{"messages": [{"content": "Find the x-coordinate of the leftmost local extremum of the function f(x) = (-3(1sin(2\u03c0(2|((-2x + 2)/(-3x + 2)) - 1| - 3) - 3) - 3) - 2)/(-2(1sin(2\u03c0(2|((-2x + 2)/(-3x + 2)) - 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": "0", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the rightmost local extremum of the function f(x) = 4(-1((1(3cos(1\u03c0x + 2)) - 3)/(-2(3cos(1\u03c0x + 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": "9", "dataset": "MATH"}
{"messages": [{"content": "How many local extrema (both minima and maxima) does the function f(x) = -2|(-1(1sin(2\u03c0(-2x - 4) + 2) + 3)^2) - 2| - 1 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "80", "dataset": "MATH"}
{"messages": [{"content": "How many local minima does the function f(x) = 3|(5(-1e^(2(-3x^2 + 2x + 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 leftmost local extremum of the function f(x) = (-2(-4((-2(-1x^2 - 3x + 3) + 3)/(-3(-1x^2 - 3x + 3) + 4))^2 - 3((-2(-1x^2 - 3x + 3) + 3)/(-3(-1x^2 - 3x + 3) + 4)) + 5) + 3)/(2(-4((-2(-1x^2 - 3x + 3) + 3)/(-3(-1x^2 - 3x + 3) + 4))^2 - 3((-2(-1x^2 - 3x + 3) + 3)/(-3(-1x^2 - 3x + 3) + 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": "-3", "dataset": "MATH"}
{"messages": [{"content": "Find the average of all x-coordinates of local minima of the function f(x) = 1(2(-5(-3x^2 + 3x + 3)^2 + 4(-3x^2 + 3x + 3))^2 - 5(-5(-3x^2 + 3x + 3)^2 + 4(-3x^2 + 3x + 3)) - 4)^2 - 2(2(-5(-3x^2 + 3x + 3)^2 + 4(-3x^2 + 3x + 3))^2 - 5(-5(-3x^2 + 3x + 3)^2 + 4(-3x^2 + 3x + 3)) - 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 extremum with the largest y-value of the function f(x) = 3(1sin(3\u03c0(3(-2|x - 2|)^2 - 3(-2|x - 2|) - 1)) - 2) - 2 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-10", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local extremum of the function f(x) = (1(3((-3(-4x^2 - 2x - 2) - 1)/(-3(-4x^2 - 2x - 2) + 1)) - 2) - 2)/(-3(3((-3(-4x^2 - 2x - 2) - 1)/(-3(-4x^2 - 2x - 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 rightmost local minimum of the function f(x) = 5(3sin(3\u03c0((-1((-2x)/(-2x - 1)) + 3)/(-3((-2x)/(-2x - 1)))) - 3) - 3)^2 + 3(3sin(3\u03c0((-1((-2x)/(-2x - 1)) + 3)/(-3((-2x)/(-2x - 1)))) - 3) - 3) - 5 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "How many local extrema (both minima and maxima) does the function f(x) = -1((-1(-2cos(2\u03c0(3|x| - 3) - 3)) + 3)/(3(-2cos(2\u03c0(3|x| - 3) - 3)))) + 1 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": "How many local minima does the function f(x) = (1((-3(3(-2|x + 3| + 1)^2 - 5(-2|x + 3| + 1)) - 3)/(1(3(-2|x + 3| + 1)^2 - 5(-2|x + 3| + 1)))) + 3)/(1((-3(3(-2|x + 3| + 1)^2 - 5(-2|x + 3| + 1)) - 3)/(1(3(-2|x + 3| + 1)^2 - 5(-2|x + 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 extrema of the function f(x) = 3(-1(-3|((1x - 1)/(-2x - 1)) + 2| - 1)^2 - 3(-3|((1x - 1)/(-2x - 1)) + 2| - 1) + 2)^2 - 1(-1(-3|((1x - 1)/(-2x - 1)) + 2| - 1)^2 - 3(-3|((1x - 1)/(-2x - 1)) + 2| - 1) + 2) + 4 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-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(-3e^(-2(-3x - 1)) + 2) - 3) - 1)/(1(3(-3e^(-2(-3x - 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": "4", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local maximum of the function f(x) = 4(3(-4((1x + 2)/(-2x - 3)) - 3)^2 - 5(-4((1x + 2)/(-2x - 3)) - 3))^2 + 3(3(-4((1x + 2)/(-2x - 3)) - 3)^2 - 5(-4((1x + 2)/(-2x - 3)) - 3)) - 3 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-1", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local minimum with the smallest y-value of the function f(x) = -3(3(2sin(1\u03c0(-1x^2 + 5x - 2) - 1) + 3)^2 + 1(2sin(1\u03c0(-1x^2 + 5x - 2) - 1) + 3) + 4)^2 - 2(3(2sin(1\u03c0(-1x^2 + 5x - 2) - 1) + 3)^2 + 1(2sin(1\u03c0(-1x^2 + 5x - 2) - 1) + 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": "-10", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the rightmost local minimum of the function f(x) = 2((-3(2sin(1\u03c0(-1|x + 2| + 3)) + 3) + 3)/(-1(2sin(1\u03c0(-1|x + 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": "10", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the leftmost local minimum of the function f(x) = 3|(3(-1(-1e^(-2x) + 3)^2 + 5)^2 + 1(-1(-1e^(-2x) + 3)^2 + 5) + 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": "-1", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local minimum with the largest y-value of the function f(x) = -1cos(3\u03c0((-2(3(-3|x - 1| + 3)^2 + 5(-3|x - 1| + 3) + 5) - 1)/(-2(3(-3|x - 1| + 3)^2 + 5(-3|x - 1| + 3) + 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": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local maximum with the smallest y-value of the function f(x) = (1(-3cos(1\u03c0(-2(5x^2 - 1x - 2) - 3) - 2)) + 3)/(3(-3cos(1\u03c0(-2(5x^2 - 1x - 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": "How many local minima does the function f(x) = -3(-4(2|(-2e^(-1x) + 2) + 3| + 3)^2 + 1(2|(-2e^(-1x) + 2) + 3| + 3) - 2)^2 + 3(-4(2|(-2e^(-1x) + 2) + 3| + 3)^2 + 1(2|(-2e^(-1x) + 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 local extremum with the smallest y-value of the function f(x) = 2|(-1sin(2\u03c0(3(5x + 3) + 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 rightmost local minimum of the function f(x) = 1(-3|(2cos(1\u03c0((-2x - 2)/(-2x)) + 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 extremum of the function f(x) = (2(-1|(2((3x + 3)/(1x)) - 5) + 1| + 3) + 1)/(2(-1|(2((3x + 3)/(1x)) - 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": "0", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local minimum with the smallest y-value of the function f(x) = 4(-3(5(-2cos(2\u03c0x - 1) + 2) + 1)^2 + 2(5(-2cos(2\u03c0x - 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": "-9", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the leftmost local maximum of the function f(x) = 1(3sin(2\u03c0((1(-3x^2 - 5x - 1) - 2)/(1(-3x^2 - 5x - 1))) - 1) + 3)^2 - 1(3sin(2\u03c0((1(-3x^2 - 5x - 1) - 2)/(1(-3x^2 - 5x - 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": "-2", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the rightmost local extremum of the function f(x) = (-2((-3(-3cos(1\u03c0((3x + 2)/(-3x + 4)) - 2) + 3) + 1)/(-2(-3cos(1\u03c0((3x + 2)/(-3x + 4)) - 2) + 3) - 2)))/(2((-3(-3cos(1\u03c0((3x + 2)/(-3x + 4)) - 2) + 3) + 1)/(-2(-3cos(1\u03c0((3x + 2)/(-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 extremum with the smallest y-value of the function f(x) = -3|(-1(3|(4x^2 + 4x - 4) - 3| - 2)^2 - 4(3|(4x^2 + 4x - 4) - 3| - 2) + 4) + 1| + 1 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the rightmost local extremum of the function f(x) = 3(-1cos(3\u03c0(3|(-2x) + 1| - 1) + 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 local extremum with the largest y-value of the function f(x) = -1|((-3(2sin(2\u03c0(2x + 5)) + 3) - 3)/(-1(2sin(2\u03c0(2x + 5)) + 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": "-10", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the rightmost local minimum of the function f(x) = 3(-2|((-1(1x^2 - 1x - 1) - 2)/(-3(1x^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 maxima does the function f(x) = 2|(-1(-2|((-3x + 3)/(-2x - 1)) + 1| - 2) - 5) - 1| - 2 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local maximum with the smallest y-value of the function f(x) = 1|(2(-3sin(1\u03c0(5x + 2) + 1) - 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": "-10", "dataset": "MATH"}
{"messages": [{"content": "Find the average of all x-coordinates of local maxima of the function f(x) = -3|(-1(-2sin(1\u03c0((1x + 2)/(2x - 3)) + 3) + 1)^2 - 4(-2sin(1\u03c0((1x + 2)/(2x - 3)) + 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": "1", "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(2|(-3|((-2x + 1)/(-3x - 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": "-4", "dataset": "MATH"}
{"messages": [{"content": "Find the average of all x-coordinates of local extrema of the function f(x) = 2|(-2cos(2\u03c0(4(-2|x - 3| - 1)^2 + 4(-2|x - 3| - 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": "0", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local maximum of the function f(x) = 4(-2(-5(1|x - 1| - 1) - 4)^2 + 5(-5(1|x - 1| - 1) - 4) + 4)^2 - 5(-2(-5(1|x - 1| - 1) - 4)^2 + 5(-5(1|x - 1| - 1) - 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": "Find the x-coordinate of the local minimum with the largest y-value of the function f(x) = 1((-3(2|(-1sin(1\u03c0x + 1)) - 3|))/(-1(2|(-1sin(1\u03c0x + 1)) - 3|)))^2 + 5((-3(2|(-1sin(1\u03c0x + 1)) - 3|))/(-1(2|(-1sin(1\u03c0x + 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 rightmost local minimum of the function f(x) = -5(-1((3(-3cos(1\u03c0x + 2) + 1) - 2)/(2(-3cos(1\u03c0x + 2) + 1) - 1)) + 3)^2 + 3(-1((3(-3cos(1\u03c0x + 2) + 1) - 2)/(2(-3cos(1\u03c0x + 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": "9", "dataset": "MATH"}
{"messages": [{"content": "How many local extrema (both minima and maxima) does the function f(x) = -2cos(2\u03c0(-2|((2(2x^2 - 1x + 3) - 1)/(2(2x^2 - 1x + 3)))| + 1) - 2) + 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 extremum with the smallest y-value of the function f(x) = 2(4(-5(3sin(3\u03c0x - 1) + 3)^2 - 1(3sin(3\u03c0x - 1) + 3) - 1)^2 + 4(-5(3sin(3\u03c0x - 1) + 3)^2 - 1(3sin(3\u03c0x - 1) + 3) - 1) + 5)^2 - 3(4(-5(3sin(3\u03c0x - 1) + 3)^2 - 1(3sin(3\u03c0x - 1) + 3) - 1)^2 + 4(-5(3sin(3\u03c0x - 1) + 3)^2 - 1(3sin(3\u03c0x - 1) + 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 local extremum with the smallest y-value of the function f(x) = 3|(5(1|(3|x + 1| - 1) - 2|)^2 - 4(1|(3|x + 1| - 1) - 2|)) - 2| + 3 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}
{"messages": [{"content": "Find the average of all x-coordinates of local maxima of the function f(x) = -3(-1|(-5(-3cos(1\u03c0x - 1) + 3) - 1) + 1|)^2 - 2(-1|(-5(-3cos(1\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": "-1", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local maximum with the largest y-value of the function f(x) = 1|(-2sin(2\u03c0(2(4x^2 + 5x - 2)^2 + 4(4x^2 + 5x - 2) - 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": "-5", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local extremum with the smallest y-value of the function f(x) = 1(-2|((1(2sin(2\u03c0x + 2) - 1) - 2)/(2(2sin(2\u03c0x + 2) - 1) - 3))| + 1)^2 - 1(-2|((1(2sin(2\u03c0x + 2) - 1) - 2)/(2(2sin(2\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": "-10", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local extremum with the largest y-value of the function f(x) = -2|(4(3|(4x^2 + 2x - 1) - 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 rightmost local maximum of the function f(x) = -3e^(1(-1|(-5(-1|x - 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": "8", "dataset": "MATH"}
{"messages": [{"content": "How many local extrema (both minima and maxima) does the function f(x) = -3(-4((1(3sin(1\u03c0x - 1) + 3) + 2)/(3(3sin(1\u03c0x - 1) + 3) - 1))^2 + 2((1(3sin(1\u03c0x - 1) + 3) + 2)/(3(3sin(1\u03c0x - 1) + 3) - 1)) - 4)^2 - 2(-4((1(3sin(1\u03c0x - 1) + 3) + 2)/(3(3sin(1\u03c0x - 1) + 3) - 1))^2 + 2((1(3sin(1\u03c0x - 1) + 3) + 2)/(3(3sin(1\u03c0x - 1) + 3) - 1)) - 4) + 5 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "39", "dataset": "MATH"}
{"messages": [{"content": "How many local maxima does the function f(x) = (-2(-3|(1|(-4x^2 + 5x) - 2| - 1)| - 1) - 3)/(3(-3|(1|(-4x^2 + 5x) - 2| - 1)| - 1) + 3) have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local minimum with the largest y-value of the function f(x) = (1(-4(-2e^(2((-3x + 3)/(-1x - 2))) - 2)^2 + 3(-2e^(2((-3x + 3)/(-1x - 2))) - 2) - 2) - 2)/(3(-4(-2e^(2((-3x + 3)/(-1x - 2))) - 2)^2 + 3(-2e^(2((-3x + 3)/(-1x - 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": "-4", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local extremum with the smallest y-value of the function f(x) = 2e^(-2(3|(-3|(2x + 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": "-7", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the leftmost local extremum of the function f(x) = (1((2(1sin(3\u03c0(-3|x + 2| - 1) + 1) + 1) - 1)/(1(1sin(3\u03c0(-3|x + 2| - 1) + 1) + 1))) + 1)/(-2((2(1sin(3\u03c0(-3|x + 2| - 1) + 1) + 1) - 1)/(1(1sin(3\u03c0(-3|x + 2| - 1) + 1) + 1))) + 3) in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-10", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the leftmost local maximum of the function f(x) = -3(1cos(3\u03c0(2|((-1x + 3)/(2x)) + 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": "-3", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the leftmost local extremum of the function f(x) = -1sin(3\u03c0(-1(1|(-1x^2 + 3x - 5) - 1| + 1) + 1) + 3) in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-10", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local minimum of the function f(x) = (-1(-2(-2|(4x^2 + 3x - 2) - 2|) - 4) + 3)/(1(-2(-2|(4x^2 + 3x - 2) - 2|) - 4)) in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local minimum of the function f(x) = (-1(2|(-5(4x^2 + 5x - 1)^2 - 3(4x^2 + 5x - 1) - 1) - 3| - 1) - 1)/(-3(2|(-5(4x^2 + 5x - 1)^2 - 3(4x^2 + 5x - 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": "-1", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local maximum of the function f(x) = 3e^(2(2|(1(-1x^2 + 2x + 5)^2 + 2(-1x^2 + 2x + 5) + 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 x-coordinate of the local minimum of the function f(x) = (-3(-2|(-1(3x + 5) - 5)| + 1) - 3)/(-2(-2|(-1(3x + 5) - 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": "How many local extrema (both minima and maxima) does the function f(x) = 2|(1(2cos(2\u03c0(-5x + 2) - 2) - 2) + 3) + 2| + 1 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "200", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the rightmost local maximum of the function f(x) = -4(5(1((-2x)/(-3x + 4))^2 + 4((-2x)/(-3x + 4)) + 1)^2 + 1(1((-2x)/(-3x + 4))^2 + 4((-2x)/(-3x + 4)) + 1) - 1)^2 + 1(5(1((-2x)/(-3x + 4))^2 + 4((-2x)/(-3x + 4)) + 1)^2 + 1(1((-2x)/(-3x + 4))^2 + 4((-2x)/(-3x + 4)) + 1) - 1) - 5 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local minimum of the function f(x) = -1((-3(4((3x - 3)/(-2x))^2 + 1((3x - 3)/(-2x)) + 3))/(3(4((3x - 3)/(-2x))^2 + 1((3x - 3)/(-2x)) + 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 extremum of the function f(x) = -1e^(-1(-4(5((3x - 1)/(-1x + 2))^2 - 3((3x - 1)/(-1x + 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 with the largest y-value of the function f(x) = 2(-1(4(2sin(3\u03c0x + 2) + 2)^2 + 5)^2 + 2(4(2sin(3\u03c0x + 2) + 2)^2 + 5) - 4)^2 + 2(-1(4(2sin(3\u03c0x + 2) + 2)^2 + 5)^2 + 2(4(2sin(3\u03c0x + 2) + 2)^2 + 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": "-9", "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(-4(-1|(2x^2 - 5x - 5) - 3| - 1) + 5) + 1) + 1 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-10", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local maximum of the function f(x) = (-2(-1((-2(1x + 3) - 3)/(-2(1x + 3) + 3))^2 + 3((-2(1x + 3) - 3)/(-2(1x + 3) + 3)) + 5) - 3)/(-2(-1((-2(1x + 3) - 3)/(-2(1x + 3) + 3))^2 + 3((-2(1x + 3) - 3)/(-2(1x + 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": "-2", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the leftmost local maximum of the function f(x) = 5(1|(3|(-1x^2 + 1x + 1) + 1| + 2) + 3| + 3) + 5 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}
{"messages": [{"content": "How many local extrema (both minima and maxima) does the function f(x) = -3((-1(5(-1|x + 1| + 2)^2 + 4(-1|x + 1| + 2) - 3) - 3)/(1(5(-1|x + 1| + 2)^2 + 4(-1|x + 1| + 2) - 3) + 2))^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 leftmost local maximum of the function f(x) = 2|(1|(-3((-1x + 1)/(1x + 3))^2 + 5((-1x + 1)/(1x + 3)) + 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": "-1", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local extremum of the function f(x) = (-3((-3(-2|(1x - 2) + 2| - 2) - 1)/(3(-2|(1x - 2) + 2| - 2) + 3)) + 1)/(3((-3(-2|(1x - 2) + 2| - 2) - 1)/(3(-2|(1x - 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": "How many local maxima does the function f(x) = -3(2|(-2e^(-1(4x^2 + 1x - 3)) + 3) - 3| + 1)^2 + 2(2|(-2e^(-1(4x^2 + 1x - 3)) + 3) - 3| + 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": "Find the x-coordinate of the local maximum with the smallest y-value of the function f(x) = (2((3(3(2x - 2)^2 - 2(2x - 2) - 1) + 3)/(-1(3(2x - 2)^2 - 2(2x - 2) - 1) - 1)) + 1)/(2((3(3(2x - 2)^2 - 2(2x - 2) - 1) + 3)/(-1(3(2x - 2)^2 - 2(2x - 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) = 3(1(-2sin(2\u03c0(1x - 4) - 1) - 3)^2 - 5(-2sin(2\u03c0(1x - 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": "-9", "dataset": "MATH"}
{"messages": [{"content": "Find the average of all x-coordinates of local maxima of the function f(x) = 2(-2cos(1\u03c0(2|(-3|x - 3| + 2) + 1| + 3) - 3) - 1)^2 - 3(-2cos(1\u03c0(2|(-3|x - 3| + 2) + 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": "0", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the leftmost local minimum of the function f(x) = 3sin(2\u03c0(1(2|(3|x + 2| + 1) - 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": "-10", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local extremum with the largest y-value of the function f(x) = -1(1cos(1\u03c0(-3|((3x)/(1x + 1)) - 2| + 1) + 2) - 2)^2 + 1(1cos(1\u03c0(-3|((3x)/(1x + 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": "-4", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local extremum of the function f(x) = 1(1e^(2(1|((1x - 1)/(-3x + 1)) - 1| + 3)) - 3)^2 + 2(1e^(2(1|((1x - 1)/(-3x + 1)) - 1| + 3)) - 3) - 5 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local extremum of the function f(x) = -2|(-4(2|(-1x^2 - 2) - 2| + 2)^2 + 4(2|(-1x^2 - 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": "How many local minima does the function f(x) = -5(2|((-2(2x + 5) + 3)/(-2(2x + 5) - 3)) - 3|)^2 - 1(2|((-2(2x + 5) + 3)/(-2(2x + 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 with the largest y-value of the function f(x) = (3(-1((-3(3sin(3\u03c0x) - 1) + 3)/(2(3sin(3\u03c0x) - 1) - 1))) + 3)/(-3(-1((-3(3sin(3\u03c0x) - 1) + 3)/(2(3sin(3\u03c0x) - 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": "-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|(1(1x + 2)^2 - 3) + 1| + 3)^2 - 1(2|(1(1x + 2)^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": "-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(5(-1cos(1\u03c0x - 3) - 1)^2 - 1(-1cos(1\u03c0x - 3) - 1) - 1) + 4)^2 - 3(2(5(-1cos(1\u03c0x - 3) - 1)^2 - 1(-1cos(1\u03c0x - 3) - 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": "-9", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the rightmost local minimum of the function f(x) = 5((-1(5(-1e^(-2x) - 3)^2 + 5(-1e^(-2x) - 3) + 1) + 1)/(3(5(-1e^(-2x) - 3)^2 + 5(-1e^(-2x) - 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": "-8", "dataset": "MATH"}
{"messages": [{"content": "How many local minima does the function f(x) = -3|(-1(1((1x - 2)/(1x))^2 + 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": "How many local extrema (both minima and maxima) does the function f(x) = -1(3(5(-3cos(3\u03c0x + 3) - 1)^2 - 4)^2 + 3(5(-3cos(3\u03c0x + 3) - 1)^2 - 4) - 1) - 3 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "240", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the leftmost local extremum of the function f(x) = 3(1cos(3\u03c0((3(-3x - 2))/(-3(-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": "-2", "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(1cos(2\u03c0x + 3)) + 1)/(-3(1cos(2\u03c0x + 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) = 1|(4((-1(5x + 3) - 2)/(2(5x + 3) - 1))^2 + 3((-1(5x + 3) - 2)/(2(5x + 3) - 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": "-2", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the leftmost local extremum of the function f(x) = 4(-1|(-3sin(3\u03c0(-5x - 4) + 3) + 1) - 2| - 2)^2 + 1(-1|(-3sin(3\u03c0(-5x - 4) + 3) + 1) - 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 leftmost local maximum of the function f(x) = -2|((-3(-1|(3x^2 + 2x + 2)| - 3))/(1(-1|(3x^2 + 2x + 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": "-9", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the leftmost local maximum of the function f(x) = (3(-1|(-3|(-1cos(3\u03c0x - 3) + 3)| - 2) - 2| - 1))/(-1(-1|(-3|(-1cos(3\u03c0x - 3) + 3)| - 2) - 2| - 1) - 3) in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-9", "dataset": "MATH"}
{"messages": [{"content": "Find the average of all x-coordinates of local maxima of the function f(x) = -3|(2cos(3\u03c0(-1((1x)/(3x + 1)) + 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 largest y-value of the function f(x) = -2|(3(-3((1x - 3)/(-3x - 3))^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": "3", "dataset": "MATH"}
{"messages": [{"content": "How many local minima does the function f(x) = (-3(1|(3(4x)^2 + 3(4x) + 3)| + 3) - 1)/(-1(1|(3(4x)^2 + 3(4x) + 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 maximum of the function f(x) = -5((3(-1|(4x + 2) - 2| + 3) + 1)/(1(-1|(4x + 2) - 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": "0", "dataset": "MATH"}
{"messages": [{"content": "Find the average of all x-coordinates of local extrema of the function f(x) = 1(-1e^(1((-3(-3|x - 1| + 2) - 2)/(-3(-3|x - 1| + 2)))) - 2)^2 - 2(-1e^(1((-3(-3|x - 1| + 2) - 2)/(-3(-3|x - 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": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local maximum of the function f(x) = 2|(-1(1|(-2x^2 - 2x - 1) + 1| - 2)^2 - 1(1|(-2x^2 - 2x - 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 leftmost local minimum of the function f(x) = -5((2(5(-1sin(2\u03c0x - 1) - 1)^2 - 5(-1sin(2\u03c0x - 1) - 1) - 4) + 1)/(-2(5(-1sin(2\u03c0x - 1) - 1)^2 - 5(-1sin(2\u03c0x - 1) - 1) - 4) + 1))^2 - 3((2(5(-1sin(2\u03c0x - 1) - 1)^2 - 5(-1sin(2\u03c0x - 1) - 1) - 4) + 1)/(-2(5(-1sin(2\u03c0x - 1) - 1)^2 - 5(-1sin(2\u03c0x - 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": "-9", "dataset": "MATH"}
{"messages": [{"content": "How many local minima does the function f(x) = -1(1|(-4(-3e^(1x) + 2)^2 - 3(-3e^(1x) + 2) - 3) + 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 minima does the function f(x) = -5(-3e^(2(-2((3x + 1)/(-2x + 3))^2 + 4((3x + 1)/(-2x + 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 average of all x-coordinates of local minima of the function f(x) = 3|((3(-4(3|x|)^2 + 5(3|x|) + 5) + 1)/(-2(-4(3|x|)^2 + 5(3|x|) + 5) + 3)) + 1| - 3 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}
{"messages": [{"content": "How many local minima does the function f(x) = 1|(2|(-1(-5x - 5)^2 + 2(-5x - 5) + 5) - 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) = -5(-2cos(1\u03c0((3(-2x^2 - 4x - 5) + 2)/(-2(-2x^2 - 4x - 5) - 2)) - 3) + 1)^2 + 2(-2cos(1\u03c0((3(-2x^2 - 4x - 5) + 2)/(-2(-2x^2 - 4x - 5) - 2)) - 3) + 1) + 4 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-1", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local extremum with the largest y-value of the function f(x) = 1sin(2\u03c0((-1(-5((-2x + 1)/(-2x + 3))^2 - 3((-2x + 1)/(-2x + 3)) + 3) - 2)/(3(-5((-2x + 1)/(-2x + 3))^2 - 3((-2x + 1)/(-2x + 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": "-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(-3cos(3\u03c0(1x^2 - 1x - 1) + 1) + 2)^2 + 5(-3cos(3\u03c0(1x^2 - 1x - 1) + 1) + 2) + 5) - 3)/(-1(-3(-3cos(3\u03c0(1x^2 - 1x - 1) + 1) + 2)^2 + 5(-3cos(3\u03c0(1x^2 - 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": "-10", "dataset": "MATH"}
{"messages": [{"content": "How many local minima does the function f(x) = -3((3(3(-1|x| - 2)^2 + 2(-1|x| - 2) - 2) - 2)/(-1(3(-1|x| - 2)^2 + 2(-1|x| - 2) - 2) + 3)) + 2 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local minimum of the function f(x) = (1(2(5((-1x - 1)/(-2x - 1)) - 4)^2 - 4) + 2)/(3(2(5((-1x - 1)/(-2x - 1)) - 4)^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 local minimum of the function f(x) = 3|(-2(4((3x - 3)/(-2x + 3))^2 + 5((3x - 3)/(-2x + 3)) + 3)^2 + 2(4((3x - 3)/(-2x + 3))^2 + 5((3x - 3)/(-2x + 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": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local maximum with the largest y-value of the function f(x) = 2sin(3\u03c0(-1|((2(-2|x - 2| + 1) - 2)/(-1(-2|x - 2| + 1) + 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": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local extremum with the smallest y-value of the function f(x) = 2(1|(1(-2|x + 1| - 2)^2 + 4(-2|x + 1| - 2) - 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": "-1", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the leftmost local minimum of the function f(x) = 1|(5(2((-2x - 2)/(2x + 1))^2 - 3((-2x - 2)/(2x + 1)) + 3) - 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": "-1", "dataset": "MATH"}
{"messages": [{"content": "Find the average of all x-coordinates of local minima of the function f(x) = (2(-1(-3cos(1\u03c0(-4x - 3) + 1))^2 + 4(-3cos(1\u03c0(-4x - 3) + 1)) + 5) + 1)/(2(-1(-3cos(1\u03c0(-4x - 3) + 1))^2 + 4(-3cos(1\u03c0(-4x - 3) + 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": "0", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the leftmost local extremum of the function f(x) = 5(-2(2|(3sin(2\u03c0x - 3) - 1) - 1| - 2) - 1)^2 - 4(-2(2|(3sin(2\u03c0x - 3) - 1) - 1| - 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 rightmost local minimum of the function f(x) = -1(2|(-3(-3cos(3\u03c0x - 3) + 2) - 4) - 2| + 3)^2 + 3(2|(-3(-3cos(3\u03c0x - 3) + 2) - 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": "10", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local extremum of the function f(x) = 2|(1e^(1(4(-2|x - 1| - 2)^2 + 1(-2|x - 1| - 2) + 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": "0", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local extremum with the largest y-value of the function f(x) = 1(3e^(2(-4(1x - 2)^2 + 4)) + 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": "2", "dataset": "MATH"}
{"messages": [{"content": "How many local minima does the function f(x) = (3(1((-2(1|x|) + 2)/(1(1|x|) + 2)) - 4) + 1)/(-1(1((-2(1|x|) + 2)/(1(1|x|) + 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) = 2(-3sin(1\u03c0((2((2x + 3)/(2x - 1)))/(-1((2x + 3)/(2x - 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) = 4(1|((-3(1sin(3\u03c0x + 1)) - 3)/(-3(1sin(3\u03c0x + 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 rightmost local minimum of the function f(x) = (1(2|(-1|(-1sin(2\u03c0x + 3) - 3) + 1| - 2) - 2|) + 1)/(-2(2|(-1|(-1sin(2\u03c0x + 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": "9", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the rightmost local extremum of the function f(x) = -1(5((-1((3x + 1)/(1x)))/(3((3x + 1)/(1x)) + 3))^2 + 4((-1((3x + 1)/(1x)))/(3((3x + 1)/(1x)) + 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": "0", "dataset": "MATH"}
{"messages": [{"content": "How many local minima does the function f(x) = 1(1((1(-2sin(3\u03c0x + 1) - 3) + 2)/(2(-2sin(3\u03c0x + 1) - 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 maximum with the smallest y-value of the function f(x) = -3|(1|(3cos(3\u03c0(1|x|) + 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": "-10", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local minimum of the function f(x) = 3(-2|(-3|((-3x + 3)/(-1x + 2)) - 2| + 3) - 2| - 2)^2 - 3(-2|(-3|((-3x + 3)/(-1x + 2)) - 2| + 3) - 2| - 2) + 3 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "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(-2|(1x^2 + 5x - 3) - 2| + 2)^2 + 1(-2|(1x^2 + 5x - 3) - 2| + 2) - 5) + 1)/(-2(1(-2|(1x^2 + 5x - 3) - 2| + 2)^2 + 1(-2|(1x^2 + 5x - 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": "-6", "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((-1x - 3)/(-2x - 1))^2 - 3((-1x - 3)/(-2x - 1)))^2 + 3(-4((-1x - 3)/(-2x - 1))^2 - 3((-1x - 3)/(-2x - 1))) + 1)^2 + 4(-3(-4((-1x - 3)/(-2x - 1))^2 - 3((-1x - 3)/(-2x - 1)))^2 + 3(-4((-1x - 3)/(-2x - 1))^2 - 3((-1x - 3)/(-2x - 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 local extremum with the largest y-value of the function f(x) = -1(-1(4(2cos(2\u03c0x - 2) - 3)^2 - 5(2cos(2\u03c0x - 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": "-9", "dataset": "MATH"}
