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 of the function f(x) = -4(1|(5(2e^(1(2|x + 1| - 1)) - 1) - 3) + 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 average of all x-coordinates of local minima of the function f(x) = 3(4(1(1(1|x - 1| - 3)^2 + 3(1|x - 1| - 3))^2 + 4)^2 - 1(1(1(1|x - 1| - 3)^2 + 3(1|x - 1| - 3))^2 + 4) - 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": "1", "dataset": "MATH"}