{"messages": [{"content": "How many solutions does the equation 2((3(-3sin(1\u03c0(2|x| + 2) - 2)) + 1)/(-1(-3sin(1\u03c0(2|x| + 2) - 2))))^2 + 4((3(-3sin(1\u03c0(2|x| + 2) - 2)) + 1)/(-1(-3sin(1\u03c0(2|x| + 2) - 2)))) - 2 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "80", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = 2|(-5((1(-3sin(1\u03c0x - 1) + 2) - 3)/(-2(-3sin(1\u03c0x - 1) + 2) - 3)) + 4) + 3| where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation 1cos(2\u03c0(-1(5x + 4)^2 - 5(5x + 4) - 1)) + 1 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1124", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = -1((1(1sin(3\u03c0(-1|x - 2|) + 3) + 1) + 1)/(-2(1sin(3\u03c0(-1|x - 2|) + 3) + 1) + 3)) - 4 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "60", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = -2sin(2\u03c0(5(-3x^2 - 5x - 2)) + 3) + 1 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1335", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation 2|(-1cos(1\u03c0(3((2x + 2)/(2x + 1)) + 2) - 1) - 3) + 3| - 2 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "39", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = 3(3sin(2\u03c0((-3(-3|x + 2| + 3))/(-2(-3|x + 2| + 3) - 1)) + 3) - 1) - 4 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "50", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = -1|((-1(2cos(1\u03c0x)))/(-3(2cos(1\u03c0x)) - 1)) + 1| + 1 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "40", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = 3cos(2\u03c0(5((3(-2x - 5))/(-2(-2x - 5) + 3))^2 - 4((3(-2x - 5))/(-2(-2x - 5) + 3)) - 1) - 2) + 2 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "173", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = 4(-2sin(3\u03c0(3x^2 - 1x - 3) - 2) - 1) + 5 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1442", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = 3((-2(1sin(3\u03c0x + 2) + 1) + 2)/(-2(1sin(3\u03c0x + 2) + 1) + 1)) + 5 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "60", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = 1(1cos(3\u03c0((1x - 1)/(-1x + 2)) - 3))^2 - 2(1cos(3\u03c0((1x - 1)/(-1x + 2)) - 3)) equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "64", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = 1((-2(3cos(3\u03c0x + 1)))/(-2(3cos(3\u03c0x + 1)) - 1))^2 - 5((-2(3cos(3\u03c0x + 1)))/(-2(3cos(3\u03c0x + 1)) - 1)) + 3 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": "How many solutions does the equation -3sin(1\u03c0(5((3(-3|x| - 1) - 3)/(-3(-3|x| - 1) - 1)) + 1) + 2) = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "20", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = -2|(4(-3sin(3\u03c0(5x^2 - 3x - 2)) + 2) + 3) + 2| + 2 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1079", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation (3(-1(1sin(3\u03c0(3|x| - 3) - 2))^2 + 3(1sin(3\u03c0(3|x| - 3) - 2))) - 2)/(2(-1(1sin(3\u03c0(3|x| - 3) - 2))^2 + 3(1sin(3\u03c0(3|x| - 3) - 2))) + 1) = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "180", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation (-1(1(2cos(3\u03c0(2|x + 1| + 2) - 2) + 3)) + 2)/(-2(1(2cos(3\u03c0(2|x + 1| + 2) - 2) + 3)) + 3) = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "120", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation 4((-1(-1sin(2\u03c0(-1|x| - 3) - 1) - 1) - 2)/(3(-1sin(2\u03c0(-1|x| - 3) - 1) - 1) + 2))^2 - 3((-1(-1sin(2\u03c0(-1|x| - 3) - 1) - 1) - 2)/(3(-1sin(2\u03c0(-1|x| - 3) - 1) - 1) + 2)) - 3 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "40", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = 2|(3sin(1\u03c0(-1(-5x^2 - 5x + 4) + 4) + 1) + 2) - 3| - 1 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "578", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = -4(3cos(1\u03c0((-2(-3|x| + 2) - 1)/(-3(-3|x| + 2) + 2)) + 3) + 3) + 5 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "36", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation 3|(4(-3cos(2\u03c0((3x)/(1x + 1)) + 1) + 2) - 2) - 2| - 3 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "57", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = 2cos(3\u03c0(4(-4(1|x| + 1) + 1)^2 - 1(-4(1|x| + 1) + 1) - 3) + 3) + 2 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1250", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = 1cos(3\u03c0(-3(3(-1|x + 3| + 2)^2 + 5(-1|x + 3| + 2) + 2) + 3)) equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1460", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation -1(-5((-1(-3cos(1\u03c0x + 2) + 2) + 3)/(2(-3cos(1\u03c0x + 2) + 2) - 3)) + 4)^2 - 3(-5((-1(-3cos(1\u03c0x + 2) + 2) + 3)/(2(-3cos(1\u03c0x + 2) + 2) - 3)) + 4) + 1 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "40", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = -1|(-1(-3sin(1\u03c0x))^2 - 3(-3sin(1\u03c0x)) + 