{"messages": [{"content": "Find the average of all x-coordinates of local maxima of the function f(x) = -3|(1|(-1cos(3\u03c0(4x - 4) + 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": "0", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the rightmost local minimum of the function f(x) = 3cos(1\u03c0(-4(-1((-1x + 3)/(-3x))) + 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) = 5(2e^(-1(-2(2|x + 1| + 3) + 5)) + 1)^2 - 1(2e^(-1(-2(2|x + 1| + 3) + 5)) + 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": "Find the x-coordinate of the rightmost local minimum of the function f(x) = 2((-3(3e^(1(-5x^2 - 4x + 5)) - 3) + 3)/(-2(3e^(1(-5x^2 - 4x + 5)) - 3)))^2 - 5((-3(3e^(1(-5x^2 - 4x + 5)) - 3) + 3)/(-2(3e^(1(-5x^2 - 4x + 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 extremum with the largest y-value of the function f(x) = 2cos(2\u03c0(-2(-3|(-5x^2 - 2x + 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": "-10", "dataset": "MATH"}
{"messages": [{"content": "Find the average of all x-coordinates of local minima of the function f(x) = (-1(1(2cos(1\u03c0(-2x^2 + 1x - 4) - 3) - 1) - 3) + 2)/(2(1(2cos(1\u03c0(-2x^2 + 1x - 4) - 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": "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((-1(3|(-1|x| - 1) + 2| - 2) + 2)/(-3(3|(-1|x| - 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": "-3", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the leftmost local maximum of the function f(x) = (1((2(1(2sin(3\u03c0x + 1) + 3) + 1))/(-3(1(2sin(3\u03c0x + 1) + 3) + 1) + 2)) + 1)/(1((2(1(2sin(3\u03c0x + 1) + 3) + 1))/(-3(1(2sin(3\u03c0x + 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": "-10", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the rightmost local minimum of the function f(x) = (-3(2sin(3\u03c0((-3((-3x)/(1x + 1)) - 1)/(2((-3x)/(1x + 1)) + 2)) - 2) - 3) + 2)/(-2(2sin(3\u03c0((-3((-3x)/(1x + 1)) - 1)/(2((-3x)/(1x + 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": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the average of all x-coordinates of local extrema of the function f(x) = 2cos(3\u03c0((-1(-1|(3x^2 - 5) + 1| - 2) + 3)/(-3(-1|(3x^2 - 5) + 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 x-coordinate of the local extremum with the largest y-value of the function f(x) = -1sin(2\u03c0(3(-3(1|x| - 2) - 5) + 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 local maximum with the largest y-value of the function f(x) = 3|((1(-2|((-3x + 1)/(2x - 3)) + 2| + 3) - 3)/(-2(-2|((-3x + 1)/(2x - 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": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the average of all x-coordinates of local minima of the function f(x) = 1|(-2e^(1(4(-2x - 1)^2 - 1(-2x - 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": "-1", "dataset": "MATH"}
{"messages": [{"content": "How many local extrema (both minima and maxima) does the function f(x) = 3sin(3\u03c0(-3|(2|(-2|x - 1| - 1) - 3| + 2) + 1| - 3)) + 3 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "721", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the rightmost local minimum of the function f(x) = -2(-1((2(3sin(2\u03c0x + 2) + 3) - 1)/(-1(3sin(2\u03c0x + 2) + 3)))^2 - 2((2(3sin(2\u03c0x + 2) + 3) - 1)/(-1(3sin(2\u03c0x + 2) + 3))) - 4)^2 - 3(-1((2(3sin(2\u03c0x + 2) + 3) - 1)/(-1(3sin(2\u03c0x + 2) + 3)))^2 - 2((2(3sin(2\u03c0x + 2) + 3) - 1)/(-1(3sin(2\u03c0x + 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": "10", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local extremum with the largest y-value of the function f(x) = (3(2(-2(-2sin(3\u03c0x - 1) + 3)^2 + 2(-2sin(3\u03c0x - 1) + 3) - 1) - 1) - 3)/(-3(2(-2(-2sin(3\u03c0x - 1) + 3)^2 + 2(-2sin(3\u03c0x - 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": "-9", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local extremum with the largest y-value of the function f(x) = (2(-2sin(2\u03c0((3(-4x^2 - 5x - 5) + 3)/(-2(-4x^2 - 5x - 5) - 2)) - 1) + 2) + 2)/(-3(-2sin(2\u03c0((3(-4x^2 - 5x - 5) + 3)/(-2(-4x^2 - 5x - 5) - 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": "-10", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local minimum with the smallest y-value of the function f(x) = 3sin(3\u03c0((-2(-1(3|x + 2| - 3) - 5) - 2)/(1(-1(3|x + 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": "-3", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local maximum with the smallest y-value of the function f(x) = 5(1|(-3((-2x - 1)/(-1x))^2 - 5((-2x - 1)/(-1x)) + 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": "0", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local maximum of the function f(x) = 5(3|(-2(1x^2 - 3x + 1) + 5) - 1| - 2)^2 + 3(3|(-2(1x^2 - 3x + 1) + 5) - 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": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the rightmost local maximum of the function f(x) = 2(-1(4(3sin(3\u03c0x + 2) - 1) - 5)^2 + 4(4(3sin(3\u03c0x + 2) - 1) - 5) - 2) + 3 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "How many local minima does the function f(x) = -1((1((-3(-2|x - 1| - 2) + 1)/(-2(-2|x - 1| - 2) - 1)) - 2)/(3((-3(-2|x - 1| - 2) + 1)/(-2(-2|x - 1| - 2) - 1)) - 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 local extremum with the smallest y-value of the function f(x) = -2|(-1e^(1(1(-4x^2 + 5)^2 + 4(-4x^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": "0", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the leftmost local extremum of the function f(x) = -1|(-1|(-3(-2x^2 + 5x + 4) + 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": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local minimum of the function f(x) = 1(-4((1((3x + 1)/(-2x + 3)) - 3)/(-1((3x + 1)/(-2x + 3)) - 1)) - 2)^2 - 3(-4((1((3x + 1)/(-2x + 3)) - 3)/(-1((3x + 1)/(-2x + 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": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the average of all x-coordinates of local maxima of the function f(x) = -4(-2sin(2\u03c0(-4((-1x - 3)/(-1x - 1))^2 - 4((-1x - 3)/(-1x - 1))) - 2) + 2)^2 + 3(-2sin(2\u03c0(-4((-1x - 3)/(-1x - 1))^2 - 4((-1x - 3)/(-1x - 1))) - 2) + 2) - 4 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local extremum with the largest y-value of the function f(x) = 3(-2(-3|(4x^2 + 1x - 3) + 3| - 1)^2 - 2(-3|(4x^2 + 1x - 3) + 3| - 1) + 1)^2 + 3(-2(-3|(4x^2 + 1x - 3) + 3| - 1)^2 - 2(-3|(4x^2 + 1x - 3) + 3| - 1) + 1) - 1 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}
{"messages": [{"content": "Find the average of all x-coordinates of local minima of the function f(x) = 2(3|((-1(-2|x + 2| + 2) - 3)/(-2(-2|x + 2| + 2) - 1))|)^2 + 5(3|((-1(-2|x + 2| + 2) - 3)/(-2(-2|x + 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": "-2", "dataset": "MATH"}
{"messages": [{"content": "Find the average of all x-coordinates of local maxima of the function f(x) = 2sin(3\u03c0(1|(4(3x + 1) - 2) + 3| + 3) + 2) + 3 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the rightmost local minimum of the function f(x) = 2(1cos(1\u03c0((1(-5x^2 + 3x + 4) + 3)/(1(-5x^2 + 3x + 4) + 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 local extremum with the smallest y-value of the function f(x) = 2sin(1\u03c0(4(2|((2x)/(-2x + 3)) + 2| + 3)^2 - 1(2|((2x)/(-2x + 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 rightmost local maximum of the function f(x) = -3e^(-1(1|(1(1x - 1)^2 + 5(1x - 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": "4", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the rightmost local minimum of the function f(x) = 2|(3sin(2\u03c0(-2((-3x)/(-3x - 1))^2 - 1((-3x)/(-3x - 1))) + 1)) + 3| + 2 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local extremum of the function f(x) = -2|((2(-2(-3x^2 + 4x - 2)^2 + 5(-3x^2 + 4x - 2) - 2) - 2)/(-1(-2(-3x^2 + 4x - 2)^2 + 5(-3x^2 + 4x - 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": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local maximum with the largest y-value of the function f(x) = 1(5(-1cos(3\u03c0(4x^2 - 5x - 2) + 3) - 1) - 1)^2 + 1(5(-1cos(3\u03c0(4x^2 - 5x - 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 leftmost local maximum of the function f(x) = 4(3(5(1cos(1\u03c0x - 3) + 1))^2 + 5(5(1cos(1\u03c0x - 3) + 1)) + 4) - 1 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-9", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local minimum of the function f(x) = -2|(-1((-1(5x^2 - 1) + 2)/(2(5x^2 - 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": "0", "dataset": "MATH"}
{"messages": [{"content": "How many local minima does the function f(x) = -1(3((3(2cos(2\u03c0x + 1) - 1) - 2)/(3(2cos(2\u03c0x + 1) - 1) + 2)) - 3)^2 - 4(3((3(2cos(2\u03c0x + 1) - 1) - 2)/(3(2cos(2\u03c0x + 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 leftmost local maximum of the function f(x) = -1(1((-2((2x - 3)/(-2x - 1)) + 2)/(3((2x - 3)/(-2x - 1)) - 1))^2)^2 + 4(1((-2((2x - 3)/(-2x - 1)) + 2)/(3((2x - 3)/(-2x - 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) = (2((-1(-3(-2sin(2\u03c0x + 3) + 2)^2 - 4(-2sin(2\u03c0x + 3) + 2) + 2) + 2)/(-2(-3(-2sin(2\u03c0x + 3) + 2)^2 - 4(-2sin(2\u03c0x + 3) + 2) + 2) - 1)) - 3)/(-3((-1(-3(-2sin(2\u03c0x + 3) + 2)^2 - 4(-2sin(2\u03c0x + 3) + 2) + 2) + 2)/(-2(-3(-2sin(2\u03c0x + 3) + 2)^2 - 4(-2sin(2\u03c0x + 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": "9", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local maximum of the function f(x) = 1(2e^(-1(-5((3x + 3)/(1x - 2))^2 + 5((3x + 3)/(1x - 2)) - 5)) - 2)^2 - 3(2e^(-1(-5((3x + 3)/(1x - 2))^2 + 5((3x + 3)/(1x - 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": "7", "dataset": "MATH"}
{"messages": [{"content": "How many local maxima does the function f(x) = (2(1|(3(-1|x + 1|) + 4) + 1|) - 2)/(-1(1|(3(-1|x + 1|) + 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": "Find the x-coordinate of the local minimum with the smallest y-value of the function f(x) = (-1(1sin(3\u03c0(-2(-2x - 3) - 5) - 2) - 3) + 2)/(2(1sin(3\u03c0(-2(-2x - 3) - 5) - 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 rightmost local maximum of the function f(x) = -4((2((2(5x - 4) + 3)/(-3(5x - 4) - 3)) - 3)/(2((2(5x - 4) + 3)/(-3(5x - 4) - 3))))^2 + 3((2((2(5x - 4) + 3)/(-3(5x - 4) - 3)) - 3)/(2((2(5x - 4) + 3)/(-3(5x - 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 average of all x-coordinates of local minima of the function f(x) = 2cos(2\u03c0(1|(3|(-2|x - 1| - 2) + 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": "0", "dataset": "MATH"}
{"messages": [{"content": "How many local minima does the function f(x) = -1e^(1(-5(-5(1|x + 1|)^2 - 4(1|x + 1|) - 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 maxima does the function f(x) = 2sin(2\u03c0(1((1(-1|x + 1|) - 1)/(2(-1|x + 1|) - 3))^2 - 3((1(-1|x + 1|) - 1)/(2(-1|x + 1|) - 3)) - 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 of the function f(x) = (-2(3|(-3(-5x + 5)^2 + 3(-5x + 5) + 2)| + 3) - 3)/(3(3|(-3(-5x + 5)^2 + 3(-5x + 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 minimum with the smallest y-value of the function f(x) = 2(2cos(3\u03c0(-2((1x + 2)/(2x + 3)) - 4)) - 3)^2 + 2(2cos(3\u03c0(-2((1x + 2)/(2x + 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": "-3", "dataset": "MATH"}
{"messages": [{"content": "How many local extrema (both minima and maxima) does the function f(x) = 3(-1(-3sin(3\u03c0((1x + 1)/(-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": "28", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local minimum of the function f(x) = (-3(1|((1(-2x^2 + 2x) + 3)/(1(-2x^2 + 2x) + 1)) - 2|) - 3)/(3(1|((1(-2x^2 + 2x) + 3)/(1(-2x^2 + 2x) + 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 average of all x-coordinates of local maxima of the function f(x) = 1(-3(-4(1cos(3\u03c0x - 1) + 2) - 5)^2 + 2(-4(1cos(3\u03c0x - 1) + 2) - 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": "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(-3|(-4(-1|x - 2| - 1) + 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 average of all x-coordinates of local extrema of the function f(x) = 3cos(1\u03c0((2(2(3x^2 + 1x + 4)^2 + 3(3x^2 + 1x + 4) - 3) + 1)/(-2(2(3x^2 + 1x + 4)^2 + 3(3x^2 + 1x + 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 local extremum of the function f(x) = 1|(3|(-1|(-1x + 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 leftmost local maximum of the function f(x) = 3sin(3\u03c0(-5(-1(-3x^2 - 1x + 5) - 3)^2 - 1(-1(-3x^2 - 1x + 5) - 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": "-4", "dataset": "MATH"}
{"messages": [{"content": "How many local minima does the function f(x) = -1|(-2((2(3|x - 1| + 1) + 1)/(-2(3|x - 1| + 1) + 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 rightmost local extremum of the function f(x) = (-3(3(-1sin(2\u03c0(5x^2 + 4x + 5) + 3) + 1)) + 3)/(2(3(-1sin(2\u03c0(5x^2 + 4x + 5) + 3) + 1)) - 1) in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "Find the average of all x-coordinates of local extrema of the function f(x) = -1e^(1((-2(1(1x^2 + 3x + 3)^2 - 4(1x^2 + 3x + 3)) - 2)/(2(1(1x^2 + 3x + 3)^2 - 4(1x^2 + 3x + 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 extremum of the function f(x) = -2|(-3|(4(2x^2 - 2x + 5)^2 + 4(2x^2 - 2x + 5) - 2) - 2| - 1)| - 1 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local extremum of the function f(x) = -4(-1|((-2(3x^2 + 3x + 2) - 1)/(2(3x^2 + 3x + 2) - 1)) - 1| - 3) - 3 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local extremum with the largest y-value of the function f(x) = -2e^(-2(5(-2(5x^2 + 1x - 4)^2 + 3(5x^2 + 1x - 4) + 1)^2 - 4(-2(5x^2 + 1x - 4)^2 + 3(5x^2 + 1x - 4) + 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 leftmost local maximum of the function f(x) = 2sin(2\u03c0(-1((-3(-1x + 3) + 1)/(3(-1x + 3) - 2))^2 + 1((-3(-1x + 3) + 1)/(3(-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": "1", "dataset": "MATH"}
{"messages": [{"content": "How many local maxima does the function f(x) = 1e^(-2((-1(-1|(2|x - 3| - 3) - 1| - 3) + 3)/(2(-1|(2|x - 3| - 3) - 1| - 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 average of all x-coordinates of local extrema of the function f(x) = (-1(-2e^(2(-3((2x + 3)/(1x - 2)) - 3)) + 3) - 2)/(-3(-2e^(2(-3((2x + 3)/(1x - 2)) - 3)) + 3) - 2) in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local minimum of the function f(x) = (-1(4(-3e^(-1((-1x + 2)/(-3x - 1))) + 2)^2 + 2(-3e^(-1((-1x + 2)/(-3x - 1))) + 2)) - 2)/(2(4(-3e^(-1((-1x + 2)/(-3x - 1))) + 2)^2 + 2(-3e^(-1((-1x + 2)/(-3x - 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) = -1(2cos(2\u03c0(-3(-1|x - 3| - 1)^2 + 5(-1|x - 3| - 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": "-10", "dataset": "MATH"}
{"messages": [{"content": "Find the average of all x-coordinates of local extrema of the function f(x) = 2e^(-2(-3|(5(3x^2 - 2x - 1)^2 - 4(3x^2 - 2x - 1) - 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 maximum of the function f(x) = 4((-1(2|(1|x - 1|) - 3| - 2))/(-2(2|(1|x - 1|) - 3| - 2) + 3))^2 - 1((-1(2|(1|x - 1|) - 3| - 2))/(-2(2|(1|x - 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": "4", "dataset": "MATH"}
{"messages": [{"content": "How many local extrema (both minima and maxima) does the function f(x) = -3((3(3cos(3\u03c0(2|x + 2| + 3) + 2) - 2) + 1)/(-2(3cos(3\u03c0(2|x + 2| + 3) + 2) - 2)))^2 - 3((3(3cos(3\u03c0(2|x + 2| + 3) + 2) - 2) + 1)/(-2(3cos(3\u03c0(2|x + 2| + 3) + 2) - 2))) + 4 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "249", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the rightmost local minimum of the function f(x) = 3(2(1cos(2\u03c0((1x - 1)/(-1x + 2))) + 3)^2 + 4(1cos(2\u03c0((1x - 1)/(-1x + 2))) + 3) - 5)^2 - 3(2(1cos(2\u03c0((1x - 1)/(-1x + 2))) + 3)^2 + 4(1cos(2\u03c0((1x - 1)/(-1x + 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": "4", "dataset": "MATH"}
{"messages": [{"content": "Find the average of all x-coordinates of local minima of the function f(x) = 2|(1e^(-2(-1(-3x - 3)^2 + 5(-3x - 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) = -3(1e^(-2((1(-5x^2 - 3x + 4) - 2)/(-2(-5x^2 - 3x + 4) + 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 local maximum of the function f(x) = (-1((-2((3(1x^2 + 4x - 3) + 1)/(3(1x^2 + 4x - 3) + 3)) + 1)/(2((3(1x^2 + 4x - 3) + 1)/(3(1x^2 + 4x - 3) + 3)) + 1)) - 2)/(2((-2((3(1x^2 + 4x - 3) + 1)/(3(1x^2 + 4x - 3) + 3)) + 1)/(2((3(1x^2 + 4x - 3) + 1)/(3(1x^2 + 4x - 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": "Find the x-coordinate of the local minimum of the function f(x) = (-2((-1(3((-1x - 3)/(-3x - 2))^2 + 3((-1x - 3)/(-3x - 2)) + 5) + 1)/(-3(3((-1x - 3)/(-3x - 2))^2 + 3((-1x - 3)/(-3x - 2)) + 5) - 2)) + 3)/(1((-1(3((-1x - 3)/(-3x - 2))^2 + 3((-1x - 3)/(-3x - 2)) + 5) + 1)/(-3(3((-1x - 3)/(-3x - 2))^2 + 3((-1x - 3)/(-3x - 2)) + 5) - 2)) + 1) in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-1", "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(2\u03c0(3|x - 2| + 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": "-10", "dataset": "MATH"}
{"messages": [{"content": "How many local minima does the function f(x) = 2|(-1|((-1(3cos(1\u03c0x + 3) - 3) + 1)/(1(3cos(1\u03c0x + 3) - 3))) + 2| - 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 local extremum with the largest y-value of the function f(x) = (1(2(1|(3|x + 2|) - 3| + 1)^2 - 3(1|(3|x + 2|) - 3| + 1)) + 1)/(1(2(1|(3|x + 2|) - 3| + 1)^2 - 3(1|(3|x + 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 local extremum with the smallest y-value of the function f(x) = -3|(-1|(1sin(2\u03c0(-4x^2 - 3x + 2) - 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 average of all x-coordinates of local extrema of the function f(x) = -4((-3(3(-1x^2 - 3x + 1)^2 - 4(-1x^2 - 3x + 1) + 3) + 1)/(-1(3(-1x^2 - 3x + 1)^2 - 4(-1x^2 - 3x + 1) + 3) - 1))^2 + 3((-3(3(-1x^2 - 3x + 1)^2 - 4(-1x^2 - 3x + 1) + 3) + 1)/(-1(3(-1x^2 - 3x + 1)^2 - 4(-1x^2 - 3x + 1) + 3) - 1)) - 1 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-1", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the leftmost local maximum of the function f(x) = 2|(-1|(-5(-1e^(2x) + 1)^2 - 1(-1e^(2x) + 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 rightmost local minimum of the function f(x) = (-2(-1|(-2cos(3\u03c0(4x - 1) + 2) - 2) + 2| + 2) + 3)/(-1(-1|(-2cos(3\u03c0(4x - 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": "10", "dataset": "MATH"}
{"messages": [{"content": "How many local maxima does the function f(x) = 2(-3e^(2(2|(-3|x + 3| + 2)| + 1)) - 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 of the function f(x) = -5(2(-2|(1x^2 + 5x - 3) - 2| + 1)^2 - 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": "-2", "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(4x - 1) + 3) - 2)/(-1(-3(4x - 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 average of all x-coordinates of local extrema of the function f(x) = (2(2((-2(1x - 2) + 3)/(2(1x - 2) - 1))^2 - 5((-2(1x - 2) + 3)/(2(1x - 2) - 1)) - 3) - 2)/(3(2((-2(1x - 2) + 3)/(2(1x - 2) - 1))^2 - 5((-2(1x - 2) + 3)/(2(1x - 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": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the rightmost local extremum of the function f(x) = -1|(1(-1(-1cos(3\u03c0x + 1) + 3)^2 - 5) - 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": "10", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local maximum with the smallest y-value of the function f(x) = -3(2(1(3cos(3\u03c0x) - 3)^2 + 4(3cos(3\u03c0x) - 3) - 1)^2 + 5(1(3cos(3\u03c0x) - 3)^2 + 4(3cos(3\u03c0x) - 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": "-10", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local minimum with the largest y-value of the function f(x) = (-3(4(1sin(1\u03c0(-3|x - 3|) - 3) - 1) - 3) + 2)/(1(4(1sin(1\u03c0(-3|x - 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": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local minimum with the smallest y-value of the function f(x) = -1(-3((-3(1sin(1\u03c0x - 1) - 3) + 1)/(3(1sin(1\u03c0x - 1) - 3) + 3)))^2 + 2(-3((-3(1sin(1\u03c0x - 1) - 3) + 1)/(3(1sin(1\u03c0x - 1) - 3) + 3))) + 3 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-9", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the leftmost local minimum of the function f(x) = 2cos(1\u03c0(-1(-2|(3x - 5) + 3| - 1)^2 - 3(-2|(3x - 5) + 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": "-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(-2|(-1x^2 + 2x) + 1| - 3) - 5)^2 + 1(-3(-2|(-1x^2 + 2x) + 1| - 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": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the rightmost local extremum of the function f(x) = 3|(-2|(2sin(1\u03c0((-3x + 3)/(2x - 1)) + 2) - 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": "3", "dataset": "MATH"}
{"messages": [{"content": "How many local maxima does the function f(x) = 2|((1(-5(-1|x + 2| + 2) + 3) - 3)/(-1(-5(-1|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 extrema (both minima and maxima) does the function f(x) = (3(1e^(-2((-3(2|x| - 1) - 2)/(3(2|x| - 1) - 1)))) - 2)/(-3(1e^(-2((-3(2|x| - 1) - 2)/(3(2|x| - 1) - 1)))) - 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": "How many local minima does the function f(x) = -3((-3((1((-2x - 2)/(-2x + 3)) - 1)/(3((-2x - 2)/(-2x + 3)) + 2)) - 3)/(-1((1((-2x - 2)/(-2x + 3)) - 1)/(3((-2x - 2)/(-2x + 3)) + 2)) + 2))^2 + 3((-3((1((-2x - 2)/(-2x + 3)) - 1)/(3((-2x - 2)/(-2x + 3)) + 2)) - 3)/(-1((1((-2x - 2)/(-2x + 3)) - 1)/(3((-2x - 2)/(-2x + 3)) + 2)) + 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 extremum with the smallest y-value of the function f(x) = (2(-1(-3|((3x)/(2x - 1)) - 2|)^2 - 1(-3|((3x)/(2x - 1)) - 2|) - 5) + 1)/(-1(-1(-3|((3x)/(2x - 1)) - 2|)^2 - 1(-3|((3x)/(2x - 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": "0", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the leftmost local extremum of the function f(x) = -1(1(4(3|x - 1| - 2)^2 - 1(3|x - 1| - 2)) + 5)^2 - 4(1(4(3|x - 1| - 2)^2 - 1(3|x - 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 average of all x-coordinates of local extrema of the function f(x) = 5(1sin(3\u03c0(-2|(-4x + 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": "How many local maxima does the function f(x) = 3(5((-2(4x^2 - 4x - 5) + 2)/(-2(4x^2 - 4x - 5)))^2 - 5((-2(4x^2 - 4x - 5) + 2)/(-2(4x^2 - 4x - 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": "How many local minima does the function f(x) = 3(-4(-3e^(-1((2x - 3)/(3x - 1))) + 1)^2 - 4(-3e^(-1((2x - 3)/(3x - 1))) + 1) - 2)^2 + 1(-4(-3e^(-1((2x - 3)/(3x - 1))) + 1)^2 - 4(-3e^(-1((2x - 3)/(3x - 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 extrema of the function f(x) = 3cos(3\u03c0((3(-2(-1x^2 - 5x - 1) - 2) - 1)/(-3(-2(-1x^2 - 5x - 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": "-2", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the leftmost local minimum of the function f(x) = -3sin(3\u03c0(-1|(-1(-2|x + 2| - 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": "-10", "dataset": "MATH"}
{"messages": [{"content": "How many local maxima does the function f(x) = -4(4((2(4x^2 - 4x + 4) - 1)/(-3(4x^2 - 4x + 4) + 2)) + 1)^2 - 5(4((2(4x^2 - 4x + 4) - 1)/(-3(4x^2 - 4x + 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": "Find the x-coordinate of the leftmost local maximum of the function f(x) = 1(-3cos(1\u03c0(4(5x^2 + 1x + 2)^2 + 4(5x^2 + 1x + 2) + 3)) - 1)^2 - 3(-3cos(1\u03c0(4(5x^2 + 1x + 2)^2 + 4(5x^2 + 1x + 2) + 3)) - 1) - 3 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-3", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the rightmost local maximum of the function f(x) = -2(-1|(-1cos(3\u03c0(-1x - 3) + 3) + 3)| - 3)^2 - 2(-1|(-1cos(3\u03c0(-1x - 3) + 3) + 3)| - 3) + 5 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "Find the average of all x-coordinates of local extrema of the function f(x) = 2sin(3\u03c0(-2|(-1(-1x - 5)^2 - 1(-1x - 5) + 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": "Find the x-coordinate of the leftmost local extremum of the function f(x) = -1|(-1((-2(5x - 5) - 1)/(-2(5x - 5) - 3))^2 - 2((-2(5x - 5) - 1)/(-2(5x - 5) - 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": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the average of all x-coordinates of local extrema of the function f(x) = -3|((-2(3|(3cos(1\u03c0x - 3) - 1) - 2|))/(1(3|(3cos(1\u03c0x - 3) - 1) - 2|) + 2)) + 1| in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "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(1sin(3\u03c0x - 3) - 3) + 3)) + 2)/(-2(-1(-2(1sin(3\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 rightmost local extremum of the function f(x) = (-2(-3|(-1|(-5x + 5)| + 3) - 1| - 1) - 2)/(-1(-3|(-1|(-5x + 5)| + 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 local maximum with the smallest y-value of the function f(x) = (2(1e^(2(2((-1x - 3)/(2x + 3)) - 3))) + 2)/(-1(1e^(2(2((-1x - 3)/(2x + 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 leftmost local extremum of the function f(x) = 1(1cos(2\u03c0((-2((1x + 1)/(-2x + 1)) - 2)/(-1((1x + 1)/(-2x + 1))))) - 2) - 1 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-7", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the leftmost local maximum of the function f(x) = 2(1cos(2\u03c0(1|((-2x + 3)/(1x + 2)) + 2|) - 3) - 2)^2 + 4(1cos(2\u03c0(1|((-2x + 3)/(1x + 2)) + 2|) - 3) - 2) - 2 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-9", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local maximum with the largest y-value of the function f(x) = -5(-2cos(1\u03c0(5(-1|x - 1| + 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": "How many local extrema (both minima and maxima) does the function f(x) = -2|(1e^(2(2|(1|x - 2|)| - 3)) - 3) - 1| - 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 rightmost local maximum of the function f(x) = -4(1sin(3\u03c0((-2(2|x + 1| - 3) + 3)/(-3(2|x + 1| - 3) + 2)) - 1) - 1)^2 - 5(1sin(3\u03c0((-2(2|x + 1| - 3) + 3)/(-3(2|x + 1| - 3) + 2)) - 1) - 1) - 4 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local maximum of the function f(x) = 3(-4(-1e^(1((1x - 3)/(-3x + 4)))) + 1)^2 - 4(-4(-1e^(1((1x - 3)/(-3x + 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 average of all x-coordinates of local extrema of the function f(x) = -3|((1(1|(1sin(1\u03c0x + 2) - 2) + 3| - 3) + 2)/(2(1|(1sin(1\u03c0x + 2) - 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": "0", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the leftmost local maximum of the function f(x) = -1|(-4(2cos(2\u03c0(-3|x - 2| - 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": "Find the x-coordinate of the local extremum of the function f(x) = 1(-2(-3|(2e^(2x) + 1) - 3| - 2))^2 + 2(-2(-3|(2e^(2x) + 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 average of all x-coordinates of local maxima of the function f(x) = 1|(3(1(3cos(3\u03c0x - 1)) - 5) - 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 local minimum with the largest y-value of the function f(x) = (1((1(-3sin(2\u03c0(-2|x + 1| + 3)) + 2) + 3)/(-2(-3sin(2\u03c0(-2|x + 1| + 3)) + 2) + 1)))/(-2((1(-3sin(2\u03c0(-2|x + 1| + 3)) + 2) + 3)/(-2(-3sin(2\u03c0(-2|x + 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": "-10", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the rightmost local minimum of the function f(x) = -2|(3(2((-3x)/(-2x - 1))^2 - 1((-3x)/(-2x - 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": "Find the x-coordinate of the leftmost local minimum of the function f(x) = 3cos(3\u03c0(-3(1|(-2x) - 3| - 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": "-10", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local minimum of the function f(x) = 2(3|(2|(-5x^2 - 1x - 5) - 3| + 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": "0", "dataset": "MATH"}
{"messages": [{"content": "How many local maxima does the function f(x) = 2(-1|(-2((2x - 2)/(-1x - 2)) - 1) - 1| - 1)^2 + 5(-1|(-2((2x - 2)/(-1x - 2)) - 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 average of all x-coordinates of local maxima of the function f(x) = (-1(1sin(2\u03c0(-4(1|x - 1| + 1) - 2) + 1) - 1) - 2)/(2(1sin(2\u03c0(-4(1|x - 1| + 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": "0", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local maximum with the smallest y-value of the function f(x) = -3sin(2\u03c0((-3(-5(3x + 2) - 3))/(2(-5(3x + 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": "-2", "dataset": "MATH"}
{"messages": [{"content": "How many local maxima does the function f(x) = 1|(-2|(2(5x + 5)^2 + 2(5x + 5) - 2) + 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 rightmost local extremum of the function f(x) = (-1(2(-4(-2e^(-2x))^2 + 2) - 3) + 3)/(-1(2(-4(-2e^(-2x))^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": "-8", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local maximum of the function f(x) = 1(-3e^(2((-1(-1x^2 + 2x - 3))/(-3(-1x^2 + 2x - 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 maxima of the function f(x) = (-1(-1sin(2\u03c0(2(-3x^2 + 5x - 3) + 3) + 1) + 1) - 2)/(2(-1sin(2\u03c0(2(-3x^2 + 5x - 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 smallest y-value of the function f(x) = -1sin(2\u03c0(1(-3((2x)/(-2x - 3)) + 5)^2 + 2(-3((2x)/(-2x - 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": "-10", "dataset": "MATH"}
{"messages": [{"content": "Find the average of all x-coordinates of local extrema of the function f(x) = 3((3(-5(1x + 4)^2 + 4(1x + 4) + 2) + 2)/(-2(-5(1x + 4)^2 + 4(1x + 4) + 2) + 3))^2 - 1((3(-5(1x + 4)^2 + 4(1x + 4) + 2) + 2)/(-2(-5(1x + 4)^2 + 4(1x + 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": "-3", "dataset": "MATH"}
{"messages": [{"content": "How many local maxima does the function f(x) = 3|((2(2|(-1x^2 + 4x + 2) + 3| - 2) + 2)/(1(2|(-1x^2 + 4x + 2) + 3| - 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 local extremum of the function f(x) = 1e^(-1(2|(5(5x + 5)^2 - 4(5x + 5) + 5) - 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 average of all x-coordinates of local extrema of the function f(x) = 4((-1(-1|(1cos(3\u03c0x - 1)) - 3| - 1) - 2)/(-3(-1|(1cos(3\u03c0x - 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": "0", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local extremum of the function f(x) = 2(4(2|((1x - 2)/(1x - 3)) + 1| + 3)^2 - 5(2|((1x - 2)/(1x - 3)) + 1| + 3) - 1)^2 - 4(4(2|((1x - 2)/(1x - 3)) + 1| + 3)^2 - 5(2|((1x - 2)/(1x - 3)) + 1| + 3) - 1) - 3 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "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((2(-1x^2 - 1x - 5) - 3)/(1(-1x^2 - 1x - 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": "-2", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the rightmost local minimum of the function f(x) = 5(1(3cos(1\u03c0(-1x^2 - 3x + 4) + 3))^2 + 1(3cos(1\u03c0(-1x^2 - 3x + 4) + 3)) - 2)^2 + 2(1(3cos(1\u03c0(-1x^2 - 3x + 4) + 3))^2 + 1(3cos(1\u03c0(-1x^2 - 3x + 4) + 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": "10", "dataset": "MATH"}
{"messages": [{"content": "How many local minima does the function f(x) = 2|(2(-2|(-4x - 5)|)^2 - 1(-2|(-4x - 5)|) + 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 rightmost local extremum of the function f(x) = 2|(5(-4(-1sin(2\u03c0x - 1) + 3) - 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": "10", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local minimum with the largest y-value of the function f(x) = 2((-2(3e^(-2(-1x^2 + 5x - 5)) - 3) + 1)/(-3(3e^(-2(-1x^2 + 5x - 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": "-5", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the rightmost local extremum of the function f(x) = (2(4(4(4x^2 - 4x - 5)^2 + 5(4x^2 - 4x - 5) - 2)^2 + 5(4(4x^2 - 4x - 5)^2 + 5(4x^2 - 4x - 5) - 2) - 4) - 3)/(-3(4(4(4x^2 - 4x - 5)^2 + 5(4x^2 - 4x - 5) - 2)^2 + 5(4(4x^2 - 4x - 5)^2 + 5(4x^2 - 4x - 5) - 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": "10", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local maximum of the function f(x) = 1(2|(5(-1x^2 - 1x + 2) - 4)| - 1)^2 + 5(2|(5(-1x^2 - 1x + 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|(3sin(2\u03c0(-5(1x) - 1) - 2))| - 2 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-10", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local extremum with the largest y-value of the function f(x) = -4(2e^(-1(2|((1x + 3)/(-1x + 2)) + 3|)) - 3)^2 - 4(2e^(-1(2|((1x + 3)/(-1x + 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": "4", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local maximum of the function f(x) = (-2(-1(-3|(5x^2 + 5x - 5) - 2|)^2 - 3(-3|(5x^2 + 5x - 5) - 2|)) + 1)/(2(-1(-3|(5x^2 + 5x - 5) - 2|)^2 - 3(-3|(5x^2 + 5x - 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 local minimum with the largest y-value of the function f(x) = -1|(-3cos(2\u03c0(-2((3x + 3)/(-1x + 2))^2 - 3((3x + 3)/(-1x + 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": "-10", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local maximum with the smallest y-value of the function f(x) = -4(-2|(-2((2x - 2)/(-2x - 3))^2 - 5((2x - 2)/(-2x - 3)) + 4)|)^2 + 3(-2|(-2((2x - 2)/(-2x - 3))^2 - 5((2x - 2)/(-2x - 3)) + 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": "-3", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local extremum of the function f(x) = 1|((-2(1(-5x^2 - 5) - 4) + 3)/(2(1(-5x^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": "0", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local minimum of the function f(x) = 2|(-2e^(-1(5(-3x + 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": "-2", "dataset": "MATH"}
{"messages": [{"content": "How many local extrema (both minima and maxima) does the function f(x) = 3cos(1\u03c0((3(-3|(4x^2 - 4x - 4)| + 1) + 1)/(-2(-3|(4x^2 - 4x - 4)| + 1) - 3))) - 1 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "20", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local minimum with the smallest y-value of the function f(x) = -4(4(-2(-1|x - 3| + 3) - 5)^2 - 3(-2(-1|x - 3| + 3) - 5))^2 - 4(4(-2(-1|x - 3| + 3) - 5)^2 - 3(-2(-1|x - 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": "-3", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the leftmost local minimum of the function f(x) = -3((3(-2e^(-2(-1|x - 1| - 3)) + 3) + 2)/(1(-2e^(-2(-1|x - 1| - 3)) + 3)))^2 - 5((3(-2e^(-2(-1|x - 1| - 3)) + 3) + 2)/(1(-2e^(-2(-1|x - 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 extremum of the function f(x) = -2sin(3\u03c0((-1(-2(1x^2 + 2x - 3)^2 - 3(1x^2 + 2x - 3) + 5) + 1)/(2(-2(1x^2 + 2x - 3)^2 - 3(1x^2 + 2x - 3) + 5) - 1)) + 2) - 3 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local extremum with the largest y-value of the function f(x) = (-2(2(-2cos(3\u03c0(-2|x + 3| + 3) + 3)) - 3) + 2)/(-3(2(-2cos(3\u03c0(-2|x + 3| + 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 extremum with the smallest y-value of the function f(x) = -2|(-3(-5(1x^2 - 5x - 4) + 3)^2 - 3(-5(1x^2 - 5x - 4) + 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": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the rightmost local maximum of the function f(x) = -2(-1cos(1\u03c0(-3((-2x - 2)/(1x)) + 1)) + 2)^2 + 5(-1cos(1\u03c0(-3((-2x - 2)/(1x)) + 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 extrema of the function f(x) = -1(-3((-3(-1x - 3) + 3)/(2(-1x - 3)))^2 - 2)^2 + 4(-3((-3(-1x - 3) + 3)/(2(-1x - 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": "-4", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the rightmost local extremum of the function f(x) = (-1(2e^(-1(-2(3|x - 1|) + 4)) + 2) - 2)/(-1(2e^(-1(-2(3|x - 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": "7", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local minimum with the smallest y-value of the function f(x) = -2e^(-2(-2|((-3(-5x^2 + 2x + 3))/(1(-5x^2 + 2x + 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 maximum of the function f(x) = -5(4(1sin(1\u03c0(2|x + 3| - 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": "10", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local maximum of the function f(x) = (-1(-3|(3((1x - 1)/(2x - 3))^2 + 5((1x - 1)/(2x - 3))) + 3|))/(1(-3|(3((1x - 1)/(2x - 3))^2 + 5((1x - 1)/(2x - 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": "How many local minima does the function f(x) = (-1(3(-3((1x + 2)/(3x - 2))^2 - 2)^2 - 4(-3((1x + 2)/(3x - 2))^2 - 2) + 5) + 3)/(2(3(-3((1x + 2)/(3x - 2))^2 - 2)^2 - 4(-3((1x + 2)/(3x - 2))^2 - 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 x-coordinate of the leftmost local maximum of the function f(x) = -4(-1|(2(5x^2 - 4x - 2)^2 - 4(5x^2 - 4x - 2) - 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 local minimum of the function f(x) = (-1(2cos(3\u03c0(-3((-1x)/(2x + 1))^2 + 2((-1x)/(2x + 1))) + 2) - 3) - 2)/(-3(2cos(3\u03c0(-3((-1x)/(2x + 1))^2 + 2((-1x)/(2x + 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 rightmost local maximum of the function f(x) = -2|((-1(3cos(1\u03c0(1|x + 1| + 3) - 2) - 1))/(-2(3cos(1\u03c0(1|x + 1| + 3) - 2) - 1) + 1)) - 2| + 1 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local maximum with the largest y-value of the function f(x) = (1(-1e^(-1(-3((-3x - 3)/(-1x + 2))^2 + 2((-3x - 3)/(-1x + 2)) - 1)) - 2) + 2)/(-3(-1e^(-1(-3((-3x - 3)/(-1x + 2))^2 + 2((-3x - 3)/(-1x + 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 average of all x-coordinates of local extrema of the function f(x) = -3(-3(-3cos(2\u03c0(1|x + 1| - 3)) + 3)^2 + 2(-3cos(2\u03c0(1|x + 1| - 3)) + 3)) - 5 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}
{"messages": [{"content": "Find the average of all x-coordinates of local extrema of the function f(x) = 2(-1|(-3(4x + 5)^2 + 4(4x + 5) + 2) - 2| - 3)^2 - 5(-1|(-3(4x + 5)^2 + 4(4x + 5) + 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 average of all x-coordinates of local minima of the function f(x) = -2cos(2\u03c0((2(-5(1|x + 3| - 1) + 4) - 2)/(1(-5(1|x + 3| - 1) + 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": "-3", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local maximum of the function f(x) = (-1(-3|(4(-2x^2 + 2x)^2 + 4(-2x^2 + 2x) + 3) - 2| - 1) + 2)/(3(-3|(4(-2x^2 + 2x)^2 + 4(-2x^2 + 2x) + 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": "How many local maxima does the function f(x) = 1(1(1|(-2|x + 2| - 1) + 3| + 1)^2 - 4(1|(-2|x + 2| - 1) + 3| + 1) - 5) + 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 minima of the function f(x) = (3(-3|(-1|(2sin(2\u03c0x - 3) - 1) - 1| + 2) - 1| - 2) + 2)/(-2(-3|(-1|(2sin(2\u03c0x - 3) - 1) - 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 of the function f(x) = (1(-5(4(-1e^(-1x) + 1)^2 - 3) - 3) - 1)/(-1(-5(4(-1e^(-1x) + 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": "0", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local maximum with the smallest y-value of the function f(x) = 3(4(-2(-2|x + 2| + 1)^2 - 2(-2|x + 2| + 1) + 3) + 3)^2 + 3(4(-2(-2|x + 2| + 1)^2 - 2(-2|x + 2| + 1) + 3) + 3) - 4 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-3", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the leftmost local extremum of the function f(x) = (-2(1sin(3\u03c0(-3(1x) + 2) + 3) - 1) + 2)/(-1(1sin(3\u03c0(-3(1x) + 2) + 3) - 1) - 3) in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-10", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local maximum of the function f(x) = -4(3|(-2sin(1\u03c0(-1x^2 - 3x - 2)) + 2) - 3| - 3) - 5 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-10", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local minimum of the function f(x) = -1((-3(4((-3x + 3)/(2x + 1))^2 - 5((-3x + 3)/(2x + 1)) + 2) - 1)/(-3(4((-3x + 3)/(2x + 1))^2 - 5((-3x + 3)/(2x + 1)) + 2) - 3))^2 + 5((-3(4((-3x + 3)/(2x + 1))^2 - 5((-3x + 3)/(2x + 1)) + 2) - 1)/(-3(4((-3x + 3)/(2x + 1))^2 - 5((-3x + 3)/(2x + 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) = 1|(3|(-3e^(-2(-2|x - 2| - 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": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the average of all x-coordinates of local extrema of the function f(x) = 1e^(1((-3((-1(3x^2 - 2x - 2) - 2)/(3(3x^2 - 2x - 2) + 1)) + 2)/(-3((-1(3x^2 - 2x - 2) - 2)/(3(3x^2 - 2x - 2) + 1)) - 2))) - 1 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local maximum with the largest y-value of the function f(x) = -2cos(3\u03c0((-3(-2(2|x + 2| + 1) + 1) + 3)/(-1(-2(2|x + 2| + 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": "-6", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the leftmost local minimum of the function f(x) = -1|(-2(1sin(3\u03c0(1x - 1) + 3))^2 + 3(1sin(3\u03c0(1x - 1) + 3)) + 1) - 3| in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-10", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the rightmost local minimum of the function f(x) = 2|(-4((2((2x)/(2x - 3)) + 1)/(2((2x)/(2x - 3)) + 2))^2 - 4((2((2x)/(2x - 3)) + 1)/(2((2x)/(2x - 3)) + 2)) - 3) - 2| + 1 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local extremum with the smallest y-value of the function f(x) = 1|(-1(-2cos(2\u03c0(4x^2 + 1x - 4) + 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": "Find the x-coordinate of the local minimum of the function f(x) = (-2(-1|(-4((1x - 2)/(3x)) - 4)|) + 2)/(-2(-1|(-4((1x - 2)/(3x)) - 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 with the smallest y-value of the function f(x) = 3|(4(-1sin(1\u03c0((-2x)/(1x + 2)) - 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": "-5", "dataset": "MATH"}
{"messages": [{"content": "How many local minima does the function f(x) = (-3(3|((-1(2x + 3) + 1)/(-1(2x + 3) + 3)) - 1| + 1) + 3)/(-3(3|((-1(2x + 3) + 1)/(-1(2x + 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": "How many local maxima does the function f(x) = -1(2|(-5(2x^2 + 2x - 5)^2 - 3(2x^2 + 2x - 5) + 3) - 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) = -3e^(-2(3|(4(2x^2 + 4x + 1)^2 + 5(2x^2 + 4x + 1)) + 1| - 1)) + 1 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the rightmost local minimum of the function f(x) = 5(1(-4((3x + 2)/(-1x))^2 + 1((3x + 2)/(-1x)))^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 average of all x-coordinates of local extrema of the function f(x) = 2|(-1|(-1(3|x + 1| - 3)^2 - 5(3|x + 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": "-1", "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|(-2cos(3\u03c0x - 1) - 1)| + 2) - 3| - 3) - 2 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-10", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the rightmost local maximum of the function f(x) = 3|(-1cos(2\u03c0(-4(2|x - 3| + 1) + 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": "10", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local maximum with the largest y-value of the function f(x) = (-3(2cos(2\u03c0(3|(-3x + 5) + 1| + 3) + 3) + 3) + 2)/(-2(2cos(2\u03c0(3|(-3x + 5) + 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": "-10", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the leftmost local extremum of the function f(x) = 2|(3|(-2|(-2x^2 - 3x - 1) + 3| - 1) - 3| - 1) - 1| - 2 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-1", "dataset": "MATH"}
{"messages": [{"content": "How many local minima does the function f(x) = 1(4(3e^(1(-2x^2 + 4x - 4)) + 3)^2 + 1(3e^(1(-2x^2 + 4x - 4)) + 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 minimum with the largest y-value of the function f(x) = 1(-3|(1|(1sin(3\u03c0x - 3)) + 1| + 2) + 1| + 1)^2 + 2(-3|(1|(1sin(3\u03c0x - 3)) + 1| + 2) + 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 extremum with the smallest y-value of the function f(x) = 5((3(4(3cos(2\u03c0x - 3) + 2)^2 - 5(3cos(2\u03c0x - 3) + 2) + 5) - 3)/(2(4(3cos(2\u03c0x - 3) + 2)^2 - 5(3cos(2\u03c0x - 3) + 2) + 5) + 3))^2 - 2((3(4(3cos(2\u03c0x - 3) + 2)^2 - 5(3cos(2\u03c0x - 3) + 2) + 5) - 3)/(2(4(3cos(2\u03c0x - 3) + 2)^2 - 5(3cos(2\u03c0x - 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": "-10", "dataset": "MATH"}
{"messages": [{"content": "How many local minima does the function f(x) = 1(3cos(2\u03c0((-2(5x^2 + 5) - 1)/(3(5x^2 + 5) - 2))) + 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 rightmost local maximum of the function f(x) = (2(-5(2e^(1(1x^2 + 4x + 3)) + 2) - 5) + 2)/(-2(-5(2e^(1(1x^2 + 4x + 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": "4", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local maximum with the largest y-value of the function f(x) = -3(3(-3(-1cos(3\u03c0x - 3) - 3) - 2) + 5)^2 + 4(3(-3(-1cos(3\u03c0x - 3) - 3) - 2) + 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": "-9", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local extremum of the function f(x) = (1(-1(3|((-1x - 2)/(2x + 1)) + 1| + 3)^2 - 2(3|((-1x - 2)/(2x + 1)) + 1| + 3) - 4) - 2)/(2(-1(3|((-1x - 2)/(2x + 1)) + 1| + 3)^2 - 2(3|((-1x - 2)/(2x + 1)) + 1| + 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 minima of the function f(x) = 1sin(1\u03c0(-3|(2|((-3x)/(-2x - 1)) - 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 rightmost local extremum of the function f(x) = 1(2(-2(-3sin(1\u03c0x + 2) - 2)^2 - 1(-3sin(1\u03c0x + 2) - 2) - 1)^2 + 1(-2(-3sin(1\u03c0x + 2) - 2)^2 - 1(-3sin(1\u03c0x + 2) - 2) - 1) - 3) - 2 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "How many local maxima does the function f(x) = 4(2((-1(1x^2 - 3x - 5) - 1)/(-2(1x^2 - 3x - 5) + 1))^2 - 2((-1(1x^2 - 3x - 5) - 1)/(-2(1x^2 - 3x - 5) + 1)))^2 + 5(2((-1(1x^2 - 3x - 5) - 1)/(-2(1x^2 - 3x - 5) + 1))^2 - 2((-1(1x^2 - 3x - 5) - 1)/(-2(1x^2 - 3x - 5) + 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": "Find the x-coordinate of the leftmost local extremum of the function f(x) = -1(2sin(2\u03c0(-2|(1x + 5) - 2|) + 2) + 1)^2 - 4(2sin(2\u03c0(-2|(1x + 5) - 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": "-10", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local maximum with the largest y-value of the function f(x) = 4(-1(-5(1cos(3\u03c0x + 3) + 1) - 5) + 3)^2 + 1(-1(-5(1cos(3\u03c0x + 3) + 1) - 5) + 3) - 1 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-10", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local minimum of the function f(x) = -1e^(-1((-3(1|(-1x^2 - 3x + 3)| - 2) - 1)/(2(1|(-1x^2 - 3x + 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": "How many local extrema (both minima and maxima) does the function f(x) = -3((-1(-1(1cos(2\u03c0x + 1) + 3)^2 + 3(1cos(2\u03c0x + 1) + 3)) - 1)/(2(-1(1cos(2\u03c0x + 1) + 3)^2 + 3(1cos(2\u03c0x + 1) + 3)))) + 3 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "40", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local maximum of the function f(x) = -2|(-2|(-5(-3|x + 2| - 2)^2 + 2(-3|x + 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": "Find the average of all x-coordinates of local maxima of the function f(x) = -3((-3(-2|((-3x + 3)/(2x + 3)) + 3| - 1) - 2)/(3(-2|((-3x + 3)/(2x + 3)) + 3| - 1) - 1))^2 - 3((-3(-2|((-3x + 3)/(2x + 3)) + 3| - 1) - 2)/(3(-2|((-3x + 3)/(2x + 3)) + 3| - 1) - 1)) + 3 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-4", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the leftmost local extremum of the function f(x) = -3e^(1(-1|(-2|(-2|x + 2| + 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": "-2", "dataset": "MATH"}
{"messages": [{"content": "How many local maxima does the function f(x) = -3|(-5(-1|(2|x| + 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) = 2(2sin(1\u03c0((2(-2x - 3) - 1)/(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 x-coordinate of the rightmost local extremum of the function f(x) = 3cos(2\u03c0(4(2|(2x + 2) + 1| + 1)^2 + 1(2|(2x + 2) + 1| + 1) - 4) + 3) - 1 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "How many local maxima does the function f(x) = (-2(2|(5(1|x + 1|)^2 - 2(1|x + 1|) + 5) - 2| - 2) - 1)/(2(2|(5(1|x + 1|)^2 - 2(1|x + 1|) + 5) - 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) = -5((1(-1(5x + 4)^2 - 1) - 3)/(3(-1(5x + 4)^2 - 1) + 1))^2 - 4((1(-1(5x + 4)^2 - 1) - 3)/(3(-1(5x + 4)^2 - 1) + 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": "Find the average of all x-coordinates of local minima of the function f(x) = -2|(1sin(2\u03c0(2(1|x + 1| + 1) + 5) + 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": "How many local maxima does the function f(x) = 2|(2((-3(-3|x| - 3) - 2)/(2(-3|x| - 3)))^2 + 1((-3(-3|x| - 3) - 2)/(2(-3|x| - 3))) + 5) - 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 of the function f(x) = (-2(-5(-1e^(1(-3|x + 1| + 3)))^2 - 4(-1e^(1(-3|x + 1| + 3))) - 3) + 2)/(2(-5(-1e^(1(-3|x + 1| + 3)))^2 - 4(-1e^(1(-3|x + 1| + 3))) - 3)) in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-1", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local extremum of the function f(x) = -3|(-5((1(-2x - 1) + 3)/(3(-2x - 1)))^2 - 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 leftmost local extremum of the function f(x) = 4((-3(2|(-3|x|) + 2| + 2) + 1)/(-3(2|(-3|x|) + 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(2|(-2|(1|x| + 2) + 2| - 1) + 2|))/(-2(2|(-2|(1|x| + 2) + 2| - 1) + 2|) + 1) have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}
{"messages": [{"content": "How many local extrema (both minima and maxima) does the function f(x) = 4(3|(1|(2|x - 2|) - 3|) - 3| - 2)^2 - 2(3|(1|(2|x - 2|) - 3|) - 3| - 2) - 1 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "How many local minima does the function f(x) = 3(-1e^(-1(-4((-2x - 2)/(1x))^2 + 1((-2x - 2)/(1x)) + 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 local extremum of the function f(x) = -2((-1(-3|((-2x + 3)/(3x + 1)) - 3| - 3))/(-3(-3|((-2x + 3)/(3x + 1)) - 3| - 3) + 1)) - 4 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the leftmost local minimum of the function f(x) = -5(1|(-1(3cos(1\u03c0x + 3) + 1)^2 - 3(3cos(1\u03c0x + 3) + 1) + 3) - 2| - 3)^2 + 2(1|(-1(3cos(1\u03c0x + 3) + 1)^2 - 3(3cos(1\u03c0x + 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": "-10", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local extremum of the function f(x) = 2e^(-2((-2((-3(-3x + 5) + 3)/(-2(-3x + 5) - 1)) + 2)/(-1((-3(-3x + 5) + 3)/(-2(-3x + 5) - 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 extremum with the smallest y-value of the function f(x) = -3|(1(-5((3x - 2)/(2x + 3))^2 - 2((3x - 2)/(2x + 3)) + 2)^2 + 3(-5((3x - 2)/(2x + 3))^2 - 2((3x - 2)/(2x + 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": "0", "dataset": "MATH"}
{"messages": [{"content": "Find the average of all x-coordinates of local minima of the function f(x) = -3(3cos(1\u03c0((-1(-3|x + 1| - 1))/(-3(-3|x + 1| - 1))) + 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": "How many local minima does the function f(x) = -1|((1(-1(3x + 3)^2 - 2(3x + 3) - 4) + 1)/(-1(-1(3x + 3)^2 - 2(3x + 3) - 4) + 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 leftmost local extremum of the function f(x) = -1(-1sin(2\u03c0(2|((2x)/(1x - 3)) + 3| + 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": "-8", "dataset": "MATH"}
{"messages": [{"content": "How many local maxima does the function f(x) = 3(2|(4((1x - 2)/(3x + 2)) + 4) - 2| + 2)^2 + 4(2|(4((1x - 2)/(3x + 2)) + 4) - 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) = 3|((1(-2(1x + 3)^2 - 4(1x + 3)) + 1)/(-2(-2(1x + 3)^2 - 4(1x + 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 minimum of the function f(x) = (2(2((-1((2x)/(2x + 2)) - 2)/(1((2x)/(2x + 2)) - 2))^2 + 2((-1((2x)/(2x + 2)) - 2)/(1((2x)/(2x + 2)) - 2)) - 3) + 1)/(3(2((-1((2x)/(2x + 2)) - 2)/(1((2x)/(2x + 2)) - 2))^2 + 2((-1((2x)/(2x + 2)) - 2)/(1((2x)/(2x + 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 local maximum with the largest y-value of the function f(x) = 3(-1cos(3\u03c0((1(3x^2 - 4) + 3)/(-2(3x^2 - 4) - 3)) - 1) - 3)^2 - 3(-1cos(3\u03c0((1(3x^2 - 4) + 3)/(-2(3x^2 - 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": "-2", "dataset": "MATH"}
{"messages": [{"content": "Find the average of all x-coordinates of local minima of the function f(x) = 4(2|((1(-4x^2 - 5x + 1) + 1)/(1(-4x^2 - 5x + 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": "-1", "dataset": "MATH"}
{"messages": [{"content": "Find the average of all x-coordinates of local extrema of the function f(x) = 1|(3((1(-2|x - 1| + 1) + 3)/(-3(-2|x - 1| + 1) + 1))^2 - 2((1(-2|x - 1| + 1) + 3)/(-3(-2|x - 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": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local minimum with the largest y-value of the function f(x) = -2|(3sin(3\u03c0(2((3x + 2)/(3x + 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 of the function f(x) = -2|(-4(-1|((3x + 1)/(-1x)) + 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": "0", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local extremum with the smallest y-value of the function f(x) = 2((3(-5((-1x)/(3x - 2))^2 - 2((-1x)/(3x - 2)) - 2) + 1)/(1(-5((-1x)/(3x - 2))^2 - 2((-1x)/(3x - 2)) - 2) - 2)) + 3 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-1", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the rightmost local minimum of the function f(x) = -1cos(3\u03c0(2|(2(3x^2 + 1x - 4)^2 - 5(3x^2 + 1x - 4) + 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": "4", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the rightmost local extremum of the function f(x) = (2(1|(2(2sin(1\u03c0x - 3) - 3) - 1) + 1| + 3))/(-1(1|(2(2sin(1\u03c0x - 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": "9", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the leftmost local extremum of the function f(x) = 2(-2|(-3e^(-2(4x + 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 maximum of the function f(x) = 3e^(-2(1(1((2x - 3)/(-1x + 3))^2 + 4((2x - 3)/(-1x + 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 average of all x-coordinates of local maxima of the function f(x) = 1(-5(2sin(3\u03c0(-1x + 2) + 1) - 2)^2 - 2(2sin(3\u03c0(-1x + 2) + 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 extremum with the smallest y-value of the function f(x) = 1|((-3(-1sin(1\u03c0(1|x - 2| + 3) + 3) + 2) + 2)/(2(-1sin(1\u03c0(1|x - 2| + 3) + 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": "-10", "dataset": "MATH"}
{"messages": [{"content": "Find the average of all x-coordinates of local maxima of the function f(x) = 2cos(1\u03c0(1|((2(1x^2 - 1x - 4) + 1)/(2(1x^2 - 1x - 4) - 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": "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(1(-5x + 2)^2 - 5(-5x + 2) + 4) - 1) + 3) - 2)/(-3(3cos(3\u03c0(1(-5x + 2)^2 - 5(-5x + 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": "0", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local minimum with the smallest y-value of the function f(x) = -4(-3cos(1\u03c0(4((3x - 3)/(2x))^2 - 4((3x - 3)/(2x)) - 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": "-7", "dataset": "MATH"}
{"messages": [{"content": "Find the average of all x-coordinates of local extrema of the function f(x) = -2(-2cos(3\u03c0(-5(2|x + 3| + 1)^2 - 1(2|x + 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": "Find the x-coordinate of the leftmost local minimum of the function f(x) = -1(2((2(1cos(3\u03c0x - 3) - 1) + 2)/(3(1cos(3\u03c0x - 3) - 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": "-9", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local maximum with the largest y-value of the function f(x) = 2(-3(-1(1sin(3\u03c0x + 3) - 1)^2 + 4(1sin(3\u03c0x + 3) - 1) + 3) - 3)^2 - 1(-3(-1(1sin(3\u03c0x + 3) - 1)^2 + 4(1sin(3\u03c0x + 3) - 1) + 3) - 3) + 4 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-10", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the rightmost local maximum of the function f(x) = 1|(3sin(3\u03c0(1|(2|x - 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": "10", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the rightmost local maximum of the function f(x) = 2cos(2\u03c0(-2(-2((-3x + 2)/(-2x + 3))^2 + 2((-3x + 2)/(-2x + 3)) + 4)^2 - 2(-2((-3x + 2)/(-2x + 3))^2 + 2((-3x + 2)/(-2x + 3)) + 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 x-coordinate of the leftmost local maximum of the function f(x) = -2(-1((-3(-5x^2 - 4x) + 1)/(-3(-5x^2 - 4x) - 2)) + 2)^2 + 5(-1((-3(-5x^2 - 4x) + 1)/(-3(-5x^2 - 4x) - 2)) + 2) + 4 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local minimum of the function f(x) = (-2(-2(-1sin(3\u03c0(-2x^2 - 1x - 3) - 2) - 2) - 5) + 3)/(-1(-2(-1sin(3\u03c0(-2x^2 - 1x - 3) - 2) - 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 rightmost local minimum of the function f(x) = -2cos(1\u03c0(3(1(-1|x| - 2)^2 + 5(-1|x| - 2) - 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 leftmost local minimum of the function f(x) = (-1(-2|(3|(5x^2 - 2x - 5) - 1| + 1) - 3| + 1) + 3)/(-2(-2|(3|(5x^2 - 2x - 5) - 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": "-1", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local minimum with the largest y-value of the function f(x) = -4(-1sin(2\u03c0(-1(-2x^2 + 1x - 2) + 1) - 1) + 1) - 3 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-10", "dataset": "MATH"}
{"messages": [{"content": "How many local maxima does the function f(x) = 3(-1(-4(-1|x + 1| + 2)^2 - 4)^2 + 3(-4(-1|x + 1| + 2)^2 - 4) + 3)^2 + 5(-1(-4(-1|x + 1| + 2)^2 - 4)^2 + 3(-4(-1|x + 1| + 2)^2 - 4) + 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 local minimum of the function f(x) = 3sin(3\u03c0((-1((-1(-5x^2 + 3x - 2) - 2)/(2(-5x^2 + 3x - 2) - 1)) - 1)/(2((-1(-5x^2 + 3x - 2) - 2)/(2(-5x^2 + 3x - 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": "0", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local minimum with the smallest y-value of the function f(x) = (3(2(1sin(2\u03c0(1|x - 1| + 3) + 2) + 3)) - 3)/(-1(2(1sin(2\u03c0(1|x - 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": "How many local maxima does the function f(x) = 1|(-3((-1(3|x - 1| - 3) - 2)/(1(3|x - 1| - 3) + 3))^2 - 1((-1(3|x - 1| - 3) - 2)/(1(3|x - 1| - 3) + 3)) - 5) + 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) = 5((-3(-2(-4x^2 + 3x + 1) + 2) - 1)/(1(-2(-4x^2 + 3x + 1) + 2)))^2 - 1((-3(-2(-4x^2 + 3x + 1) + 2) - 1)/(1(-2(-4x^2 + 3x + 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": "Find the average of all x-coordinates of local maxima of the function f(x) = 2(-1sin(3\u03c0(-1(-2|x + 3|)^2 - 2(-2|x + 3|) - 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": "0", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the rightmost local maximum of the function f(x) = -1(-2((2(-2sin(1\u03c0x - 2) + 1) + 2)/(-3(-2sin(1\u03c0x - 2) + 1)))^2 - 3((2(-2sin(1\u03c0x - 2) + 1) + 2)/(-3(-2sin(1\u03c0x - 2) + 1))) - 2)^2 + 1(-2((2(-2sin(1\u03c0x - 2) + 1) + 2)/(-3(-2sin(1\u03c0x - 2) + 1)))^2 - 3((2(-2sin(1\u03c0x - 2) + 1) + 2)/(-3(-2sin(1\u03c0x - 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": "9", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the rightmost local minimum of the function f(x) = (3(2|(2|(-4x - 1)| - 1) - 3| + 2) - 1)/(-1(2|(2|(-4x - 1)| - 1) - 3| + 2)) in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local maximum with the smallest y-value of the function f(x) = 1|(-3|(3(2x + 1)^2 - 4(2x + 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": "How many local minima does the function f(x) = -1|(5(-3|(3x^2 - 5x + 2) + 3| + 2)^2 + 2(-3|(3x^2 - 5x + 2) + 3| + 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": "How many local maxima does the function f(x) = (1(2|(5((-3x + 2)/(-2x - 1)) + 2) + 3| - 3) + 2)/(-2(2|(5((-3x + 2)/(-2x - 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": "Find the x-coordinate of the leftmost local extremum of the function f(x) = 1(-1cos(1\u03c0(-4(3|x + 3| + 1) - 3) + 1) + 2)^2 - 3(-1cos(1\u03c0(-4(3|x + 3| + 1) - 3) + 1) + 2) - 4 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-10", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local extremum of the function f(x) = (-3(-2|(5(-3x^2 - 2x - 5) + 3)| + 2) + 3)/(2(-2|(5(-3x^2 - 2x - 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": "0", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the leftmost local minimum of the function f(x) = -3|((-2(-3cos(2\u03c0(4x - 5) + 3) - 2) - 1)/(-2(-3cos(2\u03c0(4x - 5) + 3) - 2) - 2)) + 3| in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-10", "dataset": "MATH"}
{"messages": [{"content": "How many local extrema (both minima and maxima) does the function f(x) = (-3(-3|(-2|(-2x^2 - 4x + 5) - 2| - 2)| + 1) + 3)/(-1(-3|(-2|(-2x^2 - 4x + 5) - 2| - 2)| + 1) - 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 leftmost local minimum of the function f(x) = (-3((-3((-3(-2e^(-1x) - 2) - 1)/(-1(-2e^(-1x) - 2) - 2)))/(2((-3(-2e^(-1x) - 2) - 1)/(-1(-2e^(-1x) - 2) - 2)) - 1)))/(-2((-3((-3(-2e^(-1x) - 2) - 1)/(-1(-2e^(-1x) - 2) - 2)))/(2((-3(-2e^(-1x) - 2) - 1)/(-1(-2e^(-1x) - 2) - 2)) - 1))) in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-10", "dataset": "MATH"}
{"messages": [{"content": "Find the average of all x-coordinates of local minima of the function f(x) = 4((-3(4(-2|x| - 1) + 2) + 2)/(1(4(-2|x| - 1) + 2) + 3))^2 - 3((-3(4(-2|x| - 1) + 2) + 2)/(1(4(-2|x| - 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": "Find the x-coordinate of the local maximum of the function f(x) = 4(-3|(3|(-1x^2 + 5x) - 2|) + 1| - 3)^2 + 4(-3|(3|(-1x^2 + 5x) - 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": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local maximum with the largest y-value of the function f(x) = -3e^(-1(-2(-2|(4x^2 - 4x - 1) - 2|)^2 + 4(-2|(4x^2 - 4x - 1) - 2|) - 4)) - 1 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local extremum with the largest y-value of the function f(x) = -5(-1sin(3\u03c0(1|(-2x + 4) + 2| - 1) + 3) + 3)^2 + 3(-1sin(3\u03c0(1|(-2x + 4) + 2| - 1) + 3) + 3) + 1 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-10", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local minimum with the smallest y-value of the function f(x) = (3((2(2sin(1\u03c0(-2|x - 1| - 3) + 3) + 2) + 2)/(-2(2sin(1\u03c0(-2|x - 1| - 3) + 3) + 2) + 1)))/(1((2(2sin(1\u03c0(-2|x - 1| - 3) + 3) + 2) + 2)/(-2(2sin(1\u03c0(-2|x - 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": "-10", "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((-2(-5x^2 + 5x - 3) - 2)/(-3(-5x^2 + 5x - 3) - 2)) + 3) + 3) - 2)/(1(1sin(3\u03c0((-2(-5x^2 + 5x - 3) - 2)/(-3(-5x^2 + 5x - 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 leftmost local maximum of the function f(x) = (-1(-1(4(-2|x| - 2)^2 - 2(-2|x| - 2) - 1) + 4) - 1)/(3(-1(4(-2|x| - 2)^2 - 2(-2|x| - 2) - 1) + 4) + 3) in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-10", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the rightmost local extremum of the function f(x) = (-2(2((1(2|x| + 1) + 2)/(-1(2|x| + 1) + 3))^2 - 5((1(2|x| + 1) + 2)/(-1(2|x| + 1) + 3)) + 1) + 3)/(-1(2((1(2|x| + 1) + 2)/(-1(2|x| + 1) + 3))^2 - 5((1(2|x| + 1) + 2)/(-1(2|x| + 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) = -5(-1|((-2(1cos(2\u03c0x + 1) + 1) - 1)/(-2(1cos(2\u03c0x + 1) + 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": "120", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local minimum with the largest y-value of the function f(x) = (2(5((2(1sin(3\u03c0x) + 2) - 1)/(2(1sin(3\u03c0x) + 2) - 3))^2 + 1((2(1sin(3\u03c0x) + 2) - 1)/(2(1sin(3\u03c0x) + 2) - 3)) + 1) - 2)/(-2(5((2(1sin(3\u03c0x) + 2) - 1)/(2(1sin(3\u03c0x) + 2) - 3))^2 + 1((2(1sin(3\u03c0x) + 2) - 1)/(2(1sin(3\u03c0x) + 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 extrema (both minima and maxima) does the function f(x) = -5(2|(-2(2e^(-1x) - 1)^2 + 4(2e^(-1x) - 1) + 4) - 3| - 2)^2 - 4(2|(-2(2e^(-1x) - 1)^2 + 4(2e^(-1x) - 1) + 4) - 3| - 2) - 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 local extremum with the largest y-value of the function f(x) = 1|(-1(-2|(1|x + 2|) - 3|)^2 - 1(-2|(1|x + 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": "-5", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the rightmost local extremum of the function f(x) = 1|(-1cos(2\u03c0(3|(-3|x - 2| - 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": "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(3sin(2\u03c0(1|x|) + 1))^2 + 5(3sin(2\u03c0(1|x|) + 1))) in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-9", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the rightmost local extremum of the function f(x) = 3|(-5(1(-4x^2 - 5x + 2) - 3)^2 + 4(1(-4x^2 - 5x + 2) - 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": "0", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local extremum with the largest y-value of the function f(x) = 5((2(5(3x + 1)^2 - 2(3x + 1) - 5) + 3)/(-1(5(3x + 1)^2 - 2(3x + 1) - 5) - 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) = (-2((1((-1(1x^2 + 4x - 4))/(-2(1x^2 + 4x - 4) + 3)) + 1)/(-2((-1(1x^2 + 4x - 4))/(-2(1x^2 + 4x - 4) + 3)) + 3)) + 3)/(1((1((-1(1x^2 + 4x - 4))/(-2(1x^2 + 4x - 4) + 3)) + 1)/(-2((-1(1x^2 + 4x - 4))/(-2(1x^2 + 4x - 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": "-2", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the leftmost local maximum of the function f(x) = 5(-1sin(1\u03c0(-3(5x^2 + 3x + 2)^2 + 2(5x^2 + 3x + 2) - 4) - 2) - 2)^2 - 4(-1sin(1\u03c0(-3(5x^2 + 3x + 2)^2 + 2(5x^2 + 3x + 2) - 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": "-4", "dataset": "MATH"}
{"messages": [{"content": "Find the average of all x-coordinates of local minima of the function f(x) = (-3((1(2cos(1\u03c0((2x - 1)/(2x)) + 2) - 2) + 2)/(2(2cos(1\u03c0((2x - 1)/(2x)) + 2) - 2))) + 3)/(2((1(2cos(1\u03c0((2x - 1)/(2x)) + 2) - 2) + 2)/(2(2cos(1\u03c0((2x - 1)/(2x)) + 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 local maximum with the smallest y-value of the function f(x) = 1|(-1|(1(1|x + 1| - 2)^2 + 4(1|x + 1| - 2) - 5) + 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": "-1", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local extremum of the function f(x) = 3(1|(-3(-2|x - 1| - 1)^2 + 5(-2|x - 1| - 1) - 5) + 1| - 1)^2 - 4(1|(-3(-2|x - 1| - 1)^2 + 5(-2|x - 1| - 1) - 5) + 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) = -4(1(2cos(2\u03c0((-3x + 1)/(1x)) - 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": "-3", "dataset": "MATH"}
{"messages": [{"content": "How many local minima does the function f(x) = -1((1(-1|(-4x - 3) - 3| + 3) + 3)/(3(-1|(-4x - 3) - 3| + 3) - 2))^2 + 2((1(-1|(-4x - 3) - 3| + 3) + 3)/(3(-1|(-4x - 3) - 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 x-coordinate of the local minimum with the smallest y-value of the function f(x) = (-3(2|(2cos(3\u03c0(-2x^2 - 2x - 2) - 3) - 1) - 3| + 1) + 2)/(3(2|(2cos(3\u03c0(-2x^2 - 2x - 2) - 3) - 1) - 3| + 1) + 3) in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-10", "dataset": "MATH"}
{"messages": [{"content": "How many local minima does the function f(x) = (-1(5(-5(-1|x| - 2)^2 - 4(-1|x| - 2) + 3)^2 + 4) + 2)/(2(5(-5(-1|x| - 2)^2 - 4(-1|x| - 2) + 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 leftmost local minimum of the function f(x) = (1((2((2(-1sin(3\u03c0x + 1) - 2) + 2)/(-2(-1sin(3\u03c0x + 1) - 2) + 3)) - 1)/(2((2(-1sin(3\u03c0x + 1) - 2) + 2)/(-2(-1sin(3\u03c0x + 1) - 2) + 3)) + 2)) - 3)/(-3((2((2(-1sin(3\u03c0x + 1) - 2) + 2)/(-2(-1sin(3\u03c0x + 1) - 2) + 3)) - 1)/(2((2(-1sin(3\u03c0x + 1) - 2) + 2)/(-2(-1sin(3\u03c0x + 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 local minimum of the function f(x) = -3(2|(-3(-1x^2 - 4x + 4) + 1) + 1| + 1)^2 - 4(2|(-3(-1x^2 - 4x + 4) + 1) + 1| + 1) in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-2", "dataset": "MATH"}
{"messages": [{"content": "How many local extrema (both minima and maxima) does the function f(x) = 2cos(1\u03c0(-4(4(-4x + 3)^2 + 3(-4x + 3) + 5) - 2) - 2) + 3 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "352", "dataset": "MATH"}
{"messages": [{"content": "Find the average of all x-coordinates of local maxima of the function f(x) = (-3(3(-2sin(3\u03c0(-3|x + 2| + 1) - 2) - 3)^2 - 1(-2sin(3\u03c0(-3|x + 2| + 1) - 2) - 3) - 5) - 3)/(1(3(-2sin(3\u03c0(-3|x + 2| + 1) - 2) - 3)^2 - 1(-2sin(3\u03c0(-3|x + 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": "0", "dataset": "MATH"}
{"messages": [{"content": "Find the average of all x-coordinates of local extrema of the function f(x) = 2cos(2\u03c0(-1|((3(-5x + 3) - 1)/(2(-5x + 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": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the rightmost local extremum of the function f(x) = -1|(1(1((-3x + 1)/(-1x - 1))^2 + 5((-3x + 1)/(-1x - 1)) - 3)^2 + 2(1((-3x + 1)/(-1x - 1))^2 + 5((-3x + 1)/(-1x - 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": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the average of all x-coordinates of local minima of the function f(x) = (1(1(3sin(1\u03c0(-1x + 1) - 1) + 3)^2 + 1(3sin(1\u03c0(-1x + 1) - 1) + 3) - 5) - 2)/(-3(1(3sin(1\u03c0(-1x + 1) - 1) + 3)^2 + 1(3sin(1\u03c0(-1x + 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 rightmost local maximum of the function f(x) = -5(-2e^(-1(-1|(5x^2 - 4x) - 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": "How many local maxima does the function f(x) = 4((-3((1(3x - 1) + 3)/(3(3x - 1))) + 1)/(-1((1(3x - 1) + 3)/(3(3x - 1))) + 2))^2 - 1((-3((1(3x - 1) + 3)/(3(3x - 1))) + 1)/(-1((1(3x - 1) + 3)/(3(3x - 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|(2|(-2sin(2\u03c0x + 3) + 2) - 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": "-10", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the leftmost local minimum of the function f(x) = 1((2(-2(-1cos(2\u03c0x + 1) + 2) - 1) + 3)/(-3(-2(-1cos(2\u03c0x + 1) + 2) - 1) - 1)) in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-10", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the leftmost local maximum of the function f(x) = 2(-1e^(-2(-3(-2|x + 3| - 1) + 3)))^2 + 1(-1e^(-2(-3(-2|x + 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": "-5", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the leftmost local extremum of the function f(x) = -1|(2|((-1(-1x^2 - 1x + 2) - 1)/(-2(-1x^2 - 1x + 2) - 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": "-2", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the leftmost local maximum of the function f(x) = 2|(-3|(-1|(-5x^2 + 4x + 2) + 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 with the largest y-value of the function f(x) = -1|(-3cos(1\u03c0(-4((1x + 1)/(-2x)) + 2) + 3) + 2) + 2| in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-2", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the rightmost local extremum of the function f(x) = 1((-1((-3(1|x - 3| - 1))/(2(1|x - 3| - 1) + 3)) - 2)/(-1((-3(1|x - 3| - 1))/(2(1|x - 3| - 1) + 3)) + 2))^2 - 5((-1((-3(1|x - 3| - 1))/(2(1|x - 3| - 1) + 3)) - 2)/(-1((-3(1|x - 3| - 1))/(2(1|x - 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 rightmost local extremum of the function f(x) = 3(1sin(1\u03c0(-2|((2x + 2)/(-1x - 3)) - 2| - 2)))^2 + 2(1sin(1\u03c0(-2|((2x + 2)/(-1x - 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": "4", "dataset": "MATH"}
{"messages": [{"content": "How many local extrema (both minima and maxima) does the function f(x) = 4(-2sin(3\u03c0(3|(2|x + 2| + 2)| - 2) + 2) + 1)^2 - 3(-2sin(3\u03c0(3|(2|x + 2| + 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": "721", "dataset": "MATH"}
{"messages": [{"content": "How many local maxima does the function f(x) = -3sin(2\u03c0((1(-2|(-5x^2 - 1x - 2)| - 3) - 2)/(-3(-2|(-5x^2 - 1x - 2)| - 3) + 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": "Find the x-coordinate of the rightmost local minimum of the function f(x) = 1(-1|(-3|(-3sin(3\u03c0x) + 2) + 1| - 3) + 1| - 1)^2 - 2(-1|(-3|(-3sin(3\u03c0x) + 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": "10", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the leftmost local extremum of the function f(x) = -1sin(2\u03c0(-1|(-3|((-2x - 1)/(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": "-5", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the leftmost local minimum of the function f(x) = -3((-2((-1(2cos(3\u03c0x + 1) + 1) - 2)/(2(2cos(3\u03c0x + 1) + 1) - 1)) + 1)/(-2((-1(2cos(3\u03c0x + 1) + 1) - 2)/(2(2cos(3\u03c0x + 1) + 1) - 1)) - 3))^2 + 5((-2((-1(2cos(3\u03c0x + 1) + 1) - 2)/(2(2cos(3\u03c0x + 1) + 1) - 1)) + 1)/(-2((-1(2cos(3\u03c0x + 1) + 1) - 2)/(2(2cos(3\u03c0x + 1) + 1) - 1)) - 3)) + 4 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-10", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local minimum with the smallest y-value of the function f(x) = -3(3sin(1\u03c0(-1(3x^2 + 4x) + 2) + 1) + 2)^2 - 5(3sin(1\u03c0(-1(3x^2 + 4x) + 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 average of all x-coordinates of local minima of the function f(x) = 2|((-2(1(5x - 4)^2 - 4(5x - 4) + 2) - 2)/(1(1(5x - 4)^2 - 4(5x - 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 rightmost local minimum of the function f(x) = -1((-1(1e^(2(3x + 2)) - 1) + 3)/(-2(1e^(2(3x + 2)) - 1) - 1))^2 + 3((-1(1e^(2(3x + 2)) - 1) + 3)/(-2(1e^(2(3x + 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": "4", "dataset": "MATH"}
{"messages": [{"content": "Find the average of all x-coordinates of local extrema of the function f(x) = (-3((-2(-1e^(-2((2x - 2)/(-1x - 2))) + 2) + 3)/(-2(-1e^(-2((2x - 2)/(-1x - 2))) + 2) + 1)) - 3)/(2((-2(-1e^(-2((2x - 2)/(-1x - 2))) + 2) + 3)/(-2(-1e^(-2((2x - 2)/(-1x - 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": "-2", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the rightmost local maximum of the function f(x) = 2(2e^(-1(4(-3|x - 1| + 2)^2 - 4(-3|x - 1| + 2) + 1)) + 3)^2 - 2(2e^(-1(4(-3|x - 1| + 2)^2 - 4(-3|x - 1| + 2) + 1)) + 3) in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the leftmost local minimum of the function f(x) = 2|(-5(-2|(-3|x - 2| + 1) - 2| + 3)^2 + 4(-2|(-3|x - 2| + 1) - 2| + 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": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local minimum of the function f(x) = -1sin(3\u03c0((-3(3|(2|x - 1| - 3) + 3| + 3) + 1)/(2(3|(2|x - 1| - 3) + 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": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local extremum with the largest y-value of the function f(x) = (-3(2|(-5((-1x)/(-2x - 2))^2 + 3((-1x)/(-2x - 2)) - 1) - 1| - 3) + 3)/(-3(2|(-5((-1x)/(-2x - 2))^2 + 3((-1x)/(-2x - 2)) - 1) - 1| - 3) - 3) in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-1", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the leftmost local extremum of the function f(x) = 1(-1e^(-1(1(-2|x + 3| - 2)^2 + 1(-2|x + 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": "-5", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local extremum with the largest y-value of the function f(x) = -2|((-1(4((-3x - 1)/(-1x - 3))^2 - 4) - 3)/(-3(4((-3x - 1)/(-1x - 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": "0", "dataset": "MATH"}
{"messages": [{"content": "How many local minima does the function f(x) = 2|(2e^(1(-1(4x - 1)^2 - 1(4x - 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 minima does the function f(x) = -3(1(-2e^(-2((2x + 2)/(3x + 3))) + 1) - 1)^2 - 4(1(-2e^(-2((2x + 2)/(3x + 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 average of all x-coordinates of local maxima of the function f(x) = 1(-3(3|(2cos(3\u03c0x) + 1) - 2| - 1)^2 + 5(3|(2cos(3\u03c0x) + 1) - 2| - 1) - 2)^2 + 1(-3(3|(2cos(3\u03c0x) + 1) - 2| - 1)^2 + 5(3|(2cos(3\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": "0", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local extremum with the smallest y-value of the function f(x) = -5(-3|(-4((1x + 2)/(-1x + 2))^2 - 2((1x + 2)/(-1x + 2))) + 2| + 3) in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-3", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local minimum with the largest y-value of the function f(x) = -3(-3sin(2\u03c0((2((-2x + 2)/(1x - 3)) - 3)/(2((-2x + 2)/(1x - 3)) + 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": "-3", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local extremum with the largest y-value of the function f(x) = -1(-1sin(3\u03c0(1(1|x - 3| + 3)^2 - 3(1|x - 3| + 3) - 3) + 1) + 2)^2 + 2(-1sin(3\u03c0(1(1|x - 3| + 3)^2 - 3(1|x - 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": "-10", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the leftmost local extremum of the function f(x) = -2(1cos(1\u03c0(-4((-1x - 2)/(1x - 3)) - 2) + 3) - 1)^2 + 3(1cos(1\u03c0(-4((-1x - 2)/(1x - 3)) - 2) + 3) - 1) - 2 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-7", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local maximum with the smallest y-value of the function f(x) = -1cos(2\u03c0((-1(-5(4x^2 + 2x - 5)^2 - 4) - 3)/(-1(-5(4x^2 + 2x - 5)^2 - 4) + 3)) + 1) - 2 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the leftmost local extremum of the function f(x) = 1((3(-3|(1x + 3) - 1| + 3) - 2)/(-3(-3|(1x + 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 local minimum with the largest y-value of the function f(x) = -1(-2sin(2\u03c0(-1(-2|x - 3| + 3)^2 + 3(-2|x - 3| + 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": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local maximum with the largest y-value of the function f(x) = (2(-2|(1sin(2\u03c0(1x^2 + 2x + 5) - 3) - 3) - 2| - 3) - 2)/(1(-2|(1sin(2\u03c0(1x^2 + 2x + 5) - 3) - 3) - 2| - 3) - 3) in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-10", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local minimum of the function f(x) = -1|(3e^(1(-5(1x^2 + 2x - 2)^2 - 2(1x^2 + 2x - 2) - 5)) - 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) = -4(-1(2sin(3\u03c0(-1|x - 3| + 2) - 2) + 2)^2 - 3(2sin(3\u03c0(-1|x - 3| + 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 average of all x-coordinates of local extrema of the function f(x) = -3|((1(4(-1sin(3\u03c0x) - 1)^2 + 1(-1sin(3\u03c0x) - 1) - 5) + 3)/(1(4(-1sin(3\u03c0x) - 1)^2 + 1(-1sin(3\u03c0x) - 1) - 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": "0", "dataset": "MATH"}
{"messages": [{"content": "Find the average of all x-coordinates of local extrema of the function f(x) = -1|(-1cos(3\u03c0(-1(-1|x| + 3)^2 + 5(-1|x| + 3) + 1) + 2) - 3) - 2| in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the leftmost local maximum of the function f(x) = (2(-2(1sin(2\u03c0(1x^2 + 3x - 3) - 2) - 1) - 2) + 1)/(-3(-2(1sin(2\u03c0(1x^2 + 3x - 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": "-10", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the leftmost local minimum of the function f(x) = 5(5(1cos(2\u03c0(1|x - 1| - 2)) - 1)^2 + 5(1cos(2\u03c0(1|x - 1| - 2)) - 1) + 1)^2 - 1(5(1cos(2\u03c0(1|x - 1| - 2)) - 1)^2 + 5(1cos(2\u03c0(1|x - 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": "-10", "dataset": "MATH"}
{"messages": [{"content": "Find the average of all x-coordinates of local maxima of the function f(x) = -1sin(2\u03c0((-3(4(-4x + 2) + 3) + 2)/(-2(4(-4x + 2) + 3) + 3)) - 2) - 2 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local maximum with the largest y-value of the function f(x) = -1(5(2(-3|x + 1| + 3) + 1)^2 + 1(2(-3|x + 1| + 3) + 1) - 5)^2 + 3(5(2(-3|x + 1| + 3) + 1)^2 + 1(2(-3|x + 1| + 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": "-2", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local maximum of the function f(x) = 3((3(-5(-5x^2 + 1x - 5)^2 - 5(-5x^2 + 1x - 5) - 3) - 1)/(3(-5(-5x^2 + 1x - 5)^2 - 5(-5x^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": "Find the x-coordinate of the local extremum with the largest y-value of the function f(x) = (2(-3(-1e^(-2(1|x - 1| - 2)) + 2)^2 + 3(-1e^(-2(1|x - 1| - 2)) + 2) - 4) + 1)/(3(-3(-1e^(-2(1|x - 1| - 2)) + 2)^2 + 3(-1e^(-2(1|x - 1| - 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 rightmost local minimum of the function f(x) = -3|(-3cos(3\u03c0(4((-3x)/(-3x + 2)) - 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": "7", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the leftmost local extremum of the function f(x) = 1(2|((-2(2|x + 2| - 1) + 1)/(3(2|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 leftmost local minimum of the function f(x) = -1|(-3|(-4((2x + 1)/(3x - 2))^2 + 2((2x + 1)/(3x - 2)) + 4) + 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": "-1", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local minimum with the largest y-value of the function f(x) = -1(2sin(3\u03c0(-3(-5x)^2 - 2(-5x) - 4) - 2) - 1)^2 + 2(2sin(3\u03c0(-3(-5x)^2 - 2(-5x) - 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": "-10", "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(2|x + 2| - 1) - 2) + 3)/(2(-3(2|x + 2| - 1) - 2) - 1))^2 - 4((2(-3(2|x + 2| - 1) - 2) + 3)/(2(-3(2|x + 2| - 1) - 2) - 1)) + 4 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-2", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local minimum with the smallest y-value of the function f(x) = -1|(-2(4(1sin(2\u03c0x + 1) - 3)^2 + 1(1sin(2\u03c0x + 1) - 3) + 1) + 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": "-9", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the rightmost local minimum of the function f(x) = -1|(-2|((1(-1sin(3\u03c0x + 3) + 2) - 1)/(-2(-1sin(3\u03c0x + 3) + 2) - 3)) - 3| - 1) + 1| - 2 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "How many local minima does the function f(x) = -1|((-2((2(-4x^2 - 5x) - 3)/(2(-4x^2 - 5x) - 1)))/(1((2(-4x^2 - 5x) - 3)/(2(-4x^2 - 5x) - 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 extremum with the smallest y-value of the function f(x) = (-3(4(1|(3x^2 - 2x - 4) + 1| + 2) + 5) + 1)/(2(4(1|(3x^2 - 2x - 4) + 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 extremum with the smallest y-value of the function f(x) = -2|(-4(-2|(-3|x - 3|) + 1|)^2 - 4(-2|(-3|x - 3|) + 1|) + 2) - 1| - 1 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the leftmost local maximum of the function f(x) = -1e^(-2((-2(1|(5x^2 + 4x - 5) + 2| + 3) + 1)/(1(1|(5x^2 + 4x - 5) + 2| + 3) - 3))) - 3 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-1", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local minimum with the largest y-value of the function f(x) = 2(1(1((3x - 1)/(-2x + 1))^2 + 4((3x - 1)/(-2x + 1)) - 5) - 1)^2 + 2(1(1((3x - 1)/(-2x + 1))^2 + 4((3x - 1)/(-2x + 1)) - 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": "0", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the rightmost local maximum of the function f(x) = 1cos(2\u03c0((1((2((-1x - 3)/(-1x - 1)) + 1)/(3((-1x - 3)/(-1x - 1)) + 3)) + 2)/(-2((2((-1x - 3)/(-1x - 1)) + 1)/(3((-1x - 3)/(-1x - 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 rightmost local extremum of the function f(x) = -1(1cos(3\u03c0((-2(-4x) + 3)/(1(-4x) + 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": "8", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the leftmost local maximum of the function f(x) = (1(2|(-1|(-1sin(2\u03c0x - 2) - 3)| - 2) + 1| + 3) + 2)/(-3(2|(-1|(-1sin(2\u03c0x - 2) - 3)| - 2) + 1| + 3) - 2) in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-9", "dataset": "MATH"}
{"messages": [{"content": "Find the average of all x-coordinates of local extrema of the function f(x) = -1|((2(-4(-3cos(2\u03c0x - 1) - 1)^2 - 5(-3cos(2\u03c0x - 1) - 1) + 5) - 2)/(-1(-4(-3cos(2\u03c0x - 1) - 1)^2 - 5(-3cos(2\u03c0x - 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": "0", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local minimum with the largest y-value of the function f(x) = (-1(-5(-2(2|x + 2| - 3) - 4)^2 - 5(-2(2|x + 2| - 3) - 4) + 4) - 2)/(-3(-5(-2(2|x + 2| - 3) - 4)^2 - 5(-2(2|x + 2| - 3) - 4) + 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": "-3", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local minimum with the smallest y-value of the function f(x) = -2|(-5(-4(-3e^(-1x) - 1)^2 - 3(-3e^(-1x) - 1) + 5)^2 + 4(-4(-3e^(-1x) - 1)^2 - 3(-3e^(-1x) - 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": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local maximum with the largest y-value of the function f(x) = 3sin(3\u03c0(-4(3(3|x + 2| + 1)^2 - 3(3|x + 2| + 1) - 3)^2 - 4(3(3|x + 2| + 1)^2 - 3(3|x + 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 average of all x-coordinates of local extrema of the function f(x) = -2|(-2(1(-3e^(-1x) + 1))^2 - 4(1(-3e^(-1x) + 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) = 4((1((1(-1|x| + 1) - 1)/(-2(-1|x| + 1) - 3)) + 1)/(2((1(-1|x| + 1) - 1)/(-2(-1|x| + 1) - 3)) - 1))^2 - 4((1((1(-1|x| + 1) - 1)/(-2(-1|x| + 1) - 3)) + 1)/(2((1(-1|x| + 1) - 1)/(-2(-1|x| + 1) - 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) = 2|(4(-2|(-1|x| + 2) - 1| - 1) + 3) + 2| - 1 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the leftmost local extremum of the function f(x) = -2(-3sin(3\u03c0((2(-1x + 3) + 3)/(1(-1x + 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": "-6", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local extremum with the largest y-value of the function f(x) = 3(1cos(2\u03c0(1((1x + 2)/(-1x))^2 - 4((1x + 2)/(-1x)) - 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": "-9", "dataset": "MATH"}
{"messages": [{"content": "How many local maxima does the function f(x) = (3(2e^(-2(1(-3|x - 3| + 3)^2 - 3(-3|x - 3| + 3) + 1))) + 3)/(3(2e^(-2(1(-3|x - 3| + 3)^2 - 3(-3|x - 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": "How many local extrema (both minima and maxima) does the function f(x) = 2sin(3\u03c0(-1(-1((-1x + 1)/(-3x + 4))^2 + 4((-1x + 1)/(-3x + 4)) + 2) - 4) + 2) + 1 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "18", "dataset": "MATH"}
{"messages": [{"content": "Find the average of all x-coordinates of local maxima of the function f(x) = 2|(5(-2e^(-1(3x^2 + 2x - 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": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local maximum with the smallest y-value of the function f(x) = 2sin(1\u03c0(2((-3(1|x + 3| + 1) - 2)/(-2(1|x + 3| + 1) - 3))^2 - 5((-3(1|x + 3| + 1) - 2)/(-2(1|x + 3| + 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": "-6", "dataset": "MATH"}
{"messages": [{"content": "Find the average of all x-coordinates of local minima of the function f(x) = -3(5(1(3sin(3\u03c0x + 1) - 3) - 3)^2 - 5(1(3sin(3\u03c0x + 1) - 3) - 3) - 3)^2 + 5(5(1(3sin(3\u03c0x + 1) - 3) - 3)^2 - 5(1(3sin(3\u03c0x + 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": "Find the x-coordinate of the leftmost local minimum of the function f(x) = 1(-4(1(2cos(1\u03c0x + 1))^2 + 1(2cos(1\u03c0x + 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": "-9", "dataset": "MATH"}
{"messages": [{"content": "How many local extrema (both minima and maxima) does the function f(x) = 2(-3|(2|(-1sin(2\u03c0x + 3) + 3) + 1|) - 3| + 2)^2 + 1(-3|(2|(-1sin(2\u03c0x + 3) + 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": "40", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local minimum of the function f(x) = 3|(-3e^(-2((1(4x^2 + 4x) + 1)/(3(4x^2 + 4x)))) - 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 rightmost local minimum of the function f(x) = -1sin(3\u03c0(-4(-3|(1|x - 2| + 3) + 2| - 1) + 2) + 1) + 1 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the rightmost local minimum of the function f(x) = (1(3(-2|(-2|x + 2| + 2)| + 3)^2 - 2(-2|(-2|x + 2| + 2)| + 3) - 4) - 3)/(2(3(-2|(-2|x + 2| + 2)| + 3)^2 - 2(-2|(-2|x + 2| + 2)| + 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 minima of the function f(x) = 1sin(2\u03c0(5(-4(1|x - 1| + 3)^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 local minimum of the function f(x) = (3(1(-1|(-3|x + 2| + 3) - 3| - 1)^2 - 4) + 3)/(-2(1(-1|(-3|x + 2| + 3) - 3| - 1)^2 - 4) - 1) in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-2", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the rightmost local maximum of the function f(x) = -5(5(1e^(1(1|x - 2| - 3)) - 1) - 5)^2 + 1 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "6", "dataset": "MATH"}
{"messages": [{"content": "How many local extrema (both minima and maxima) does the function f(x) = -4(-5(-1|(1|x - 3| + 2) - 3| + 2)^2 - 2(-1|(1|x - 3| + 2) - 3| + 2) + 2) + 4 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 local maximum with the smallest y-value of the function f(x) = 1cos(1\u03c0(-3|(-1(1|x| - 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": "-10", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local minimum of the function f(x) = (2(1((-2((-3x + 3)/(3x + 3)) + 1)/(1((-3x + 3)/(3x + 3)) + 3))^2 + 5((-2((-3x + 3)/(3x + 3)) + 1)/(1((-3x + 3)/(3x + 3)) + 3)) + 5) - 3)/(1(1((-2((-3x + 3)/(3x + 3)) + 1)/(1((-3x + 3)/(3x + 3)) + 3))^2 + 5((-2((-3x + 3)/(3x + 3)) + 1)/(1((-3x + 3)/(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 rightmost local minimum of the function f(x) = -1|((1(-4(2|x - 1| - 2)^2 + 2(2|x - 1| - 2) - 4) - 1)/(-1(-4(2|x - 1| - 2)^2 + 2(2|x - 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": "2", "dataset": "MATH"}
{"messages": [{"content": "How many local minima does the function f(x) = 3e^(-2(-5((1((2x + 3)/(3x + 3)) + 1)/(-3((2x + 3)/(3x + 3)) + 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 rightmost local extremum of the function f(x) = -3|((2(-2cos(2\u03c0(1x^2 + 4x + 5) - 2) + 1) + 2)/(-3(-2cos(2\u03c0(1x^2 + 4x + 5) - 2) + 1) + 2)) + 3| - 1 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the rightmost local maximum of the function f(x) = 1|(-2|(-2(2|x + 1| - 3)^2 - 3(2|x + 1| - 3) + 3) + 1| + 2) + 2| - 3 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local extremum with the smallest y-value of the function f(x) = (-3((1(-3|(-3sin(1\u03c0x) + 3) + 1| - 1))/(-1(-3|(-3sin(1\u03c0x) + 3) + 1| - 1) + 3)) - 3)/(-1((1(-3|(-3sin(1\u03c0x) + 3) + 1| - 1))/(-1(-3|(-3sin(1\u03c0x) + 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": "How many local maxima does the function f(x) = -1(1|(-3((-2x - 2)/(-2x))^2 + 5((-2x - 2)/(-2x)) + 1) + 3| + 2)^2 - 5(1|(-3((-2x - 2)/(-2x))^2 + 5((-2x - 2)/(-2x)) + 1) + 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 local extremum with the smallest y-value of the function f(x) = 2|(-4(2e^(-2(-5x^2 + 4)) + 3)^2 + 3(2e^(-2(-5x^2 + 4)) + 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 local extremum of the function f(x) = 3(-3|(3|((-1x - 2)/(-3x - 1)) - 2| - 1) + 2| + 3)^2 - 1(-3|(3|((-1x - 2)/(-3x - 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 rightmost local minimum of the function f(x) = -3(-2cos(1\u03c0(-1((-2x - 1)/(3x + 3))^2 - 1((-2x - 1)/(3x + 3)) + 2) + 2) - 2)^2 + 4(-2cos(1\u03c0(-1((-2x - 1)/(3x + 3))^2 - 1((-2x - 1)/(3x + 3)) + 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": "-1", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local maximum of the function f(x) = -1e^(-2((-2(-3|(4x) - 1| + 2) - 3)/(2(-3|(4x) - 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 x-coordinate of the local minimum of the function f(x) = (-3(1(-3e^(-1((-3x + 1)/(-2x + 1))) - 2)^2 + 5(-3e^(-1((-3x + 1)/(-2x + 1))) - 2) + 1) + 2)/(1(1(-3e^(-1((-3x + 1)/(-2x + 1))) - 2)^2 + 5(-3e^(-1((-3x + 1)/(-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": "1", "dataset": "MATH"}
{"messages": [{"content": "How many local minima does the function f(x) = 4(-5(-3|((2x - 1)/(1x + 1)) + 2| - 1)^2 - 1(-3|((2x - 1)/(1x + 1)) + 2| - 1) - 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 average of all x-coordinates of local extrema of the function f(x) = (-2(3cos(3\u03c0((2(3|x - 1| - 3) + 2)/(-2(3|x - 1| - 3))) - 3) - 3) + 1)/(1(3cos(3\u03c0((2(3|x - 1| - 3) + 2)/(-2(3|x - 1| - 3))) - 3) - 3) + 1) in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local extremum with the largest y-value of the function f(x) = 5(1(3cos(1\u03c0(2|x + 2| + 1) + 1) - 2)^2 + 5(3cos(1\u03c0(2|x + 2| + 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": "-9", "dataset": "MATH"}
{"messages": [{"content": "How many local maxima does the function f(x) = 3|(2(3(-3|x|)^2 - 3(-3|x|) + 4) + 5) + 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) = -3sin(1\u03c0(1((-2(3|x - 1| + 2) - 2)/(3(3|x - 1| + 2) - 2))^2 - 5((-2(3|x - 1| + 2) - 2)/(3(3|x - 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": "0", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local minimum of the function f(x) = -3|(1|(-4(3x^2 - 2x - 1)^2) - 1| + 1) - 2| - 3 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}
{"messages": [{"content": "How many local minima does the function f(x) = -4((1(-5(1e^(-1x) - 2) - 2) + 1)/(1(-5(1e^(-1x) - 2) - 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 average of all x-coordinates of local extrema of the function f(x) = -4(5((1(-2cos(1\u03c0x - 1) - 1) + 3)/(-3(-2cos(1\u03c0x - 1) - 1) - 2))^2 - 1((1(-2cos(1\u03c0x - 1) - 1) + 3)/(-3(-2cos(1\u03c0x - 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": "0", "dataset": "MATH"}
{"messages": [{"content": "How many local extrema (both minima and maxima) does the function f(x) = -2sin(2\u03c0((-1((3(-3|x| + 3) - 3)/(-1(-3|x| + 3) - 2)) + 1)/(2((3(-3|x| + 3) - 3)/(-1(-3|x| + 3) - 2)) + 1)) - 1) - 3 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "35", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local minimum with the largest y-value of the function f(x) = (2(-1|(5(-3cos(1\u03c0x - 1) + 2) - 4) - 3| - 3) + 3)/(-2(-1|(5(-3cos(1\u03c0x - 1) + 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": "-10", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local maximum of the function f(x) = 3e^(-1((-2(1(-2x^2 - 3x + 4)^2 - 2(-2x^2 - 3x + 4) + 5) - 1)/(-1(1(-2x^2 - 3x + 4)^2 - 2(-2x^2 - 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": "-1", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the leftmost local maximum of the function f(x) = 1|(-4(-4(3x^2 + 2x - 1) - 2)^2 - 1(-4(3x^2 + 2x - 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": "-1", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the leftmost local minimum of the function f(x) = 1(2(2cos(1\u03c0(-1|x - 2|) + 3)) + 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": "-10", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local minimum of the function f(x) = 5(-1e^(2(-4((2x - 3)/(3x)))) - 3)^2 - 5(-1e^(2(-4((2x - 3)/(3x)))) - 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 of the function f(x) = 2e^(-1(-1(-3(3|x| - 3) - 1)^2 - 5(-3(3|x| - 3) - 1) - 2)) - 3 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-2", "dataset": "MATH"}
{"messages": [{"content": "Find the average of all x-coordinates of local extrema of the function f(x) = 1|(-3cos(3\u03c0(3((3x - 3)/(-3x - 3))^2 + 1((3x - 3)/(-3x - 3)) - 5) + 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": "How many local maxima does the function f(x) = -2|(-1(1|(-3|x + 2|) + 1|)^2 + 3(1|(-3|x + 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": "Find the x-coordinate of the rightmost local maximum of the function f(x) = 4(-1|(-3(-1sin(3\u03c0x - 1) + 3) - 5) - 2| + 1)^2 + 1(-1|(-3(-1sin(3\u03c0x - 1) + 3) - 5) - 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) = 1sin(2\u03c0(-1|(5((-2x - 3)/(2x - 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": "-8", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local maximum of the function f(x) = (-1(-5(-3(-2x^2 - 3)^2 + 3(-2x^2 - 3) + 2)) - 2)/(-2(-5(-3(-2x^2 - 3)^2 + 3(-2x^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 rightmost local minimum of the function f(x) = -4(5((-1(-1cos(3\u03c0x + 3)) + 1)/(1(-1cos(3\u03c0x + 3)) + 2)) - 2)^2 + 4(5((-1(-1cos(3\u03c0x + 3)) + 1)/(1(-1cos(3\u03c0x + 3)) + 2)) - 2) - 3 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local maximum of the function f(x) = 4((-1(2|((-2x + 3)/(1x + 1)) - 3|) + 1)/(3(2|((-2x + 3)/(1x + 1)) - 3|) + 3)) + 4 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local maximum with the smallest y-value of the function f(x) = -1(1|(-1cos(1\u03c0(-3|x - 1| - 1) - 1) - 1) + 3| + 1)^2 - 5(1|(-1cos(1\u03c0(-3|x - 1| - 1) - 1) - 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 local extremum of the function f(x) = 2|((2((1(-1x^2 + 5x - 5) + 3)/(-3(-1x^2 + 5x - 5) + 4)))/(1((1(-1x^2 + 5x - 5) + 3)/(-3(-1x^2 + 5x - 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": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the average of all x-coordinates of local minima of the function f(x) = 1|(-2sin(2\u03c0(1(-3x^2 - 3x - 4)^2 - 4(-3x^2 - 3x - 4) - 5) - 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 extremum with the largest y-value of the function f(x) = 3((-2(1cos(1\u03c0(1|x - 2| - 1) + 2)) - 3)/(-2(1cos(1\u03c0(1|x - 2| - 1) + 2)) + 3)) - 3 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-9", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local maximum of the function f(x) = (1(2sin(1\u03c0((1(1|x + 2| + 2))/(-2(1|x + 2| + 2) + 3)) - 1) - 1) - 1)/(-3(2sin(1\u03c0((1(1|x + 2| + 2))/(-2(1|x + 2| + 2) + 3)) - 1) - 1) - 1) in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-2", "dataset": "MATH"}
{"messages": [{"content": "How many local minima does the function f(x) = -3(2e^(-2(-3(-4x^2 - 3x - 4)^2 + 4)) + 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 extremum with the largest y-value of the function f(x) = -1((2(2|(-1|x - 3| + 2) - 3| - 2) + 3)/(2(2|(-1|x - 3| + 2) - 3| - 2) - 1))^2 - 5((2(2|(-1|x - 3| + 2) - 3| - 2) + 3)/(2(2|(-1|x - 3| + 2) - 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": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the average of all x-coordinates of local extrema of the function f(x) = 1(1|((-2(-1cos(1\u03c0x - 1) - 2) - 1)/(-1(-1cos(1\u03c0x - 1) - 2) + 2)) + 3|) in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local minimum with the smallest y-value of the function f(x) = -3(1|(-1|(-1x^2 - 2x + 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": "-1", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the leftmost local extremum of the function f(x) = 2(-5(-1(2|x - 1| - 3)^2 + 5(2|x - 1| - 3))^2 - 3(-1(2|x - 1| - 3)^2 + 5(2|x - 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 extremum with the largest y-value of the function f(x) = (-1(2cos(2\u03c0(2|(3x^2 - 3x - 5) - 1| + 1) + 2)) - 1)/(2(2cos(2\u03c0(2|(3x^2 - 3x - 5) - 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": "-10", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local minimum with the smallest y-value of the function f(x) = -1|((3(3cos(1\u03c0(-2|x - 2| - 1) - 3) - 1) + 3)/(-2(3cos(1\u03c0(-2|x - 2| - 1) - 3) - 1) + 3))| in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-10", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the rightmost local extremum of the function f(x) = (2(2|(3(-1|x + 3|)^2 + 5(-1|x + 3|) + 1) + 2|))/(3(2|(3(-1|x + 3|)^2 + 5(-1|x + 3|) + 1) + 2|)) in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the rightmost local minimum of the function f(x) = 1(2|(-1cos(3\u03c0(1x) + 2) + 3) - 1| - 3)^2 + 5(2|(-1cos(3\u03c0(1x) + 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 with the largest y-value of the function f(x) = -2((2(1(1sin(1\u03c0x + 1) + 1) - 4) - 2)/(-2(1(1sin(1\u03c0x + 1) + 1) - 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": "-9", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the rightmost local maximum of the function f(x) = 3|(3|(2sin(3\u03c0(2x^2 - 4x) - 3) + 2)| + 3) + 3| - 2 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local extremum of the function f(x) = -5(5((3((3x + 1)/(-1x - 3)) - 2)/(2((3x + 1)/(-1x - 3)) + 3))^2 - 4((3((3x + 1)/(-1x - 3)) - 2)/(2((3x + 1)/(-1x - 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": "How many local maxima does the function f(x) = 4(2|((-1(1x^2 - 5x + 2) - 3)/(-3(1x^2 - 5x + 2) + 4)) + 1| - 3)^2 + 5(2|((-1(1x^2 - 5x + 2) - 3)/(-3(1x^2 - 5x + 2) + 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 leftmost local extremum of the function f(x) = (-2(-1(1|(3|x - 3| - 3) + 1| - 2)))/(-1(-1(1|(3|x - 3| - 3) + 1| - 2)) - 1) in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the rightmost local extremum of the function f(x) = 1cos(2\u03c0(-3((1(-2x^2 - 3x - 4) - 3)/(-2(-2x^2 - 3x - 4) + 3))^2 + 5((1(-2x^2 - 3x - 4) - 3)/(-2(-2x^2 - 3x - 4) + 3)) + 2)) + 2 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local minimum of the function f(x) = -2|(1|(-1|((3x - 2)/(1x)) - 1| + 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 local minimum of the function f(x) = (-2(-5(-1|(-1x - 3) - 1| + 2)^2 + 4(-1|(-1x - 3) - 1| + 2) + 1) + 2)/(-1(-5(-1|(-1x - 3) - 1| + 2)^2 + 4(-1|(-1x - 3) - 1| + 2) + 1) - 1) in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-4", "dataset": "MATH"}
{"messages": [{"content": "Find the average of all x-coordinates of local extrema of the function f(x) = 2e^(-2(-1(3((1x - 1)/(-3x - 2))^2 - 1))) - 2 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the leftmost local maximum of the function f(x) = 1|(1|(-2(2|x + 3| + 1)^2 - 3(2|x + 3| + 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": "-3", "dataset": "MATH"}
{"messages": [{"content": "Find the average of all x-coordinates of local minima of the function f(x) = 4(-5(-1sin(1\u03c0((-2x)/(2x - 1)) - 1) - 3) - 2)^2 + 2(-5(-1sin(1\u03c0((-2x)/(2x - 1)) - 1) - 3) - 2) + 2 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}
{"messages": [{"content": "How many local extrema (both minima and maxima) does the function f(x) = -4(-2|((1((1x + 2)/(-3x + 4)) + 3)/(-1((1x + 2)/(-3x + 4)) + 3)) + 2|)^2 - 5(-2|((1((1x + 2)/(-3x + 4)) + 3)/(-1((1x + 2)/(-3x + 4)) + 3)) + 2|) - 5 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 local minimum of the function f(x) = 2|(2|(2|(3|x| - 1) - 1| - 3) - 3| + 1) - 1| + 2 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local maximum of the function f(x) = (3(2|(1(-1x^2 + 1x - 5)^2 + 3(-1x^2 + 1x - 5) + 5)|) - 3)/(-3(2|(1(-1x^2 + 1x - 5)^2 + 3(-1x^2 + 1x - 5) + 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 extremum with the smallest y-value of the function f(x) = 2|(-3|(2(2e^(-1x) - 2)^2 - 2(2e^(-1x) - 2) - 1) + 1| + 2) + 3| in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "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(-1cos(2\u03c0x + 2) - 1) - 1)/(1(-1cos(2\u03c0x + 2) - 1) - 3)) - 3) + 1| - 3 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-10", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local extremum with the smallest y-value of the function f(x) = 2|((-1(3(-1x + 4)^2 + 3))/(3(3(-1x + 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": "-10", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local minimum with the largest y-value of the function f(x) = 3|(-1cos(3\u03c0(-2(-1x^2 - 1x - 2) - 3) + 3) + 2) + 3| + 2 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}
{"messages": [{"content": "Find the average of all x-coordinates of local extrema of the function f(x) = -4(-3|(-1(3x^2 - 2x - 2)^2 + 1(3x^2 - 2x - 2) + 5) + 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) = 2(-2|(-2sin(3\u03c0((-2x - 1)/(3x + 2)) + 2) + 3) + 2| + 2) - 3 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-1", "dataset": "MATH"}
{"messages": [{"content": "How many local minima does the function f(x) = (2((-2((-1(-4x^2 - 3x + 3) - 3)/(-2(-4x^2 - 3x + 3) - 2)) + 1)/(3((-1(-4x^2 - 3x + 3) - 3)/(-2(-4x^2 - 3x + 3) - 2)) + 1)) - 3)/(1((-2((-1(-4x^2 - 3x + 3) - 3)/(-2(-4x^2 - 3x + 3) - 2)) + 1)/(3((-1(-4x^2 - 3x + 3) - 3)/(-2(-4x^2 - 3x + 3) - 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 with the largest y-value of the function f(x) = -1(3e^(1(3|((3x + 2)/(-2x + 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": "Find the x-coordinate of the local maximum of the function f(x) = (1((-2(1|(2x^2 - 5x)|) - 2)/(-3(1|(2x^2 - 5x)|) + 4)) - 3)/(3((-2(1|(2x^2 - 5x)|) - 2)/(-3(1|(2x^2 - 5x)|) + 4))) in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the rightmost local extremum of the function f(x) = -1sin(3\u03c0(2(-1(-1x + 3)^2 + 3)^2 - 4(-1(-1x + 3)^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": "10", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the leftmost local maximum of the function f(x) = 4(-2(5(2sin(3\u03c0x) - 3)^2 + 1(2sin(3\u03c0x) - 3) + 2) - 1) + 4 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-10", "dataset": "MATH"}
{"messages": [{"content": "Find the average of all x-coordinates of local maxima of the function f(x) = 3|(1(-4(1sin(1\u03c0x) - 2)) - 3) + 2| + 1 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}
{"messages": [{"content": "How many local extrema (both minima and maxima) does the function f(x) = 3e^(-2(-3|((1(1x + 3) + 3)/(-1(1x + 3) + 2)) + 2| + 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 extremum with the largest y-value of the function f(x) = -3sin(3\u03c0(3(-5(1x^2 + 1x + 2)^2 + 3(1x^2 + 1x + 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": "-6", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local maximum of the function f(x) = -2((-2((3(-5x + 4))/(-3(-5x + 4) - 3)) - 1)/(-1((3(-5x + 4))/(-3(-5x + 4) - 3)) - 1))^2 + 4((-2((3(-5x + 4))/(-3(-5x + 4) - 3)) - 1)/(-1((3(-5x + 4))/(-3(-5x + 4) - 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": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local minimum with the smallest y-value of the function f(x) = (-1(1sin(1\u03c0((-2((3x - 1)/(-2x + 3)) - 2)/(-1((3x - 1)/(-2x + 3)) - 2)) - 2) + 3) - 3)/(-2(1sin(1\u03c0((-2((3x - 1)/(-2x + 3)) - 2)/(-1((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": "-7", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the leftmost local extremum of the function f(x) = (-2(-4(-2cos(2\u03c0(2|x| - 2) + 1) + 3) - 4) + 1)/(1(-4(-2cos(2\u03c0(2|x| - 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 local maximum with the smallest y-value of the function f(x) = -3sin(1\u03c0((1((-3((2x - 1)/(-1x - 2)) + 3)/(1((2x - 1)/(-1x - 2)))) + 1)/(-3((-3((2x - 1)/(-1x - 2)) + 3)/(1((2x - 1)/(-1x - 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) = -1|(2(2cos(3\u03c0((1x - 2)/(2x - 3)) + 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 extremum with the largest y-value of the function f(x) = (3(-5(-2sin(1\u03c0(-3x + 3) + 2))^2 - 5(-2sin(1\u03c0(-3x + 3) + 2)) + 4) - 2)/(3(-5(-2sin(1\u03c0(-3x + 3) + 2))^2 - 5(-2sin(1\u03c0(-3x + 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": "-10", "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|(4x^2 - 2x - 3) - 1| - 2) - 2)/(-2(-2|(4x^2 - 2x - 3) - 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": "How many local minima does the function f(x) = -2|((2(2|((-1x + 2)/(-2x + 1)) - 3| - 3) + 3)/(-2(2|((-1x + 2)/(-2x + 1)) - 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": "0", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local extremum with the largest y-value of the function f(x) = 2|(5(3|(-3sin(3\u03c0x)) + 1| - 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": "How many local maxima does the function f(x) = 2|(-4(-4(-2|x - 1| - 2)^2 - 2(-2|x - 1| - 2) + 2)^2 - 4(-4(-2|x - 1| - 2)^2 - 2(-2|x - 1| - 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": "Find the x-coordinate of the rightmost local extremum of the function f(x) = -2(5(-1|(3x - 3) + 2| + 3)^2 - 2(-1|(3x - 3) + 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": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local minimum with the largest y-value of the function f(x) = -1(2e^(-1(1(-5x^2 + 1x - 1)^2 + 3(-5x^2 + 1x - 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": "0", "dataset": "MATH"}
{"messages": [{"content": "How many local maxima does the function f(x) = 2|(2|(-2|(-4x^2 - 2x - 1)| - 3) - 2| + 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 extremum of the function f(x) = 2(2|(1|(-1x - 5) + 3| + 2) - 1| - 2)^2 - 1(2|(1|(-1x - 5) + 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": "-2", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local extremum with the largest y-value of the function f(x) = (2(3e^(1(-3|(1x + 1) - 2| - 3)) - 1) + 1)/(-1(3e^(1(-3|(1x + 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": "9", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local maximum of the function f(x) = 5(-2((-3(4x + 5) + 1)/(-3(4x + 5) - 3))^2 + 4)^2 + 4(-2((-3(4x + 5) + 1)/(-3(4x + 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": "-1", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local maximum with the smallest y-value of the function f(x) = (-3(-2(2cos(2\u03c0(1x + 5) + 2) - 3)^2 + 4(2cos(2\u03c0(1x + 5) + 2) - 3) - 3) + 2)/(-1(-2(2cos(2\u03c0(1x + 5) + 2) - 3)^2 + 4(2cos(2\u03c0(1x + 5) + 2) - 3) - 3) - 3) in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-9", "dataset": "MATH"}
{"messages": [{"content": "How many local minima does the function f(x) = (2(-5(-1(3e^(1x) - 2) + 2)^2 + 2) + 2)/(-1(-5(-1(3e^(1x) - 2) + 2)^2 + 2) + 3) have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local maximum with the largest y-value of the function f(x) = 2(-2cos(2\u03c0(4(5x^2 + 1x)^2 + 2(5x^2 + 1x) + 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 x-coordinate of the leftmost local minimum of the function f(x) = (1(1sin(2\u03c0(3(-2x^2 + 4x - 1) + 5) + 3) + 1) - 2)/(-2(1sin(2\u03c0(3(-2x^2 + 4x - 1) + 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 x-coordinate of the local maximum of the function f(x) = -3|(-1((-2(3x^2 + 1))/(-3(3x^2 + 1) + 4))^2 + 4((-2(3x^2 + 1))/(-3(3x^2 + 1) + 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": "0", "dataset": "MATH"}
{"messages": [{"content": "Find the average of all x-coordinates of local minima of the function f(x) = -1(-1|((2(-3sin(2\u03c0x - 2) + 3) - 2)/(-2(-3sin(2\u03c0x - 2) + 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": "0", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the leftmost local extremum of the function f(x) = -1(5((-2(-5x + 3) - 1)/(-1(-5x + 3) - 3))^2 - 4)^2 + 4(5((-2(-5x + 3) - 1)/(-1(-5x + 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) = -1|((1(2|(1x - 2)| - 1) + 2)/(2(2|(1x - 2)| - 1) - 1)) + 2| + 1 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "How many local minima does the function f(x) = -2|(2e^(-1(-4(-1x^2 - 4x + 4)^2 + 3(-1x^2 - 4x + 4) + 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 minimum with the smallest y-value of the function f(x) = -4((-1(2sin(2\u03c0(-1x - 4)) + 2) + 3)/(-1(2sin(2\u03c0(-1x - 4)) + 2) - 2))^2 - 1((-1(2sin(2\u03c0(-1x - 4)) + 2) + 3)/(-1(2sin(2\u03c0(-1x - 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 local minimum with the smallest y-value of the function f(x) = 1|(-4((-2(5x^2 + 4x + 2) + 1)/(-2(5x^2 + 4x + 2) - 1))^2 + 5((-2(5x^2 + 4x + 2) + 1)/(-2(5x^2 + 4x + 2) - 1)) - 3) + 1| + 1 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-1", "dataset": "MATH"}
{"messages": [{"content": "Find the average of all x-coordinates of local extrema of the function f(x) = -1|(-1|(3e^(-2(4x^2 - 5x + 3)) + 3) + 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 rightmost local maximum of the function f(x) = (-1(1sin(1\u03c0(2((1x - 1)/(2x + 3))^2 - 4((1x - 1)/(2x + 3)) + 5) - 1) - 2) - 2)/(-2(1sin(1\u03c0(2((1x - 1)/(2x + 3))^2 - 4((1x - 1)/(2x + 3)) + 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": "7", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local extremum with the smallest y-value of the function f(x) = (-2(2cos(1\u03c0(2|(-2x - 1)|)) - 3) - 1)/(1(2cos(1\u03c0(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": "-10", "dataset": "MATH"}
{"messages": [{"content": "Find the average of all x-coordinates of local minima of the function f(x) = 2|(4((-3(3x^2 - 5x - 2) - 1)/(1(3x^2 - 5x - 2) + 2))^2 + 3((-3(3x^2 - 5x - 2) - 1)/(1(3x^2 - 5x - 2) + 2)) - 3) + 1| + 2 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the leftmost local extremum of the function f(x) = 1|(3(3sin(3\u03c0((-1x + 1)/(-3x + 4)) + 3))^2 + 3(3sin(3\u03c0((-1x + 1)/(-3x + 4)) + 3)) - 3) + 1| + 2 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the rightmost local minimum of the function f(x) = -4(-3sin(1\u03c0((-1(-1x - 2) + 1)/(2(-1x - 2) + 1))) - 2) - 1 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-1", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local extremum of the function f(x) = (1(-2|((2(1x - 5))/(-1(1x - 5) + 3)) - 3| + 3) + 1)/(-3(-2|((2(1x - 5))/(-1(1x - 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": "7", "dataset": "MATH"}
{"messages": [{"content": "Find the average of all x-coordinates of local minima of the function f(x) = 3|(-4((-2(-2|x - 2| + 2) - 3)/(2(-2|x - 2| + 2) - 3)) - 3)| - 3 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the leftmost local extremum of the function f(x) = 1(-3e^(-1(2(3x - 5)^2 + 2(3x - 5) - 4)) - 3)^2 - 3(-3e^(-1(2(3x - 5)^2 + 2(3x - 5) - 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": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local maximum with the largest y-value of the function f(x) = (-3(-2(3cos(1\u03c0(2x + 4) + 2) + 1)^2 - 2(3cos(1\u03c0(2x + 4) + 2) + 1)) + 1)/(-3(-2(3cos(1\u03c0(2x + 4) + 2) + 1)^2 - 2(3cos(1\u03c0(2x + 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": "-10", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local extremum with the smallest y-value of the function f(x) = -2|(-3cos(1\u03c0(-3(1x + 1)^2 - 1(1x + 1) + 3) - 2) + 2) + 1| + 2 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-10", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the rightmost local extremum of the function f(x) = 1cos(3\u03c0(-4((-1((1x - 2)/(-2x + 1)) - 3)/(-3((1x - 2)/(-2x + 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": "7", "dataset": "MATH"}
{"messages": [{"content": "How many local minima does the function f(x) = 4((1(-5(-4x^2 + 5x - 2)^2 + 1(-4x^2 + 5x - 2) - 5) - 3)/(3(-5(-4x^2 + 5x - 2)^2 + 1(-4x^2 + 5x - 2) - 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": "How many local minima does the function f(x) = -2(1|((2(1|x + 1| - 1))/(-2(1|x + 1| - 1) + 3)) + 2| - 2)^2 - 2(1|((2(1|x + 1| - 1))/(-2(1|x + 1| - 1) + 3)) + 2| - 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 extremum of the function f(x) = (2(-4(1((-1x + 2)/(-1x - 2))^2 - 3((-1x + 2)/(-1x - 2)) + 2) + 3))/(-1(-4(1((-1x + 2)/(-1x - 2))^2 - 3((-1x + 2)/(-1x - 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": "-2", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the rightmost local extremum of the function f(x) = -2|((-2(1(-1x + 5)^2 + 3(-1x + 5) + 1))/(-3(1(-1x + 5)^2 + 3(-1x + 5) + 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": "6", "dataset": "MATH"}
{"messages": [{"content": "Find the average of all x-coordinates of local extrema of the function f(x) = 1|((3(1|(4x^2 - 2x - 3)| - 2) + 2)/(-2(1|(4x^2 - 2x - 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^(-1((3(-5(-3|x + 3| + 3)) - 3)/(-1(-5(-3|x + 3| + 3)) - 1))) - 2 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-3", "dataset": "MATH"}
{"messages": [{"content": "Find the average of all x-coordinates of local minima of the function f(x) = (-2(-2|(-1(1cos(3\u03c0x - 2) - 1)^2 - 4(1cos(3\u03c0x - 2) - 1) + 3) + 2| - 2) + 1)/(1(-2|(-1(1cos(3\u03c0x - 2) - 1)^2 - 4(1cos(3\u03c0x - 2) - 1) + 3) + 2| - 2)) in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "How many local maxima does the function f(x) = -3((-3((2(2x^2 - 5x + 2) + 1)/(-1(2x^2 - 5x + 2) - 1)) - 1)/(-3((2(2x^2 - 5x + 2) + 1)/(-1(2x^2 - 5x + 2) - 1)) - 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 maximum with the largest y-value of the function f(x) = 1|(2(-4(2|x + 1| - 1)^2 + 4)^2 - 5(-4(2|x + 1| - 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": "-2", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the leftmost local maximum of the function f(x) = -1|(-2(-2e^(-2(2x)) + 2) - 1)| in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "7", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the rightmost local minimum of the function f(x) = -3(1|(3cos(3\u03c0(2x^2 + 5x - 4) - 1) + 3) + 3| - 3)^2 - 4(1|(3cos(3\u03c0(2x^2 + 5x - 4) - 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 local maximum of the function f(x) = 5(-1((2(-4x^2 - 4x - 5) - 3)/(2(-4x^2 - 4x - 5) + 3))^2 - 3((2(-4x^2 - 4x - 5) - 3)/(2(-4x^2 - 4x - 5) + 3)) + 4)^2 + 2(-1((2(-4x^2 - 4x - 5) - 3)/(2(-4x^2 - 4x - 5) + 3))^2 - 3((2(-4x^2 - 4x - 5) - 3)/(2(-4x^2 - 4x - 5) + 3)) + 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 extremum of the function f(x) = -2e^(-1(-5(-3|((-2x + 2)/(-3x - 2)) - 2| - 3)^2 + 1(-3|((-2x + 2)/(-3x - 2)) - 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": "-2", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the rightmost local maximum of the function f(x) = 4(-1(1cos(3\u03c0(-1|x - 2|) - 2)) + 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": "9", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local minimum with the smallest y-value of the function f(x) = -1|(-3sin(1\u03c0((2((-2x + 1)/(1x - 2)) - 3)/(2((-2x + 1)/(1x - 2)) + 3)) - 2) + 3) - 3| - 2 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-10", "dataset": "MATH"}
{"messages": [{"content": "How many local minima does the function f(x) = 3|((3(-5(-3|x| - 1) + 4) + 3)/(-2(-5(-3|x| - 1) + 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 rightmost local extremum of the function f(x) = (3(1(1cos(3\u03c0(4x^2 - 1x) + 3)) - 1))/(-1(1(1cos(3\u03c0(4x^2 - 1x) + 3)) - 1) + 2) in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the leftmost local minimum of the function f(x) = 4((-1(3sin(3\u03c0(-3x^2 + 1) - 2)) - 3)/(-1(3sin(3\u03c0(-3x^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": "-10", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local extremum with the smallest y-value of the function f(x) = -2|(3cos(3\u03c0(1(-1x^2 - 5x + 2)^2 - 3(-1x^2 - 5x + 2) - 1) - 1) - 2)| + 1 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-10", "dataset": "MATH"}
{"messages": [{"content": "Find the average of all x-coordinates of local minima of the function f(x) = 4(-1sin(3\u03c0(-1|(2x - 5) - 2| - 2) - 1) + 2)^2 + 1(-1sin(3\u03c0(-1|(2x - 5) - 2| - 2) - 1) + 2) + 4 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local minimum of the function f(x) = 4((2((-2((1x + 3)/(-1x + 2)) - 2)/(-1((1x + 3)/(-1x + 2)) + 3)) + 1)/(-2((-2((1x + 3)/(-1x + 2)) - 2)/(-1((1x + 3)/(-1x + 2)) + 3)) + 3))^2 + 4((2((-2((1x + 3)/(-1x + 2)) - 2)/(-1((1x + 3)/(-1x + 2)) + 3)) + 1)/(-2((-2((1x + 3)/(-1x + 2)) - 2)/(-1((1x + 3)/(-1x + 2)) + 3)) + 3)) - 2 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}
{"messages": [{"content": "How many local minima does the function f(x) = -3|((2(-1|((1x - 3)/(-1x + 2)) + 3| + 1) + 1)/(2(-1|((1x - 3)/(-1x + 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 with the smallest y-value of the function f(x) = (1(4(-5(-1|x + 2| + 2)^2) + 2) - 2)/(3(4(-5(-1|x + 2| + 2)^2) + 2) - 1) in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-4", "dataset": "MATH"}
{"messages": [{"content": "How many local maxima does the function f(x) = 1|(-2|((-1(4x^2 + 4x - 4) + 2)/(-3(4x^2 + 4x - 4) + 2)) - 1| + 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) = -3|((2(-1|(-2x - 3) + 3| - 3) + 2)/(3(-1|(-2x - 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 extremum with the smallest y-value of the function f(x) = (2(-2|(1e^(1(-4x^2 - 5x)) - 1) + 1| + 3))/(1(-2|(1e^(1(-4x^2 - 5x)) - 1) + 1| + 3) - 3) in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local minimum with the smallest y-value of the function f(x) = -3cos(2\u03c0(-1|((2((-2x - 3)/(1x - 2)) - 2)/(-3((-2x - 3)/(1x - 2)) + 4)) + 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": "0", "dataset": "MATH"}
{"messages": [{"content": "Find the average of all x-coordinates of local minima of the function f(x) = -1|((-1(3(5x^2 + 1x - 3)^2 - 4(5x^2 + 1x - 3) - 2) - 3)/(3(3(5x^2 + 1x - 3)^2 - 4(5x^2 + 1x - 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": "0", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the leftmost local maximum of the function f(x) = 1(1|(-2sin(1\u03c0(-3|x + 2| + 3) + 3) - 2) + 1| - 1)^2 + 5(1|(-2sin(1\u03c0(-3|x + 2| + 3) + 3) - 2) + 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": "How many local maxima does the function f(x) = -1|(-5(-2(3x^2 - 3x + 1)^2 - 3(3x^2 - 3x + 1) + 3)^2 + 5(-2(3x^2 - 3x + 1)^2 - 3(3x^2 - 3x + 1) + 3) + 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": "How many local minima does the function f(x) = 2|(-1(1((-1x - 2)/(-1x - 1))^2 - 4((-1x - 2)/(-1x - 1)) + 5)^2 + 2(1((-1x - 2)/(-1x - 1))^2 - 4((-1x - 2)/(-1x - 1)) + 5) - 5) + 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) = 1cos(2\u03c0(2|(2|((-2x + 3)/(1x + 2)) + 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": "10", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local maximum of the function f(x) = 1(-1|(3|(-1x^2 - 5x - 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": "-2", "dataset": "MATH"}
{"messages": [{"content": "How many local minima does the function f(x) = (-2(-1|(-3(1x + 4)^2 - 4(1x + 4) - 5) + 2| + 2))/(2(-1|(-3(1x + 4)^2 - 4(1x + 4) - 5) + 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 rightmost local minimum of the function f(x) = 4(1cos(2\u03c0(3|((-3x + 2)/(-2x)) - 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": "How many local maxima does the function f(x) = 2|((-2(3|(-3sin(1\u03c0x))|) - 3)/(1(3|(-3sin(1\u03c0x))|) - 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) = -3|(3|(-2(-3|x - 2| - 1)^2 - 2(-3|x - 2| - 1) + 2) + 3| + 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 minima does the function f(x) = (-1(-3((1(-1x^2 - 4) - 1)/(2(-1x^2 - 4) + 1))^2 + 5) + 2)/(1(-3((1(-1x^2 - 4) - 1)/(2(-1x^2 - 4) + 1))^2 + 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 average of all x-coordinates of local minima of the function f(x) = (1(-1((2(-2|x + 1| - 1))/(-1(-2|x + 1| - 1) - 3))^2 + 4((2(-2|x + 1| - 1))/(-1(-2|x + 1| - 1) - 3))) + 2)/(3(-1((2(-2|x + 1| - 1))/(-1(-2|x + 1| - 1) - 3))^2 + 4((2(-2|x + 1| - 1))/(-1(-2|x + 1| - 1) - 3))) + 2) in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-1", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local minimum with the largest y-value of the function f(x) = (1(-3sin(3\u03c0(-5(-4x^2 + 3x + 3) + 3) - 3) - 1) + 2)/(-2(-3sin(3\u03c0(-5(-4x^2 + 3x + 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": "0", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local extremum of the function f(x) = (2(-1|((2(3x^2 + 1x + 3) + 3)/(-1(3x^2 + 1x + 3) + 2)) - 2|) + 3)/(-3(-1|((2(3x^2 + 1x + 3) + 3)/(-1(3x^2 + 1x + 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 local extremum with the smallest y-value of the function f(x) = -1(1(2|(5x^2 + 1x - 5) - 1| - 1)^2 - 2)^2 + 1(1(2|(5x^2 + 1x - 5) - 1| - 1)^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": "How many local maxima does the function f(x) = (2((-3(3(-2|x| - 1) - 4) - 2)/(2(3(-2|x| - 1) - 4) + 3)) + 2)/(-3((-3(3(-2|x| - 1) - 4) - 2)/(2(3(-2|x| - 1) - 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 rightmost local minimum of the function f(x) = -3cos(3\u03c0(4(-2|((-2x)/(-1x + 3)) + 3| - 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": "How many local minima does the function f(x) = (2((-2((3(1x^2 + 5x - 3))/(-3(1x^2 + 5x - 3) - 1)) - 2)/(-1((3(1x^2 + 5x - 3))/(-3(1x^2 + 5x - 3) - 1)) + 3)) + 1)/(3((-2((3(1x^2 + 5x - 3))/(-3(1x^2 + 5x - 3) - 1)) - 2)/(-1((3(1x^2 + 5x - 3))/(-3(1x^2 + 5x - 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 of the function f(x) = (1((3((1(-3x^2 - 3x + 4) - 3)/(2(-3x^2 - 3x + 4) - 1)) + 2)/(-2((1(-3x^2 - 3x + 4) - 3)/(2(-3x^2 - 3x + 4) - 1)) + 3)) + 2)/(-1((3((1(-3x^2 - 3x + 4) - 3)/(2(-3x^2 - 3x + 4) - 1)) + 2)/(-2((1(-3x^2 - 3x + 4) - 3)/(2(-3x^2 - 3x + 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 maximum of the function f(x) = -3sin(3\u03c0((-1((-2(1|x + 2| + 2))/(2(1|x + 2| + 2) + 1)) + 1)/(-1((-2(1|x + 2| + 2))/(2(1|x + 2| + 2) + 1)))) - 2) + 1 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "7", "dataset": "MATH"}
{"messages": [{"content": "How many local minima does the function f(x) = 3|((2(-2sin(3\u03c0(3|x - 3| - 3) - 2) - 2) + 3)/(1(-2sin(3\u03c0(3|x - 3| - 3) - 2) - 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 rightmost local extremum of the function f(x) = (2(-2(1(-5x^2 - 2x + 5)^2 + 2(-5x^2 - 2x + 5) + 4) - 3) + 2)/(3(-2(1(-5x^2 - 2x + 5)^2 + 2(-5x^2 - 2x + 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 local extremum of the function f(x) = 1(2((1((1x - 1)/(3x + 1)) - 1)/(-1((1x - 1)/(3x + 1)) + 3))^2 + 3((1((1x - 1)/(3x + 1)) - 1)/(-1((1x - 1)/(3x + 1)) + 3)) + 2)^2 + 4(2((1((1x - 1)/(3x + 1)) - 1)/(-1((1x - 1)/(3x + 1)) + 3))^2 + 3((1((1x - 1)/(3x + 1)) - 1)/(-1((1x - 1)/(3x + 1)) + 3)) + 2) + 3 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the rightmost local extremum of the function f(x) = (-2(3cos(2\u03c0(-1(-1x^2 - 1x + 5) - 1) + 1) + 1) - 1)/(-1(3cos(2\u03c0(-1(-1x^2 - 1x + 5) - 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) = -3(-1|(-1|(3x^2 + 5x + 1) + 1| + 1) - 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": "How many local minima does the function f(x) = 2|(-2|(-1((1x + 1)/(-2x - 3))^2 + 5((1x + 1)/(-2x - 3)) - 2) - 1| + 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 minimum of the function f(x) = (-3(-1(1(4x^2 - 4x + 2) + 1)^2 - 3(1(4x^2 - 4x + 2) + 1) - 3) - 1)/(3(-1(1(4x^2 - 4x + 2) + 1)^2 - 3(1(4x^2 - 4x + 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": "Find the x-coordinate of the local minimum with the largest y-value of the function f(x) = -5(-2sin(1\u03c0(2|(-2|x - 3| - 3) - 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": "How many local minima does the function f(x) = 3|((3(4(-2x^2 - 2x + 4) + 4) - 1)/(1(4(-2x^2 - 2x + 4) + 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 x-coordinate of the leftmost local minimum of the function f(x) = 4((-2(4(-2x + 3) - 5) - 3)/(1(4(-2x + 3) - 5) + 2))^2 - 1((-2(4(-2x + 3) - 5) - 3)/(1(4(-2x + 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 extremum with the smallest y-value of the function f(x) = 1(-3cos(1\u03c0(-1((1x - 2)/(-2x - 2)) - 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": "-3", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local extremum with the largest y-value of the function f(x) = 4(-2|(2|(3|x + 3|)|) - 2|)^2 + 1(-2|(2|(3|x + 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": "-3", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local maximum of the function f(x) = -3e^(1(2|(-3|(1|x + 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 minimum of the function f(x) = -5(4(4(-2cos(1\u03c0x - 2) + 3)^2 + 5(-2cos(1\u03c0x - 2) + 3) + 3)^2 + 3(4(-2cos(1\u03c0x - 2) + 3)^2 + 5(-2cos(1\u03c0x - 2) + 3) + 3) - 2)^2 + 1(4(4(-2cos(1\u03c0x - 2) + 3)^2 + 5(-2cos(1\u03c0x - 2) + 3) + 3)^2 + 3(4(-2cos(1\u03c0x - 2) + 3)^2 + 5(-2cos(1\u03c0x - 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": "2", "dataset": "MATH"}
{"messages": [{"content": "How many local maxima does the function f(x) = 3|(-3(-4(-2x^2 + 4x - 4)^2 - 4(-2x^2 + 4x - 4) - 1)^2 + 3(-4(-2x^2 + 4x - 4)^2 - 4(-2x^2 + 4x - 4) - 1) - 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": "Find the x-coordinate of the rightmost local maximum of the function f(x) = -3(1sin(1\u03c0((1(-1x - 1) + 3)/(-3(-1x - 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": "-1", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the leftmost local minimum of the function f(x) = -5(-3(-3|(-1sin(2\u03c0x - 2) + 2) - 2| - 2)^2 + 5(-3|(-1sin(2\u03c0x - 2) + 2) - 2| - 2) + 4)^2 - 4(-3(-3|(-1sin(2\u03c0x - 2) + 2) - 2| - 2)^2 + 5(-3|(-1sin(2\u03c0x - 2) + 2) - 2| - 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 maximum of the function f(x) = -1((-2(-3((-2x + 1)/(3x)) - 5) - 3)/(1(-3((-2x + 1)/(3x)) - 5)))^2 - 4((-2(-3((-2x + 1)/(3x)) - 5) - 3)/(1(-3((-2x + 1)/(3x)) - 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 extremum with the smallest y-value of the function f(x) = -1cos(2\u03c0(2|((-1(2|x + 3| - 1) - 3)/(-1(2|x + 3| - 1))) + 3| + 1) + 3) + 1 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-9", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the rightmost local extremum of the function f(x) = 1cos(2\u03c0((-3(3(-2x - 1)^2 - 3(-2x - 1) - 5) - 2)/(2(3(-2x - 1)^2 - 3(-2x - 1) - 5) + 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 minima does the function f(x) = -5(1(2(-1|x - 3| + 1)^2 + 4))^2 + 3(1(2(-1|x - 3| + 1)^2 + 4)) + 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 with the largest y-value of the function f(x) = (-1((2(2(-3|x + 3| + 2)^2 + 4) - 1)/(3(2(-3|x + 3| + 2)^2 + 4))) + 1)/(1((2(2(-3|x + 3| + 2)^2 + 4) - 1)/(3(2(-3|x + 3| + 2)^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": "-4", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the rightmost local maximum of the function f(x) = (3((3(-1(-5x + 4)^2 - 1(-5x + 4) - 4) - 2)/(1(-1(-5x + 4)^2 - 1(-5x + 4) - 4) - 2)) + 3)/(-2((3(-1(-5x + 4)^2 - 1(-5x + 4) - 4) - 2)/(1(-1(-5x + 4)^2 - 1(-5x + 4) - 4) - 2)) - 2) in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "How many local maxima does the function f(x) = -1|(2|(-3(1e^(-1x) - 2)^2 + 4(1e^(-1x) - 2) + 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": "Find the x-coordinate of the local minimum of the function f(x) = (2((2(-1(-5x)^2 - 1(-5x) - 2))/(1(-1(-5x)^2 - 1(-5x) - 2) - 2)) + 3)/(-2((2(-1(-5x)^2 - 1(-5x) - 2))/(1(-1(-5x)^2 - 1(-5x) - 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 leftmost local maximum of the function f(x) = -3((-3(-4(1cos(2\u03c0x + 3) - 3) - 4) + 3)/(2(-4(1cos(2\u03c0x + 3) - 3) - 4) - 3))^2 + 3((-3(-4(1cos(2\u03c0x + 3) - 3) - 4) + 3)/(2(-4(1cos(2\u03c0x + 3) - 3) - 4) - 3)) + 1 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-10", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local maximum with the largest y-value of the function f(x) = 1sin(1\u03c0(5(-1(-5x - 3)^2 + 5)^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": "-2", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local extremum with the largest y-value of the function f(x) = 3sin(3\u03c0(-1((2(-2x - 3) - 3)/(-1(-2x - 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": "-4", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local maximum with the largest y-value of the function f(x) = 2|(2(3(-2sin(3\u03c0x + 3) + 2) - 4)^2 + 4(3(-2sin(3\u03c0x + 3) + 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": "-10", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local extremum with the largest y-value of the function f(x) = -4(-2e^(-1(-2|(-5x^2 + 4x - 4) + 3|)) + 2)^2 - 1(-2e^(-1(-2|(-5x^2 + 4x - 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": "How many local minima does the function f(x) = (3(-1|(-3e^(-2(2|x + 2|)) + 2) - 2| - 1) + 1)/(-1(-1|(-3e^(-2(2|x + 2|)) + 2) - 2| - 1) - 1) have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local minimum with the smallest y-value of the function f(x) = -2((-3(1cos(2\u03c0(3|x + 2| + 2)) - 1) + 1)/(-2(1cos(2\u03c0(3|x + 2| + 2)) - 1) - 3)) + 2 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-10", "dataset": "MATH"}
{"messages": [{"content": "Find the average of all x-coordinates of local minima of the function f(x) = 2cos(1\u03c0(5((-3(3x^2 + 3x + 1) + 1)/(3(3x^2 + 3x + 1) + 2))^2 - 1((-3(3x^2 + 3x + 1) + 1)/(3(3x^2 + 3x + 1) + 2)) + 4)) + 1 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local minimum with the smallest y-value of the function f(x) = -4(-3|(3(3x^2 - 3)^2 + 5(3x^2 - 3) - 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 average of all x-coordinates of local maxima of the function f(x) = -1(1(-1|(-2sin(3\u03c0x - 1) + 2)| - 2)^2 - 2(-1|(-2sin(3\u03c0x - 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 extremum with the smallest y-value of the function f(x) = (1(-3sin(2\u03c0(-1((-2x - 3)/(3x + 3)) - 3) - 1) - 3) + 3)/(3(-3sin(2\u03c0(-1((-2x - 3)/(3x + 3)) - 3) - 1) - 3) + 3) in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-2", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the rightmost local minimum of the function f(x) = -4(-1cos(3\u03c0(1(-4x^2 - 3)^2 - 2(-4x^2 - 3) + 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": "Find the x-coordinate of the local extremum of the function f(x) = 2|(-3|(-5(-5x^2 + 2x - 2)^2 + 4(-5x^2 + 2x - 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 leftmost local maximum of the function f(x) = (1(1cos(1\u03c0(3(-4x^2 + 4x + 3) - 4))) + 1)/(2(1cos(1\u03c0(3(-4x^2 + 4x + 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": "-10", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local maximum with the smallest y-value of the function f(x) = (-1(-3e^(-1((-1(1|x - 3|) - 3)/(3(1|x - 3|) - 2))) + 2) + 3)/(-1(-3e^(-1((-1(1|x - 3|) - 3)/(3(1|x - 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": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the average of all x-coordinates of local extrema of the function f(x) = (-3(-1e^(-1(-5((-1x + 2)/(-1x))^2 - 5((-1x + 2)/(-1x)) - 1)) + 2) + 3)/(-2(-1e^(-1(-5((-1x + 2)/(-1x))^2 - 5((-1x + 2)/(-1x)) - 1)) + 2) + 1) in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-1", "dataset": "MATH"}
{"messages": [{"content": "Find the average of all x-coordinates of local extrema of the function f(x) = -3cos(2\u03c0(-4(4(1x^2 - 4x - 3)^2 - 2(1x^2 - 4x - 3) + 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": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the leftmost local minimum of the function f(x) = -2sin(3\u03c0(-4(1|(-3|x| - 3)| + 1) - 1) + 1) + 3 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-10", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local minimum of the function f(x) = 5((-2(-2|(5x^2 - 5x + 2) - 2| + 2) - 2)/(2(-2|(5x^2 - 5x + 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": "0", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local extremum of the function f(x) = 1(-2|((1(4x^2 - 2x + 2) - 2)/(-3(4x^2 - 2x + 2))) - 1| + 2) - 2 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}
{"messages": [{"content": "How many local maxima does the function f(x) = -1|(-4((-1(1|x| + 1) - 1)/(-2(1|x| + 1) + 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 leftmost local extremum of the function f(x) = 2|(2|(-2sin(3\u03c0(2|x + 1| + 2) - 2) + 3) - 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": "-10", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local minimum with the largest y-value of the function f(x) = 3sin(3\u03c0(5((-1((2x)/(-2x - 2)) - 3)/(1((2x)/(-2x - 2)) - 3))^2 - 2((-1((2x)/(-2x - 2)) - 3)/(1((2x)/(-2x - 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": "-2", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the rightmost local minimum of the function f(x) = -2(2cos(2\u03c0(2|(3|x + 1| - 1) - 2| + 1)) + 2) + 5 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local minimum of the function f(x) = -2(-3(2((-1x + 2)/(3x - 1))^2 + 1((-1x + 2)/(3x - 1)) - 1) + 2)^2 + 2(-3(2((-1x + 2)/(3x - 1))^2 + 1((-1x + 2)/(3x - 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": "7", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local extremum of the function f(x) = 1|(-2(-2((-3x - 3)/(1x - 3))^2 - 1((-3x - 3)/(1x - 3)) - 1) + 5) - 3| + 1 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-1", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local minimum with the largest y-value of the function f(x) = (-3(4(-1e^(2(-3x - 5)))))/(-2(4(-1e^(2(-3x - 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 local maximum of the function f(x) = (-3(1|(5((1x - 2)/(2x)) + 4) - 1| - 1))/(-1(1|(5((1x - 2)/(2x)) + 4) - 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 average of all x-coordinates of local maxima of the function f(x) = -2|((-3(1cos(1\u03c0((1x - 1)/(-1x)) + 2) - 3) + 1)/(-2(1cos(1\u03c0((1x - 1)/(-1x)) + 2) - 3) - 2)) + 2| in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local extremum with the smallest y-value of the function f(x) = -3|(-5(-1sin(1\u03c0(-2x^2 - 2x - 2) - 3) - 1)^2 + 4(-1sin(1\u03c0(-2x^2 - 2x - 2) - 3) - 1) + 1) + 1| + 2 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-10", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the leftmost local minimum of the function f(x) = -1(3sin(1\u03c0(4(-4x - 1)^2 + 3(-4x - 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": "How many local extrema (both minima and maxima) does the function f(x) = -2e^(-2(2((-2(-2x^2 - 2x - 2) - 1)/(-2(-2x^2 - 2x - 2) + 3))^2 - 2((-2(-2x^2 - 2x - 2) - 1)/(-2(-2x^2 - 2x - 2) + 3)) + 4)) - 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 maxima does the function f(x) = 1|((-3(-2|(-2cos(3\u03c0x - 3) + 3)|) - 2)/(-1(-2|(-2cos(3\u03c0x - 3) + 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 average of all x-coordinates of local extrema of the function f(x) = 2|(-2sin(2\u03c0(-2|((-2x)/(-3x)) - 2| + 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": "0", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the rightmost local minimum of the function f(x) = -2|(-1(2((2x - 2)/(1x + 3))^2 - 1((2x - 2)/(1x + 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": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the leftmost local minimum of the function f(x) = -2e^(-1(2|(-3((-1x - 1)/(-1x + 2))^2 - 3((-1x - 1)/(-1x + 2)) - 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": "-7", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local minimum of the function f(x) = (-1(3|(1(-3x^2)^2 + 5(-3x^2) - 4) - 1| + 2) + 3)/(-1(3|(1(-3x^2)^2 + 5(-3x^2) - 4) - 1| + 2) - 1) in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local maximum with the smallest y-value of the function f(x) = 4(-3(3|(-1e^(1x) + 1) + 3| - 2)^2 - 1(3|(-1e^(1x) + 1) + 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": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the leftmost local maximum of the function f(x) = 1(5(4(2x^2 - 5x - 5)^2 - 5(2x^2 - 5x - 5) - 5)^2 - 1(4(2x^2 - 5x - 5)^2 - 5(2x^2 - 5x - 5) - 5) - 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": "-1", "dataset": "MATH"}
{"messages": [{"content": "Find the average of all x-coordinates of local maxima of the function f(x) = 3|(-1cos(1\u03c0(5(-5x^2 + 3x - 5)^2 + 2(-5x^2 + 3x - 5) - 5)) + 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 extremum of the function f(x) = 3|(1(-1(-2|x + 3| - 3)^2 - 5(-2|x + 3| - 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": "-3", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local maximum with the largest y-value of the function f(x) = 5(-2(-2cos(2\u03c0((1x)/(-1x + 2)) + 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": "-1", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the leftmost local minimum of the function f(x) = 2sin(2\u03c0(5((2(4x^2 + 5x - 1) - 2)/(1(4x^2 + 5x - 1) + 1))^2 + 5((2(4x^2 + 5x - 1) - 2)/(1(4x^2 + 5x - 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": "-5", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local maximum with the largest y-value of the function f(x) = (1(3|(-1|(-2cos(1\u03c0x - 1) + 3) + 3|) + 3| + 3) + 2)/(-1(3|(-1|(-2cos(1\u03c0x - 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": "-9", "dataset": "MATH"}
{"messages": [{"content": "Find the average of all x-coordinates of local maxima of the function f(x) = (-1(2sin(1\u03c0(3|(-1x^2 - 1x - 2) - 2| - 3))))/(3(2sin(1\u03c0(3|(-1x^2 - 1x - 2) - 2| - 3))) - 1) in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "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((-1(-2|((1x + 2)/(1x + 1)) - 3| - 1) + 2)/(-2(-2|((1x + 2)/(1x + 1)) - 3| - 1))) - 3) + 2 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-1", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the leftmost local minimum of the function f(x) = -3cos(2\u03c0(1|(-1((-2x - 2)/(-2x + 3))^2 + 3((-2x - 2)/(-2x + 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": "-8", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the rightmost local maximum of the function f(x) = 5(1|(4(2sin(1\u03c0x + 1) - 3)^2 - 2(2sin(1\u03c0x + 1) - 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": "9", "dataset": "MATH"}
{"messages": [{"content": "Find the average of all x-coordinates of local maxima of the function f(x) = 1(3cos(3\u03c0(-4(1x - 5)^2 - 4(1x - 5) + 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 average of all x-coordinates of local extrema of the function f(x) = (-3(-1|(-5((-2x + 3)/(-3x + 4))^2 + 4((-2x + 3)/(-3x + 4)) - 4) - 3|) + 1)/(-2(-1|(-5((-2x + 3)/(-3x + 4))^2 + 4((-2x + 3)/(-3x + 4)) - 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 local maximum with the largest y-value of the function f(x) = 1|(2|(-1(2sin(3\u03c0x) - 1)^2 + 4(2sin(3\u03c0x) - 1) - 4)| - 3) - 2| - 2 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-10", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local maximum of the function f(x) = -1(2|(-4(-1x + 4)^2 - 4(-1x + 4) + 3) - 3| + 1)^2 - 4(2|(-4(-1x + 4)^2 - 4(-1x + 4) + 3) - 3| + 1) + 3 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the rightmost local minimum of the function f(x) = (1((3((3(-1sin(1\u03c0x + 1) - 2))/(-2(-1sin(1\u03c0x + 1) - 2) - 2)) + 2)/(-2((3(-1sin(1\u03c0x + 1) - 2))/(-2(-1sin(1\u03c0x + 1) - 2) - 2)) - 2)) + 1)/(1((3((3(-1sin(1\u03c0x + 1) - 2))/(-2(-1sin(1\u03c0x + 1) - 2) - 2)) + 2)/(-2((3(-1sin(1\u03c0x + 1) - 2))/(-2(-1sin(1\u03c0x + 1) - 2) - 2)) - 2)) - 2) in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "9", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local maximum with the largest y-value of the function f(x) = -3(-2((2(-2sin(1\u03c0x) - 2))/(-3(-2sin(1\u03c0x) - 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": "-10", "dataset": "MATH"}
{"messages": [{"content": "Find the average of all x-coordinates of local minima of the function f(x) = 2cos(3\u03c0(2|(-4(2|x + 1| + 1)^2 - 5(2|x + 1| + 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": "0", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local extremum of the function f(x) = (3((1(-5(4x - 3)^2 + 2(4x - 3) - 1) + 3)/(-2(-5(4x - 3)^2 + 2(4x - 3) - 1))) + 1)/(2((1(-5(4x - 3)^2 + 2(4x - 3) - 1) + 3)/(-2(-5(4x - 3)^2 + 2(4x - 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 local extremum of the function f(x) = (-3(-1(1|(1|x| + 2) + 2| - 2) - 1) + 3)/(1(-1(1|(1|x| + 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": "0", "dataset": "MATH"}
{"messages": [{"content": "How many local extrema (both minima and maxima) does the function f(x) = -2cos(3\u03c0(-3|(-4(-2|x| + 2)^2 + 2(-2|x| + 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": "413", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the leftmost local maximum of the function f(x) = -1(-3(1cos(1\u03c0(-3x^2 + 4x + 4) + 1) + 3)^2 + 1(1cos(1\u03c0(-3x^2 + 4x + 4) + 1) + 3) + 4)^2 + 1(-3(1cos(1\u03c0(-3x^2 + 4x + 4) + 1) + 3)^2 + 1(1cos(1\u03c0(-3x^2 + 4x + 4) + 1) + 3) + 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": "-10", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the leftmost local maximum of the function f(x) = -1(-2|(1((3x - 2)/(3x - 1))^2 + 3((3x - 2)/(3x - 1)) - 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 average of all x-coordinates of local maxima of the function f(x) = -5(1sin(2\u03c0(3|(-5x + 5) - 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": "Find the x-coordinate of the local extremum with the largest y-value of the function f(x) = 2sin(3\u03c0((2((-3(4x^2 - 5) - 3)/(-2(4x^2 - 5) + 1)) - 1)/(-3((-3(4x^2 - 5) - 3)/(-2(4x^2 - 5) + 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": "-1", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local minimum with the smallest y-value of the function f(x) = (-2(-2cos(1\u03c0(2|(3|x - 1|)| + 2) + 2) - 1) + 2)/(-1(-2cos(1\u03c0(2|(3|x - 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 leftmost local maximum of the function f(x) = -3((-2(-3|(1x - 3) - 2|) + 2)/(2(-3|(1x - 3) - 2|) + 2))^2 + 4((-2(-3|(1x - 3) - 2|) + 2)/(2(-3|(1x - 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 minimum of the function f(x) = (1(-5(4(-2e^(-1x) + 1)^2 - 4(-2e^(-1x) + 1) - 1) + 1) + 2)/(1(-5(4(-2e^(-1x) + 1)^2 - 4(-2e^(-1x) + 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 rightmost local minimum of the function f(x) = -2|(1(-1sin(3\u03c0(-3|x + 2| - 1) - 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": "10", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the rightmost local minimum of the function f(x) = 1|(2sin(2\u03c0(1(-3|x + 2| + 3)^2 - 2(-3|x + 2| + 3) + 3) - 2))| - 3 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "7", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local minimum of the function f(x) = (3(-2(-5((3x - 3)/(1x))^2 - 2((3x - 3)/(1x)) + 2)^2 + 5(-5((3x - 3)/(1x))^2 - 2((3x - 3)/(1x)) + 2) - 1) - 3)/(2(-2(-5((3x - 3)/(1x))^2 - 2((3x - 3)/(1x)) + 2)^2 + 5(-5((3x - 3)/(1x))^2 - 2((3x - 3)/(1x)) + 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 rightmost local extremum of the function f(x) = 3|(2(3cos(1\u03c0(-2|x + 3| - 3) + 2) - 3)^2 + 4(3cos(1\u03c0(-2|x + 3| - 3) + 2) - 3) + 3) + 2| - 3 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "How many local extrema (both minima and maxima) does the function f(x) = 4(-5(3|(-2sin(2\u03c0x - 2) + 1)| + 2) + 2) + 3 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "80", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local maximum of the function f(x) = -4(3(-1|(-3|x - 2| - 1) - 2| - 3)^2 + 5(-1|(-3|x - 2| - 1) - 2| - 3) - 3)^2 + 4(3(-1|(-3|x - 2| - 1) - 2| - 3)^2 + 5(-1|(-3|x - 2| - 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": "2", "dataset": "MATH"}
{"messages": [{"content": "How many local minima does the function f(x) = 2|(-1(2|((3x + 3)/(-3x + 2))| - 3)^2 - 2(2|((3x + 3)/(-3x + 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 extrema of the function f(x) = (1(2(5(3sin(1\u03c0x + 1) - 3)^2 + 5(3sin(1\u03c0x + 1) - 3) + 2) + 4))/(-1(2(5(3sin(1\u03c0x + 1) - 3)^2 + 5(3sin(1\u03c0x + 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": "0", "dataset": "MATH"}
{"messages": [{"content": "Find the average of all x-coordinates of local extrema of the function f(x) = 5(2((-1(3|x - 3| - 2) + 1)/(1(3|x - 3| - 2) - 2)) - 5)^2 + 3(2((-1(3|x - 3| - 2) + 1)/(1(3|x - 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": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the average of all x-coordinates of local maxima of the function f(x) = 1sin(2\u03c0(3(1(3x^2 - 3x)^2 - 1(3x^2 - 3x) - 3)^2 + 1(1(3x^2 - 3x)^2 - 1(3x^2 - 3x) - 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 local minimum with the smallest y-value of the function f(x) = (-1(3|(-1|(-4x^2 + 5x + 5) + 2| + 1) + 1| + 2) - 1)/(-1(3|(-1|(-4x^2 + 5x + 5) + 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 maximum of the function f(x) = 3e^(-2(-1(-3|(1|x| - 2) + 2| + 1) - 1)) - 3 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "6", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local minimum of the function f(x) = -3(-3|((-1(-1|x| - 3) + 3)/(-1(-1|x| - 3) - 2)) + 2| + 2)^2 + 4 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}
{"messages": [{"content": "How many local extrema (both minima and maxima) does the function f(x) = 1cos(2\u03c0(-3|(4(-2|x|) + 3) - 2| + 1) + 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": "Find the x-coordinate of the local maximum with the smallest y-value of the function f(x) = -2cos(1\u03c0(3|(1|(-3x^2 - 2x + 3) - 1| + 3) + 1|) - 1) + 1 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local extremum with the largest y-value of the function f(x) = (2(-1|(-2|(-1cos(2\u03c0x + 3) - 2)| + 2) - 1| - 1) + 2)/(-1(-1|(-2|(-1cos(2\u03c0x + 3) - 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": "-10", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the leftmost local maximum of the function f(x) = -4(-2|(-2(2sin(1\u03c0x + 1) + 2)^2 - 4(2sin(1\u03c0x + 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 average of all x-coordinates of local maxima of the function f(x) = -4(-3(5(-3sin(3\u03c0x - 2) + 2)^2 + 1(-3sin(3\u03c0x - 2) + 2) + 3) + 5)^2 - 1(-3(5(-3sin(3\u03c0x - 2) + 2)^2 + 1(-3sin(3\u03c0x - 2) + 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": "0", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the leftmost local minimum of the function f(x) = -1|(3|((2(-2|x| + 3) - 2)/(2(-2|x| + 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(-3(-2cos(1\u03c0x + 1) - 2)^2 + 3(-2cos(1\u03c0x + 1) - 2) - 4)^2 - 2(-3(-2cos(1\u03c0x + 1) - 2)^2 + 3(-2cos(1\u03c0x + 1) - 2) - 4) - 4) - 2)/(1(-3(-3(-2cos(1\u03c0x + 1) - 2)^2 + 3(-2cos(1\u03c0x + 1) - 2) - 4)^2 - 2(-3(-2cos(1\u03c0x + 1) - 2)^2 + 3(-2cos(1\u03c0x + 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 of the function f(x) = 1|((-1(-2(-5x^2 - 4x + 3)^2 + 1(-5x^2 - 4x + 3) - 1) - 2)/(2(-2(-5x^2 - 4x + 3)^2 + 1(-5x^2 - 4x + 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": "0", "dataset": "MATH"}
{"messages": [{"content": "How many local maxima does the function f(x) = (-3(-3(-3|(-4x + 1) - 1| + 3) + 2) + 2)/(-1(-3(-3|(-4x + 1) - 1| + 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) = (1(-2|(-2sin(1\u03c0(4x^2 + 5x + 4) - 1) - 2) + 2| + 1) + 1)/(-2(-2|(-2sin(1\u03c0(4x^2 + 5x + 4) - 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": "6", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the rightmost local extremum of the function f(x) = 1(-2|(-2e^(2(5x - 1)) + 1) + 2| - 2)^2 - 2(-2|(-2e^(2(5x - 1)) + 1) + 2| - 2) + 4 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local maximum with the largest y-value of the function f(x) = -2(1(2|(-4x^2 + 2x + 5) + 2| - 2) - 1)^2 - 5(1(2|(-4x^2 + 2x + 5) + 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": "-1", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the rightmost local minimum of the function f(x) = 4(2((3(-2|x| + 1) + 3)/(3(-2|x| + 1) + 1))^2 - 5((3(-2|x| + 1) + 3)/(3(-2|x| + 1) + 1)) - 3)^2 - 3(2((3(-2|x| + 1) + 3)/(3(-2|x| + 1) + 1))^2 - 5((3(-2|x| + 1) + 3)/(3(-2|x| + 1) + 1)) - 3) + 2 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the leftmost local extremum of the function f(x) = (-2(1|((-3(3cos(3\u03c0x) + 2) - 2)/(1(3cos(3\u03c0x) + 2) - 2)) - 1| + 1) - 2)/(-2(1|((-3(3cos(3\u03c0x) + 2) - 2)/(1(3cos(3\u03c0x) + 2) - 2)) - 1| + 1) - 3) in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-10", "dataset": "MATH"}
{"messages": [{"content": "Find the average of all x-coordinates of local extrema of the function f(x) = 2|((1(-3cos(1\u03c0(3x^2 - 2x - 3) - 1) + 3))/(1(-3cos(1\u03c0(3x^2 - 2x - 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) = -4(-4((3(5x^2 - 4x + 4) + 3)/(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": "Find the average of all x-coordinates of local minima of the function f(x) = 3(1|(-3sin(1\u03c0(4x^2 + 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": "0", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the rightmost local minimum of the function f(x) = (-2(1(-2sin(3\u03c0(-2|x - 2| + 1) - 3) - 2)^2 - 5(-2sin(3\u03c0(-2|x - 2| + 1) - 3) - 2) + 5) + 2)/(-2(1(-2sin(3\u03c0(-2|x - 2| + 1) - 3) - 2)^2 - 5(-2sin(3\u03c0(-2|x - 2| + 1) - 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": "10", "dataset": "MATH"}
{"messages": [{"content": "How many local minima does the function f(x) = (-3(5(-3|(3e^(-1x) - 3) - 1| + 3) - 4) - 3)/(2(5(-3|(3e^(-1x) - 3) - 1| + 3) - 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 local minimum with the largest y-value of the function f(x) = 1sin(3\u03c0((3(5(2x^2 - 3x) + 3))/(-2(5(2x^2 - 3x) + 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) = (-2(-1(-2cos(2\u03c0(1|x + 3| + 2) + 2) + 2)^2 + 3(-2cos(2\u03c0(1|x + 3| + 2) + 2) + 2) - 4) + 3)/(3(-1(-2cos(2\u03c0(1|x + 3| + 2) + 2) + 2)^2 + 3(-2cos(2\u03c0(1|x + 3| + 2) + 2) + 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 average of all x-coordinates of local minima of the function f(x) = (2((-3(-4(-1sin(3\u03c0x) + 3) + 5) + 3)/(-2(-4(-1sin(3\u03c0x) + 3) + 5) + 3)) + 1)/(1((-3(-4(-1sin(3\u03c0x) + 3) + 5) + 3)/(-2(-4(-1sin(3\u03c0x) + 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": "0", "dataset": "MATH"}
{"messages": [{"content": "Find the average of all x-coordinates of local minima of the function f(x) = 1cos(2\u03c0(-1(-3|(-3|x + 2|)| - 3)^2 + 2(-3|(-3|x + 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": "0", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the leftmost local minimum of the function f(x) = -3cos(2\u03c0(-1(-1|(3|x - 1| - 3) + 2| - 2)^2 + 3(-1|(3|x - 1| - 3) + 2| - 2) + 5) - 1) - 1 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-10", "dataset": "MATH"}
{"messages": [{"content": "How many local minima does the function f(x) = -5(3|((-3(-3sin(1\u03c0x - 3) + 1) + 3)/(-3(-3sin(1\u03c0x - 3) + 1) + 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 minimum with the smallest y-value of the function f(x) = -1|(-3cos(2\u03c0(-2(-3|x| + 2)^2 - 4) - 1) + 1)| - 1 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-10", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the rightmost local minimum of the function f(x) = (2(1sin(3\u03c0(-1|(4x^2 + 1x - 3) - 1| + 3) - 1)) + 1)/(-1(1sin(3\u03c0(-1|(4x^2 + 1x - 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": "10", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local minimum of the function f(x) = (2(-4((1(-1|x + 1| + 2) - 3)/(3(-1|x + 1| + 2) - 2)) - 5) + 2)/(-2(-4((1(-1|x + 1| + 2) - 3)/(3(-1|x + 1| + 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": "-1", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the rightmost local maximum of the function f(x) = 4(5(3e^(2((1x + 3)/(1x - 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 rightmost local minimum of the function f(x) = (2(2cos(3\u03c0((-3(1|x - 1| + 1) + 3)/(1(1|x - 1| + 1))) + 3)) + 2)/(-2(2cos(3\u03c0((-3(1|x - 1| + 1) + 3)/(1(1|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": "How many local maxima does the function f(x) = (-2((-1(1|(1x + 1) - 1| + 2) - 3)/(2(1|(1x + 1) - 1| + 2) - 3)) - 2)/(1((-1(1|(1x + 1) - 1| + 2) - 3)/(2(1|(1x + 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 minima does the function f(x) = 3|(-2e^(2(-1|(-1x - 3) + 3| - 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 average of all x-coordinates of local maxima of the function f(x) = 3(2sin(2\u03c0(-5(5x^2 + 5x + 5)^2 + 5(5x^2 + 5x + 5) + 5) - 3) + 3)^2 - 4(2sin(2\u03c0(-5(5x^2 + 5x + 5)^2 + 5(5x^2 + 5x + 5) + 5) - 3) + 3) - 2 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local maximum with the largest y-value of the function f(x) = -5((1(3((-2x + 2)/(3x + 1)) + 5) - 1)/(2(3((-2x + 2)/(3x + 1)) + 5) + 1))^2 - 4((1(3((-2x + 2)/(3x + 1)) + 5) - 1)/(2(3((-2x + 2)/(3x + 1)) + 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": "-1", "dataset": "MATH"}
{"messages": [{"content": "How many local minima does the function f(x) = (1(4(1|(2x^2 + 3) - 2| - 2) + 2) - 1)/(-2(4(1|(2x^2 + 3) - 2| - 2) + 2) + 1) have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the leftmost local maximum of the function f(x) = -3|(1(-2sin(1\u03c0(1x^2 + 2x) + 3) - 2) + 4) + 1| + 1 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-10", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the leftmost local extremum of the function f(x) = 3|((3(-1|(3sin(1\u03c0x + 1) + 2)| + 2))/(1(-1|(3sin(1\u03c0x + 1) + 2)| + 2) + 2))| + 2 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-10", "dataset": "MATH"}
{"messages": [{"content": "How many local extrema (both minima and maxima) does the function f(x) = (-1(4(-1|(-2x - 4) - 3| - 3)^2 + 1(-1|(-2x - 4) - 3| - 3) - 4))/(-3(4(-1|(-2x - 4) - 3| - 3)^2 + 1(-1|(-2x - 4) - 3| - 3) - 4)) have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "304", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the leftmost local extremum of the function f(x) = 1(5(3sin(2\u03c0(1x^2 - 4) + 1) + 3)^2 + 5(3sin(2\u03c0(1x^2 - 4) + 1) + 3) + 5)^2 - 3(5(3sin(2\u03c0(1x^2 - 4) + 1) + 3)^2 + 5(3sin(2\u03c0(1x^2 - 4) + 1) + 3) + 5) - 1 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-10", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local minimum with the largest y-value of the function f(x) = 1|(1cos(1\u03c0((3(1|x - 3| - 2) + 2)/(1(1|x - 3| - 2) + 1)) - 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 rightmost local minimum of the function f(x) = -4(-5((3((-1x - 1)/(2x - 1)) + 1)/(-2((-1x - 1)/(2x - 1))))^2 + 4((3((-1x - 1)/(2x - 1)) + 1)/(-2((-1x - 1)/(2x - 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": "-3", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the leftmost local maximum of the function f(x) = 2((-1(3sin(3\u03c0(1x) - 3) - 2) - 1)/(3(3sin(3\u03c0(1x) - 3) - 2) - 1)) - 3 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-10", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the leftmost local extremum of the function f(x) = 3|(-4(-3cos(3\u03c0(-2x^2 - 1x - 1))) + 2) - 2| in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-10", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local maximum of the function f(x) = -1(3(-3e^(1(1|x - 1| + 2)))^2 - 3(-3e^(1(1|x - 1| + 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 x-coordinate of the local extremum of the function f(x) = 1((2(1|((3x - 2)/(3x - 1)) + 2|))/(-1(1|((3x - 2)/(3x - 1)) + 2|) + 2)) + 4 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local extremum of the function f(x) = -1((3(2|(4x^2 - 3x + 4) + 2| - 3) + 2)/(3(2|(4x^2 - 3x + 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": "0", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local minimum with the smallest y-value of the function f(x) = 3cos(3\u03c0((3((2(-4x + 1) + 2)/(-3(-4x + 1) - 2)) + 1)/(1((2(-4x + 1) + 2)/(-3(-4x + 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": "How many local extrema (both minima and maxima) does the function f(x) = -3|(1(1((-3x + 1)/(1x))^2 + 4((-3x + 1)/(1x)) - 5)^2 + 2(1((-3x + 1)/(1x))^2 + 4((-3x + 1)/(1x)) - 5) - 5) + 3| + 1 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 local extremum of the function f(x) = (3(-1(-1|(-5x^2 + 1) + 2| - 3)^2 + 1) - 1)/(2(-1(-1|(-5x^2 + 1) + 2| - 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 average of all x-coordinates of local extrema of the function f(x) = 1(-5(1|((3x + 2)/(-2x + 3)) - 2| - 1) - 4)^2 + 5(-5(1|((3x + 2)/(-2x + 3)) - 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": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the leftmost local minimum of the function f(x) = 3|(-3((2(-2sin(2\u03c0x) - 2))/(3(-2sin(2\u03c0x) - 2) - 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": "-10", "dataset": "MATH"}
{"messages": [{"content": "How many local maxima does the function f(x) = -3|(1(-1|(-2sin(3\u03c0x + 3)) + 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 leftmost local maximum of the function f(x) = (-1(-2(2cos(3\u03c0(-1|x + 2| - 3) + 2) + 3)^2 + 3(2cos(3\u03c0(-1|x + 2| - 3) + 2) + 3)) - 1)/(3(-2(2cos(3\u03c0(-1|x + 2| - 3) + 2) + 3)^2 + 3(2cos(3\u03c0(-1|x + 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": "How many local maxima does the function f(x) = (-2(-2(1|(2e^(1x) + 2) - 2| - 2)^2 - 4(1|(2e^(1x) + 2) - 2| - 2) - 4) - 2)/(-2(-2(1|(2e^(1x) + 2) - 2| - 2)^2 - 4(1|(2e^(1x) + 2) - 2| - 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 extremum of the function f(x) = -5(-3cos(2\u03c0(2|(3x^2 + 3x + 1) + 2| + 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": "-10", "dataset": "MATH"}
{"messages": [{"content": "How many local minima does the function f(x) = 2|(1e^(-1(-2|(-1x^2 + 5) + 3|)) - 1) - 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 average of all x-coordinates of local maxima of the function f(x) = (3(-1sin(3\u03c0(1|(-3x^2 + 3x + 2) - 1| + 2) + 2)) + 1)/(1(-1sin(3\u03c0(1|(-3x^2 + 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": "0", "dataset": "MATH"}
{"messages": [{"content": "Find the average of all x-coordinates of local minima of the function f(x) = -1e^(-2(5((-3(-1|x - 3|) - 1)/(3(-1|x - 3|)))^2 - 3((-3(-1|x - 3|) - 1)/(3(-1|x - 3|))) - 1)) + 3 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local minimum of the function f(x) = (1(2(5((-2x - 2)/(3x + 1))^2 - 2((-2x - 2)/(3x + 1)) + 4) - 3) - 2)/(-2(2(5((-2x - 2)/(3x + 1))^2 - 2((-2x - 2)/(3x + 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": "0", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the leftmost local minimum of the function f(x) = -2(-3sin(3\u03c0(-3((3x - 2)/(1x - 2))^2 + 3((3x - 2)/(1x - 2)) + 3) + 1) + 1)^2 - 3(-3sin(3\u03c0(-3((3x - 2)/(1x - 2))^2 + 3((3x - 2)/(1x - 2)) + 3) + 1) + 1) - 3 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-10", "dataset": "MATH"}
{"messages": [{"content": "How many local extrema (both minima and maxima) does the function f(x) = 3(2sin(1\u03c0(1|((-3x - 3)/(-3x + 2))|) - 3) - 3) + 5 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "28", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local maximum with the largest y-value of the function f(x) = -5(1(3|(3x - 4) + 1| - 2)^2 - 4(3|(3x - 4) + 1| - 2) - 1)^2 - 2(1(3|(3x - 4) + 1| - 2)^2 - 4(3|(3x - 4) + 1| - 2) - 1) + 3 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local extremum of the function f(x) = -1e^(1(-3(1(3|x| - 1)^2 + 3(3|x| - 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": "0", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the rightmost local extremum of the function f(x) = -1cos(1\u03c0(2|((1(2|x - 2|) - 3)/(-3(2|x - 2|) - 3))| - 1) + 2) - 3 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "6", "dataset": "MATH"}
{"messages": [{"content": "Find the average of all x-coordinates of local maxima of the function f(x) = 4(4(-2cos(2\u03c0(-1x + 3) + 1) + 2) + 4)^2 + 1(4(-2cos(2\u03c0(-1x + 3) + 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": "How many local maxima does the function f(x) = 5(-4((1(3x^2 + 1x + 3) + 1)/(2(3x^2 + 1x + 3) + 1))^2 + 2((1(3x^2 + 1x + 3) + 1)/(2(3x^2 + 1x + 3) + 1)) + 3)^2 + 5(-4((1(3x^2 + 1x + 3) + 1)/(2(3x^2 + 1x + 3) + 1))^2 + 2((1(3x^2 + 1x + 3) + 1)/(2(3x^2 + 1x + 3) + 1)) + 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 largest y-value of the function f(x) = -2cos(1\u03c0((-2(-4(-2|x + 1|)^2 + 4(-2|x + 1|) + 2) + 2)/(1(-4(-2|x + 1|)^2 + 4(-2|x + 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": "-1", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local minimum with the largest y-value of the function f(x) = -1((-2(-1sin(2\u03c0(1|x - 2| + 1) - 1) - 2) - 2)/(1(-1sin(2\u03c0(1|x - 2| + 1) - 1) - 2))) + 2 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-10", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the rightmost local extremum of the function f(x) = 3(-5(-1((3x + 1)/(-1x + 2))^2 + 2)^2 + 1)^2 - 3(-5(-1((3x + 1)/(-1x + 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": "0", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the rightmost local minimum of the function f(x) = -3|(2cos(2\u03c0(1(-5x^2 - 4x + 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": "10", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local minimum with the largest y-value of the function f(x) = 2((3(-4(-2sin(1\u03c0x - 2))^2 + 1(-2sin(1\u03c0x - 2)) + 3) + 3)/(-1(-4(-2sin(1\u03c0x - 2))^2 + 1(-2sin(1\u03c0x - 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": "-9", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the leftmost local minimum of the function f(x) = -3sin(2\u03c0((3(-2|(-5x + 4) - 3|) - 3)/(3(-2|(-5x + 4) - 3|) + 2)) - 2) in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}
{"messages": [{"content": "How many local maxima does the function f(x) = 3((3((1(1x^2 - 3) - 1)/(-1(1x^2 - 3))) - 3)/(-2((1(1x^2 - 3) - 1)/(-1(1x^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": "Find the x-coordinate of the rightmost local extremum of the function f(x) = 2cos(3\u03c0(-1|(-5(-5x^2 - 1x) - 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 maxima does the function f(x) = -5(3cos(1\u03c0((3(2x^2 - 1x + 3) + 3)/(-2(2x^2 - 1x + 3) - 1))) + 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) = 3(2|(4(2x - 2)^2 + 3(2x - 2) - 2) + 1| - 1)^2 + 3(2|(4(2x - 2)^2 + 3(2x - 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 local maximum with the largest y-value of the function f(x) = 2(-5((-1(-1cos(3\u03c0x - 3) - 1) - 3)/(2(-1cos(3\u03c0x - 3) - 1) - 1))^2 + 1((-1(-1cos(3\u03c0x - 3) - 1) - 3)/(2(-1cos(3\u03c0x - 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": "-10", "dataset": "MATH"}
{"messages": [{"content": "How many local extrema (both minima and maxima) does the function f(x) = -4(1cos(2\u03c0(-3|((1x - 2)/(2x + 3)) - 1| - 3) + 3) - 1)^2 - 5(1cos(2\u03c0(-3|((1x - 2)/(2x + 3)) - 1| - 3) + 3) - 1) + 2 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "98", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the leftmost local maximum of the function f(x) = (1(5(-3(2sin(2\u03c0x - 3) + 2) - 3) - 5) - 2)/(-1(5(-3(2sin(2\u03c0x - 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 leftmost local extremum of the function f(x) = 3sin(2\u03c0(-5(4(-3x^2 + 2x)^2 - 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": "-3", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local maximum with the largest y-value of the function f(x) = 2cos(3\u03c0(1|((3((3x + 2)/(-2x - 1)) + 2)/(2((3x + 2)/(-2x - 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 maximum with the largest y-value of the function f(x) = 2cos(1\u03c0(-1((2((3x - 2)/(-2x - 1)) + 2)/(1((3x - 2)/(-2x - 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": "-9", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the leftmost local maximum of the function f(x) = 1cos(3\u03c0(-2(-1|(-5x - 1) + 2| - 3)^2 + 1(-1|(-5x - 1) + 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": "-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(3\u03c0(-5(1x^2 - 4x - 5)^2 + 1(1x^2 - 4x - 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": "-7", "dataset": "MATH"}
{"messages": [{"content": "How many local maxima does the function f(x) = -2|((-1(1((3x - 2)/(-3x - 3))^2 + 2((3x - 2)/(-3x - 3)) + 2) - 1)/(-1(1((3x - 2)/(-3x - 3))^2 + 2((3x - 2)/(-3x - 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 rightmost local minimum of the function f(x) = -3(-3sin(2\u03c0(1(1x - 3)^2 - 3(1x - 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": "10", "dataset": "MATH"}
{"messages": [{"content": "Find the average of all x-coordinates of local extrema of the function f(x) = (-3(5(-5(3sin(1\u03c0x - 3) - 3)^2 + 4(3sin(1\u03c0x - 3) - 3) - 5)^2 + 1(-5(3sin(1\u03c0x - 3) - 3)^2 + 4(3sin(1\u03c0x - 3) - 3) - 5) + 5) - 1)/(-2(5(-5(3sin(1\u03c0x - 3) - 3)^2 + 4(3sin(1\u03c0x - 3) - 3) - 5)^2 + 1(-5(3sin(1\u03c0x - 3) - 3)^2 + 4(3sin(1\u03c0x - 3) - 3) - 5) + 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 local extremum of the function f(x) = 1|(-2|(1((-2x - 3)/(-3x)) + 2) - 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": "0", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the leftmost local maximum of the function f(x) = (1(-2|(3|(-1|x - 3| + 1) + 2| - 3) - 1| + 2) + 3)/(1(-2|(3|(-1|x - 3| + 1) + 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": "0", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the leftmost local minimum of the function f(x) = 2(-3|(1sin(2\u03c0(-5x - 3) + 1) - 2) + 1|)^2 - 5(-3|(1sin(2\u03c0(-5x - 3) + 1) - 2) + 1|) + 4 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-10", "dataset": "MATH"}
{"messages": [{"content": "How many local extrema (both minima and maxima) does the function f(x) = -2|(-2|(3(-3x - 2)^2 - 5(-3x - 2) - 3)| + 2) + 3| + 2 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) = -4((-3(-2sin(3\u03c0(3x + 4) - 1) + 1))/(-3(-2sin(3\u03c0(3x + 4) - 1) + 1) + 4)) + 3 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "Find the average of all x-coordinates of local minima of the function f(x) = 3(4((-2(3|x - 3| - 1))/(1(3|x - 3| - 1) + 3))^2 - 2((-2(3|x - 3| - 1))/(1(3|x - 3| - 1) + 3)) - 4)^2 + 1(4((-2(3|x - 3| - 1))/(1(3|x - 3| - 1) + 3))^2 - 2((-2(3|x - 3| - 1))/(1(3|x - 3| - 1) + 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": "3", "dataset": "MATH"}
{"messages": [{"content": "How many local minima does the function f(x) = (2(1|(-3|(-1|x + 1| + 3) - 2| - 3) + 2| - 2) + 3)/(-1(1|(-3|(-1|x + 1| + 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 local maximum of the function f(x) = -2e^(1((-2(-1|(5x^2 - 2x - 5) - 2| + 2) - 2)/(3(-1|(5x^2 - 2x - 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": "0", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local maximum of the function f(x) = -3e^(1(1(-3((2x - 2)/(-3x + 4))^2 + 3((2x - 2)/(-3x + 4)) - 4))) - 1 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local minimum of the function f(x) = 1e^(2(-3|(1(2x - 1) + 4) - 3| - 2)) - 2 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the leftmost local maximum of the function f(x) = -4(-4(-3(-3cos(3\u03c0x))^2 - 3(-3cos(3\u03c0x)) + 4) - 2) + 1 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-10", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local maximum with the largest y-value of the function f(x) = 1|(-1|((-2(3cos(2\u03c0x + 3)))/(-2(3cos(2\u03c0x + 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": "-10", "dataset": "MATH"}
{"messages": [{"content": "Find the average of all x-coordinates of local minima of the function f(x) = 3|(5(1(2cos(1\u03c0x)) - 2)^2 - 1(1(2cos(1\u03c0x)) - 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": "1", "dataset": "MATH"}
{"messages": [{"content": "How many local minima does the function f(x) = -3(3|((-2(5x^2 + 4x + 1))/(-2(5x^2 + 4x + 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 average of all x-coordinates of local extrema of the function f(x) = (2(3(3cos(3\u03c0((3x)/(2x - 1)) - 1) + 2)^2 - 1) - 2)/(-3(3(3cos(3\u03c0((3x)/(2x - 1)) - 1) + 2)^2 - 1) + 2) in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local minimum of the function f(x) = -3|(-1|(-2(3x)^2 - 3(3x) - 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": "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(-4((3x + 2)/(-2x - 3))) + 1)) - 1)/(2(3sin(3\u03c0(-4((3x + 2)/(-2x - 3))) + 1)) - 1) in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-8", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local maximum of the function f(x) = 5(-1|((1(3|x|) + 2)/(2(3|x|) + 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": "0", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local maximum with the largest y-value of the function f(x) = -3((-2(4(3cos(2\u03c0x)) + 3))/(-2(4(3cos(2\u03c0x)) + 3) - 1))^2 - 4((-2(4(3cos(2\u03c0x)) + 3))/(-2(4(3cos(2\u03c0x)) + 3) - 1)) - 3 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-10", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local minimum with the largest y-value of the function f(x) = -2(2(-2(1cos(2\u03c0x - 2) - 3) - 5)^2 - 1(-2(1cos(2\u03c0x - 2) - 3) - 5) - 3)^2 + 4 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-10", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local maximum with the largest y-value of the function f(x) = -3(-3cos(3\u03c0((-1(-4x - 4) + 2)/(1(-4x - 4))) - 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 minimum of the function f(x) = -1|(1(-1|(-2|x|) - 1|)^2 + 5(-1|(-2|x|) - 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 extremum of the function f(x) = -1((-2(-1cos(2\u03c0(-3|x + 1| - 2) + 2) + 3) - 3)/(-2(-1cos(2\u03c0(-3|x + 1| - 2) + 2) + 3) + 1))^2 - 2((-2(-1cos(2\u03c0(-3|x + 1| - 2) + 2) + 3) - 3)/(-2(-1cos(2\u03c0(-3|x + 1| - 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 with the largest y-value of the function f(x) = (3(-2sin(1\u03c0((-2(-2|x - 2| + 1) + 1)/(1(-2|x - 2| + 1) + 1)) - 1) - 1))/(2(-2sin(1\u03c0((-2(-2|x - 2| + 1) + 1)/(1(-2|x - 2| + 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": "0", "dataset": "MATH"}
{"messages": [{"content": "Find the average of all x-coordinates of local maxima of the function f(x) = -3|(-5(2(-3sin(3\u03c0x - 1) - 3)^2 + 1(-3sin(3\u03c0x - 1) - 3) - 4)^2 + 3(2(-3sin(3\u03c0x - 1) - 3)^2 + 1(-3sin(3\u03c0x - 1) - 3) - 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": "0", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local minimum with the largest y-value of the function f(x) = -3|(-4(1(3|x - 3| - 2) - 5)^2 - 5(1(3|x - 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": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the rightmost local maximum of the function f(x) = -1|((-1(1e^(2(2x^2 + 5x + 5)) + 3) + 3)/(2(1e^(2(2x^2 + 5x + 5)) + 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) = -1|(4(-3sin(3\u03c0(-3x^2 - 3x + 3) - 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": "526", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local minimum of the function f(x) = -2(-1e^(-2(4(-2|x| - 2)^2 - 2)))^2 + 5(-1e^(-2(4(-2|x| - 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 rightmost local maximum of the function f(x) = -3e^(1(-3|(2((-1x)/(2x + 3)) - 1) - 3| - 2)) + 2 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-1", "dataset": "MATH"}
{"messages": [{"content": "How many local minima does the function f(x) = (-1(2((-3(5x^2 + 1) - 1)/(2(5x^2 + 1) - 1)) - 5) - 1)/(-1(2((-3(5x^2 + 1) - 1)/(2(5x^2 + 1) - 1)) - 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": "How many local minima does the function f(x) = -3e^(2(1((1(1|x + 3| - 3) + 3)/(2(1|x + 3| - 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": "Find the x-coordinate of the rightmost local maximum of the function f(x) = (-3(-3|(2(2x + 3)^2 - 3)| + 3) + 3)/(-2(-3|(2(2x + 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": "-1", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the rightmost local extremum of the function f(x) = -1|(5(-2|((-3x + 1)/(3x + 2)) + 2| + 2)^2 - 4(-2|((-3x + 1)/(3x + 2)) + 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": "-1", "dataset": "MATH"}
{"messages": [{"content": "Find the average of all x-coordinates of local minima of the function f(x) = 2(-3|(3(1x^2 - 5x + 4)^2 + 2(1x^2 - 5x + 4) - 2) + 2|)^2 + 2(-3|(3(1x^2 - 5x + 4)^2 + 2(1x^2 - 5x + 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": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the rightmost local extremum of the function f(x) = 2|(3(4(2sin(1\u03c0x) - 1) + 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": "10", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local maximum of the function f(x) = 1((-3(-2|(-3x - 5) + 3| + 1) - 1)/(3(-2|(-3x - 5) + 3| + 1) - 2)) + 1 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-1", "dataset": "MATH"}
{"messages": [{"content": "How many local maxima does the function f(x) = 1(1((-3((-1x + 1)/(2x - 1)))/(3((-1x + 1)/(2x - 1)) - 2)))^2 - 5(1((-3((-1x + 1)/(2x - 1)))/(3((-1x + 1)/(2x - 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 leftmost local minimum of the function f(x) = -1|(2sin(2\u03c0(-2(-1x + 2)^2 - 5(-1x + 2) + 4) - 1) + 1)| in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-10", "dataset": "MATH"}
{"messages": [{"content": "How many local maxima does the function f(x) = 2|(4(-3|(-2x^2 - 2) - 2| - 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 local extremum of the function f(x) = -1(3|(-1|(1x^2 + 1x + 5) + 1| - 1) + 1| + 3)^2 - 2(3|(-1|(1x^2 + 1x + 5) + 1| - 1) + 1| + 3) - 1 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}
{"messages": [{"content": "How many local maxima does the function f(x) = (1(-1|((-2(-1|x - 3| + 1) + 3)/(2(-1|x - 3| + 1) + 3)) + 1| + 1) - 2)/(1(-1|((-2(-1|x - 3| + 1) + 3)/(2(-1|x - 3| + 1) + 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 extremum of the function f(x) = -1|(5(-1(-1|x - 3| + 1) - 1)^2 + 1(-1(-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 rightmost local minimum of the function f(x) = (-2(-3sin(1\u03c0(1(-1x^2 - 1x + 4)^2 - 1(-1x^2 - 1x + 4) + 1) + 2) + 1) + 1)/(-3(-3sin(1\u03c0(1(-1x^2 - 1x + 4)^2 - 1(-1x^2 - 1x + 4) + 1) + 2) + 1) + 4) in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "How many local maxima does the function f(x) = 4((3(-1|(-2x + 2) - 3|) - 1)/(1(-1|(-2x + 2) - 3|) + 2))^2 + 1((3(-1|(-2x + 2) - 3|) - 1)/(1(-1|(-2x + 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 maximum of the function f(x) = (-1(-1(-1(-5x^2 - 2x - 2) + 2)^2 - 3(-1(-5x^2 - 2x - 2) + 2) - 1) + 2)/(-3(-1(-1(-5x^2 - 2x - 2) + 2)^2 - 3(-1(-5x^2 - 2x - 2) + 2) - 1) - 3) in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the rightmost local maximum of the function f(x) = 1cos(2\u03c0(-3(-1((1x + 3)/(3x + 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) = -4(2|(-3cos(1\u03c0((-2x - 2)/(-3x - 2)) - 2) - 1)| - 3)^2 + 5(2|(-3cos(1\u03c0((-2x - 2)/(-3x - 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": "-1", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the leftmost local minimum of the function f(x) = -1(-2cos(3\u03c0((-1(4x + 4) + 3)/(3(4x + 4) - 1)) - 3) - 2)^2 + 5(-2cos(3\u03c0((-1(4x + 4) + 3)/(3(4x + 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 leftmost local maximum of the function f(x) = (-3(2|(-3|(3sin(2\u03c0x - 2) - 2) + 2| - 1) - 3| - 2) - 2)/(1(2|(-3|(3sin(2\u03c0x - 2) - 2) + 2| - 1) - 3| - 2)) in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-10", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the leftmost local maximum of the function f(x) = (3(-1(3sin(1\u03c0(-3x + 5) - 1) - 3)^2 + 2(3sin(1\u03c0(-3x + 5) - 1) - 3) + 1) - 1)/(2(-1(3sin(1\u03c0(-3x + 5) - 1) - 3)^2 + 2(3sin(1\u03c0(-3x + 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": "-10", "dataset": "MATH"}
{"messages": [{"content": "Find the average of all x-coordinates of local extrema of the function f(x) = -5(-3(3|(1x^2 - 4x + 4) - 3| + 1) - 1)^2 + 1(-3(3|(1x^2 - 4x + 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 maximum of the function f(x) = 1|(-2e^(-1((1(5x^2 - 3x) + 3)/(-3(5x^2 - 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": "0", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local minimum of the function f(x) = 1|(5(-2|(-1x^2 + 3x - 3)| - 2)^2 - 2(-2|(-1x^2 + 3x - 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": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local minimum with the smallest y-value of the function f(x) = 2sin(3\u03c0(1|(2|((-3x + 1)/(-2x - 2)) + 1| + 2)| + 3) - 3) + 2 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-6", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the leftmost local extremum of the function f(x) = -1((1(1cos(1\u03c0(3|x - 2| - 2) - 1) - 3) + 1)/(1(1cos(1\u03c0(3|x - 2| - 2) - 1) - 3)))^2 + 4((1(1cos(1\u03c0(3|x - 2| - 2) - 1) - 3) + 1)/(1(1cos(1\u03c0(3|x - 2| - 2) - 1) - 3))) in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-10", "dataset": "MATH"}
{"messages": [{"content": "How many local minima does the function f(x) = (-3((-2(2|(-2|x|) + 1| - 2) + 1)/(-1(2|(-2|x|) + 1| - 2) - 2)) - 1)/(3((-2(2|(-2|x|) + 1| - 2) + 1)/(-1(2|(-2|x|) + 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 average of all x-coordinates of local extrema of the function f(x) = -2(2sin(2\u03c0(-1(2|x + 1| + 2) + 4) + 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 leftmost local minimum of the function f(x) = (-3(4(1|(-2sin(2\u03c0x + 1) + 3)| + 1)^2 + 4(1|(-2sin(2\u03c0x + 1) + 3)| + 1)) - 1)/(-2(4(1|(-2sin(2\u03c0x + 1) + 3)| + 1)^2 + 4(1|(-2sin(2\u03c0x + 1) + 3)| + 1)) + 3) in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-9", "dataset": "MATH"}
{"messages": [{"content": "How many local minima does the function f(x) = -1|(5(3|(-3|x - 1| + 3) + 1| - 2)^2 + 2(3|(-3|x - 1| + 3) + 1| - 2) + 2) - 1| + 2 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local extremum of the function f(x) = 5((3(3(-4x^2 + 1x)^2 - 4(-4x^2 + 1x) - 3) + 1)/(-2(3(-4x^2 + 1x)^2 - 4(-4x^2 + 1x) - 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) = 5(1sin(2\u03c0(-2|((-1x + 3)/(3x)) + 3| - 2) - 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": "Find the x-coordinate of the local maximum with the largest y-value of the function f(x) = 1(5(4(2|x| - 2) - 1)^2 - 3(4(2|x| - 2) - 1) - 5)^2 + 1(5(4(2|x| - 2) - 1)^2 - 3(4(2|x| - 2) - 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": "0", "dataset": "MATH"}
{"messages": [{"content": "How many local maxima does the function f(x) = 1(1((1((-3x + 3)/(-1x + 2)))/(2((-3x + 3)/(-1x + 2)) - 1))^2 + 1((1((-3x + 3)/(-1x + 2)))/(2((-3x + 3)/(-1x + 2)) - 1)) + 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 rightmost local minimum of the function f(x) = 2|(-4(-1|(2|x + 2| - 2) - 2| - 2)^2 + 4(-1|(2|x + 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": "0", "dataset": "MATH"}
{"messages": [{"content": "Find the average of all x-coordinates of local extrema of the function f(x) = -1(1sin(1\u03c0(-3((2x - 3)/(-3x - 1))^2 + 4((2x - 3)/(-3x - 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": "-1", "dataset": "MATH"}
{"messages": [{"content": "How many local extrema (both minima and maxima) does the function f(x) = -3|((-1(4(-2sin(2\u03c0x + 1) + 1) + 4) + 1)/(2(4(-2sin(2\u03c0x + 1) + 1) + 4) + 1)) - 2| - 2 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "40", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local extremum with the largest y-value of the function f(x) = -1sin(1\u03c0(-5((2((2x)/(-3x + 2)) + 2)/(-2((2x)/(-3x + 2)) + 3))^2 - 5((2((2x)/(-3x + 2)) + 2)/(-2((2x)/(-3x + 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 average of all x-coordinates of local maxima of the function f(x) = -2(-2e^(-1(-3|(-3|x + 1| + 2) + 1| + 3)) + 1)^2 + 3(-2e^(-1(-3|(-3|x + 1| + 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": "-1", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the rightmost local extremum of the function f(x) = 3|(2(1cos(3\u03c0(-3|x|)) - 2)^2 + 1(1cos(3\u03c0(-3|x|)) - 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 maximum with the smallest y-value of the function f(x) = 1(3|(-1(1x^2 - 4x + 3)^2 + 5(1x^2 - 4x + 3) + 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 average of all x-coordinates of local extrema of the function f(x) = -3(2|(-2(3sin(1\u03c0x - 3) - 3) - 3) - 1| + 3)^2 - 2(2|(-2(3sin(1\u03c0x - 3) - 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 local maximum with the smallest y-value of the function f(x) = 2|(-1|(2sin(1\u03c0(2x + 4) + 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 rightmost local maximum of the function f(x) = (1(-3|(4(1x^2 + 5x) - 3) - 2| + 1) - 3)/(3(-3|(4(1x^2 + 5x) - 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 extrema (both minima and maxima) does the function f(x) = 3(4(2|(-2e^(1x) + 1) + 3| - 1)^2 + 1(2|(-2e^(1x) + 1) + 3| - 1) + 4)^2 + 5(4(2|(-2e^(1x) + 1) + 3| - 1)^2 + 1(2|(-2e^(1x) + 1) + 3| - 1) + 4) - 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) = 4((-2(4((1x - 3)/(3x))^2 + 4((1x - 3)/(3x)) + 1) + 1)/(-3(4((1x - 3)/(3x))^2 + 4((1x - 3)/(3x)) + 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 extremum of the function f(x) = 1sin(1\u03c0(-1(1(-3x^2 + 2x - 5) + 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": "How many local minima does the function f(x) = -3(-2((-3((-1x + 3)/(3x + 2)) + 1)/(-1((-1x + 3)/(3x + 2)))) - 5)^2 + 2(-2((-3((-1x + 3)/(3x + 2)) + 1)/(-1((-1x + 3)/(3x + 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 maximum with the smallest y-value of the function f(x) = -2(3sin(3\u03c0((2(2|x| + 3))/(-3(2|x| + 3) + 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": "0", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local minimum of the function f(x) = -1((2(-2|(3x^2 + 2x - 3) + 3| - 3) + 3)/(-2(-2|(3x^2 + 2x - 3) + 3| - 3))) - 5 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local minimum of the function f(x) = (3((1(4((2x + 3)/(-1x - 1))^2 - 2((2x + 3)/(-1x - 1)) + 4) - 2)/(-3(4((2x + 3)/(-1x - 1))^2 - 2((2x + 3)/(-1x - 1)) + 4) + 4)) + 3)/(-2((1(4((2x + 3)/(-1x - 1))^2 - 2((2x + 3)/(-1x - 1)) + 4) - 2)/(-3(4((2x + 3)/(-1x - 1))^2 - 2((2x + 3)/(-1x - 1)) + 4) + 4)) + 1) in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-1", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the rightmost local extremum of the function f(x) = -2(-4(1cos(1\u03c0(-2|x + 2| - 3)) - 3) - 2)^2 + 5(-4(1cos(1\u03c0(-2|x + 2| - 3)) - 3) - 2) + 3 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local extremum of the function f(x) = (2(-1|(-3(3x + 3)^2 + 3(3x + 3) - 4) - 3| - 2) - 2)/(-3(-1|(-3(3x + 3)^2 + 3(3x + 3) - 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 maximum with the largest y-value of the function f(x) = 1((1(3e^(1(-1x^2 - 2x - 2)) - 2) + 1)/(1(3e^(1(-1x^2 - 2x - 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": "-6", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local extremum of the function f(x) = -3|((-1(3(-5x^2 - 4x - 5)^2 + 4(-5x^2 - 4x - 5) + 3))/(-2(3(-5x^2 - 4x - 5)^2 + 4(-5x^2 - 4x - 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": "Find the x-coordinate of the local extremum of the function f(x) = (1((1(-2|((1x + 1)/(1x)) - 2| - 1) + 2)/(1(-2|((1x + 1)/(1x)) - 2| - 1) + 3)) - 1)/(1((1(-2|((1x + 1)/(1x)) - 2| - 1) + 2)/(1(-2|((1x + 1)/(1x)) - 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": "Find the x-coordinate of the rightmost local extremum of the function f(x) = -1((3(2|(2sin(3\u03c0x + 1) + 2) - 3| + 2) - 3)/(3(2|(2sin(3\u03c0x + 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": "10", "dataset": "MATH"}
{"messages": [{"content": "How many local minima does the function f(x) = (1(1(-1(1x - 1)^2 - 1(1x - 1) - 2)^2 + 2(-1(1x - 1)^2 - 1(1x - 1) - 2) - 3))/(1(1(-1(1x - 1)^2 - 1(1x - 1) - 2)^2 + 2(-1(1x - 1)^2 - 1(1x - 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) = 2(-3(2cos(3\u03c0(-5x + 4) + 1) + 2) - 4)^2 + 2(-3(2cos(3\u03c0(-5x + 4) + 1) + 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": "-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(1x^2 + 4x - 2)^2 - 4)^2 + 5(-2(1x^2 + 4x - 2)^2 - 4)) - 1| + 1 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-4", "dataset": "MATH"}
{"messages": [{"content": "Find the average of all x-coordinates of local minima of the function f(x) = 4(-3e^(2(2|(2|x| - 3) - 2| - 3)) - 2)^2 - 4(-3e^(2(2|(2|x| - 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": "How many local extrema (both minima and maxima) does the function f(x) = (1((-3(5(1|x + 1| - 3)^2 + 1(1|x + 1| - 3) - 4) - 3)/(1(5(1|x + 1| - 3)^2 + 1(1|x + 1| - 3) - 4) + 2)) + 2)/(-2((-3(5(1|x + 1| - 3)^2 + 1(1|x + 1| - 3) - 4) - 3)/(1(5(1|x + 1| - 3)^2 + 1(1|x + 1| - 3) - 4) + 2)) - 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": "How many local minima does the function f(x) = -2(-3((2((-1x - 3)/(-3x - 2)) + 1)/(1((-1x - 3)/(-3x - 2)) - 3)) + 2)^2 - 5(-3((2((-1x - 3)/(-3x - 2)) + 1)/(1((-1x - 3)/(-3x - 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 x-coordinate of the local minimum of the function f(x) = (2(1e^(2(-5((1x)/(1x + 3))^2 + 1((1x)/(1x + 3)) + 2)) + 2) - 3)/(1(1e^(2(-5((1x)/(1x + 3))^2 + 1((1x)/(1x + 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 minimum of the function f(x) = -3|(-2|(1|(-1x^2 - 2x) - 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": "How many local maxima does the function f(x) = (1(3|((-1(-1x^2 - 5x - 2) - 2)/(1(-1x^2 - 5x - 2) + 1)) - 1| - 3))/(-2(3|((-1(-1x^2 - 5x - 2) - 2)/(1(-1x^2 - 5x - 2) + 1)) - 1| - 3) + 1) have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local minimum of the function f(x) = (-2((-2(-1|((2x - 2)/(-2x)) - 3|) + 3)/(-1(-1|((2x - 2)/(-2x)) - 3|) - 3)) + 2)/(-3((-2(-1|((2x - 2)/(-2x)) - 3|) + 3)/(-1(-1|((2x - 2)/(-2x)) - 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 rightmost local minimum of the function f(x) = -2|(-1|(1(-3cos(1\u03c0x + 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": "10", "dataset": "MATH"}
{"messages": [{"content": "Find the average of all x-coordinates of local maxima of the function f(x) = -3sin(1\u03c0(3|(-5(2x^2 + 2x - 3) - 1) + 1| - 3) + 2) + 2 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local minimum of the function f(x) = 4(-2e^(1(4(3x^2 + 2x - 5)^2 + 3(3x^2 + 2x - 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": "0", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the leftmost local minimum of the function f(x) = -2(3sin(3\u03c0(-1|(-1x^2 - 3x - 3) + 3| - 1) + 2) + 2)^2 - 3(3sin(3\u03c0(-1|(-1x^2 - 3x - 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": "-10", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the leftmost local minimum of the function f(x) = 5(3((-1(1sin(2\u03c0x - 3) + 2) - 3)/(-2(1sin(2\u03c0x - 3) + 2) - 2))^2 + 1((-1(1sin(2\u03c0x - 3) + 2) - 3)/(-2(1sin(2\u03c0x - 3) + 2) - 2)) + 2)^2 - 3(3((-1(1sin(2\u03c0x - 3) + 2) - 3)/(-2(1sin(2\u03c0x - 3) + 2) - 2))^2 + 1((-1(1sin(2\u03c0x - 3) + 2) - 3)/(-2(1sin(2\u03c0x - 3) + 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": "-9", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local maximum of the function f(x) = 4(-2e^(1(-3|((3x)/(2x - 1)) - 1| - 1)) + 1)^2 - 5(-2e^(1(-3|((3x)/(2x - 1)) - 1| - 1)) + 1) - 5 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local maximum of the function f(x) = (-3(4((-1(-5x^2 - 5x - 4) - 2)/(-1(-5x^2 - 5x - 4) + 3)) - 5) + 3)/(-1(4((-1(-5x^2 - 5x - 4) - 2)/(-1(-5x^2 - 5x - 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 local minimum with the smallest y-value of the function f(x) = -3sin(3\u03c0(1(-3|(-2|x + 2| - 3) + 2| + 1) + 4) + 1) in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-10", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local extremum with the smallest y-value of the function f(x) = 4(2sin(3\u03c0(-1((-1x - 2)/(-2x + 1))^2 - 4((-1x - 2)/(-2x + 1)) - 3) + 2) - 3)^2 - 1(2sin(3\u03c0(-1((-1x - 2)/(-2x + 1))^2 - 4((-1x - 2)/(-2x + 1)) - 3) + 2) - 3) - 1 in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-4", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the local minimum of the function f(x) = -3(1(5((-2x + 2)/(-2x)) + 5)^2 - 4(5((-2x + 2)/(-2x)) + 5) - 2)^2 + 2(1(5((-2x + 2)/(-2x)) + 5)^2 - 4(5((-2x + 2)/(-2x)) + 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": "1", "dataset": "MATH"}
{"messages": [{"content": "How many local minima does the function f(x) = -1((2(-1|(5x - 3) + 1| + 3) - 1)/(1(-1|(5x - 3) + 1| + 3) + 1))^2 + 1((2(-1|(5x - 3) + 1| + 3) - 1)/(1(-1|(5x - 3) + 1| + 3) + 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 extrema (both minima and maxima) does the function f(x) = -1sin(2\u03c0(4(3(-2|x - 3|)^2 + 1(-2|x - 3|) - 1)^2 + 3(3(-2|x - 3|)^2 + 1(-2|x - 3|) - 1) + 1) + 1) have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "104", "dataset": "MATH"}
{"messages": [{"content": "Find the average of all x-coordinates of local extrema of the function f(x) = -2|(-1cos(2\u03c0(-1|(-2x^2 - 1x + 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 maximum with the smallest y-value of the function f(x) = (3(3(-3sin(1\u03c0(-2x^2 - 2x - 5) - 3) + 1)^2 + 1(-3sin(1\u03c0(-2x^2 - 2x - 5) - 3) + 1) - 2) - 1)/(2(3(-3sin(1\u03c0(-2x^2 - 2x - 5) - 3) + 1)^2 + 1(-3sin(1\u03c0(-2x^2 - 2x - 5) - 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": "-10", "dataset": "MATH"}
{"messages": [{"content": "How many local minima does the function f(x) = -3e^(-2(3|(3(-5x + 3) + 4) - 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 minimum of the function f(x) = 1|((3(-1(3x)^2 + 3(3x) - 4) + 3)/(1(-1(3x)^2 + 3(3x) - 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 extrema (both minima and maxima) does the function f(x) = -1((-2(-3sin(3\u03c0(-2|x| - 3) + 3) - 2) - 3)/(1(-3sin(3\u03c0(-2|x| - 3) + 3) - 2) - 3))^2 + 5((-2(-3sin(3\u03c0(-2|x| - 3) + 3) - 2) - 3)/(1(-3sin(3\u03c0(-2|x| - 3) + 3) - 2) - 3)) + 4 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": "How many local extrema (both minima and maxima) does the function f(x) = 4(1sin(2\u03c0(1((3x - 2)/(-1x)) - 5) + 1) + 1)^2 - 1(1sin(2\u03c0(1((3x - 2)/(-1x)) - 5) + 1) + 1) - 1 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "52", "dataset": "MATH"}
{"messages": [{"content": "How many local minima does the function f(x) = 2|(5((-3(-3x^2 - 5x - 4) + 1)/(-2(-3x^2 - 5x - 4) - 1))^2 - 5((-3(-3x^2 - 5x - 4) + 1)/(-2(-3x^2 - 5x - 4) - 1)) - 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 minimum with the smallest y-value of the function f(x) = 2(-1|(-1|(1sin(2\u03c0x - 3) - 2) + 3| + 1) - 1| - 3)^2 - 1(-1|(-1|(1sin(2\u03c0x - 3) - 2) + 3| + 1) - 1| - 3) in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-10", "dataset": "MATH"}
{"messages": [{"content": "Find the average of all x-coordinates of local minima of the function f(x) = (1(-1(-5(-2cos(1\u03c0x - 1)) - 5)^2 - 4(-5(-2cos(1\u03c0x - 1)) - 5) - 3) - 3)/(3(-1(-5(-2cos(1\u03c0x - 1)) - 5)^2 - 4(-5(-2cos(1\u03c0x - 1)) - 5) - 3) + 1) in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the rightmost local extremum of the function f(x) = -3(-2|((-2(2x^2 + 4x - 3) - 3)/(-1(2x^2 + 4x - 3))) + 3| - 3)^2 + 3(-2|((-2(2x^2 + 4x - 3) - 3)/(-1(2x^2 + 4x - 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 x-coordinate of the local extremum with the largest y-value of the function f(x) = -1(5(-2(2|x - 2| - 2)^2 - 3(2|x - 2| - 2) + 4)^2 + 1(-2(2|x - 2| - 2)^2 - 3(2|x - 2| - 2) + 4) - 4)^2 - 3(5(-2(2|x - 2| - 2)^2 - 3(2|x - 2| - 2) + 4)^2 + 1(-2(2|x - 2| - 2)^2 - 3(2|x - 2| - 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": "Find the x-coordinate of the local extremum with the largest y-value of the function f(x) = 1((-3(3sin(1\u03c0((3x + 2)/(-1x)) - 3) + 1) - 1)/(-2(3sin(1\u03c0((3x + 2)/(-1x)) - 3) + 1) - 3))^2 + 5((-3(3sin(1\u03c0((3x + 2)/(-1x)) - 3) + 1) - 1)/(-2(3sin(1\u03c0((3x + 2)/(-1x)) - 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 average of all x-coordinates of local maxima of the function f(x) = (1(-2cos(1\u03c0(2|(1x^2 + 1x) - 3|) - 1) - 3))/(2(-2cos(1\u03c0(2|(1x^2 + 1x) - 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": "0", "dataset": "MATH"}
{"messages": [{"content": "Find the average of all x-coordinates of local extrema of the function f(x) = -4((-1(5((2x - 2)/(1x - 3)) - 2) - 3)/(-3(5((2x - 2)/(1x - 3)) - 2)))^2 + 3((-1(5((2x - 2)/(1x - 3)) - 2) - 3)/(-3(5((2x - 2)/(1x - 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 maxima of the function f(x) = 2|(-1(-1(-2|x + 1| + 3) - 2)^2 - 5(-1(-2|x + 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": "-1", "dataset": "MATH"}
{"messages": [{"content": "How many local extrema (both minima and maxima) does the function f(x) = -3(-1sin(2\u03c0(4(5x^2 + 1x - 1)^2 - 3) + 1) + 3)^2 - 5(-1sin(2\u03c0(4(5x^2 + 1x - 1)^2 - 3) + 1) + 3) + 1 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "113", "dataset": "MATH"}
{"messages": [{"content": "Find the x-coordinate of the leftmost local minimum of the function f(x) = 1|((-1(2|(3|x + 3| - 3) - 2| + 1) + 1)/(1(2|(3|x + 3| - 3) - 2| + 1) - 3)) + 2| in the interval [-10, 10]. Round to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-5", "dataset": "MATH"}
{"messages": [{"content": "How many local extrema (both minima and maxima) does the function f(x) = 1(-3|(3cos(1\u03c0(-1|x - 3| - 3) - 3) - 2) + 2| + 3) - 2 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "21", "dataset": "MATH"}