1) - 2| where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "21", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = -4(-3sin(1\u03c0(-1|(-2x - 5) + 3| - 2)) + 1)^2 - 1(-3sin(1\u03c0(-1|(-2x - 5) + 3| - 2)) + 1) + 5 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "78", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation -4(2(-1sin(2\u03c0x - 3) + 1)^2 - 2(-1sin(2\u03c0x - 3) + 1) - 2) + 5 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "40", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = 1cos(2\u03c0(1(2|x + 1| - 1)^2 + 3(2|x + 1| - 1) - 1) + 3) where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1424", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = 2sin(3\u03c0((2(3(1|x| - 3) + 2) - 3)/(3(3(1|x| - 3) + 2) - 2)) - 2) equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "54", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = -1cos(1\u03c0(-4(-5x^2 - 2x + 1) + 1) + 1) + 1 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1168", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = 5(1cos(3\u03c0(4x - 1) + 2))^2 - 3(1cos(3\u03c0(4x - 1) + 2)) - 1 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "480", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = 3sin(2\u03c0(-2|(3x^2 + 3x - 2) - 2| + 2)) - 1 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1523", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation -3(-1|(-1sin(3\u03c0x + 3) + 3) - 3| - 1)^2 - 5(-1|(-1sin(3\u03c0x + 3) + 3) - 3| - 1) - 1 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "120", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = -3(3sin(3\u03c0(4((3x - 1)/(1x + 3))^2 - 1) - 1) - 2) - 4 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "673", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = 1(-1(-2|(1cos(1\u03c0x) - 2) + 2| + 2)^2 - 4(-2|(1cos(1\u03c0x) - 2) + 2| + 2) + 1) - 1 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "21", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = 1|((-1(-2cos(2\u03c0x - 3) - 1) - 3)/(1(-2cos(2\u03c0x - 3) - 1))) - 2| - 2 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "60", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = -4(3cos(3\u03c0(-2|(-4x - 5) + 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": "640", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = -2|((-3(4(3sin(2\u03c0x - 2)) + 2) - 3)/(1(4(3sin(2\u03c0x - 2)) + 2))) - 2| + 2 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "51", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation 2(3sin(1\u03c0((1x - 3)/(-1x - 3)) + 1) - 2) - 2 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "47", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = -2sin(3\u03c0((-1(-4x + 1))/(3(-4x + 1) + 3)) - 3) equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "19", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation (2(-1(-1|(-2sin(2\u03c0x + 2) - 3) + 1| - 3)^2 - 3(-1|(-2sin(2\u03c0x + 2) - 3) + 1| - 3) + 2) + 2)/(2(-1(-1|(-2sin(2\u03c0x + 2) - 3) + 1| - 3)^2 - 3(-1|(-2sin(2\u03c0x + 2) - 3) + 1| - 3) + 2) + 3) = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "40", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = 2|(-1((2(1cos(1\u03c0x + 3)) - 1)/(3(1cos(1\u03c0x + 3)) - 2)) + 3) + 3| - 3 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "40", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = -1cos(2\u03c0(-2|((-2(-5x + 1) - 1)/(-1(-5x + 1) + 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": "50", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = -2|(-3sin(1\u03c0(-4x - 2) - 2) - 2) + 2| + 2 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "160", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation -3sin(3\u03c0(-3(-2|x + 1| + 1) + 2) - 3) - 3 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "177", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = -2cos(3\u03c0((-2(3|x| - 2) - 3)/(2(3|x| - 2) - 3)) - 3) + 2 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "72", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation 2|(-3cos(2\u03c0(-1x + 5) + 2) + 1) + 1| - 2 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "60", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation 4(1sin(1\u03c0(1|x - 1| + 2) - 3)) + 1 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "22", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation 3sin(3\u03c0(1((1x + 2)/(3x + 2))^2 + 3((1x + 2)/(3x + 2)) + 2) - 2) - 1 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "73", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = -2|(-2sin(1\u03c0(-3(-3x)^2 - 1(-3x) - 3) + 1) + 3) - 2| + 1 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1000", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = 3sin(2\u03c0(-1|(-5(4x^2 + 3x - 5) + 1) - 3| + 1) + 2) - 1 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1518", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation 3sin(2\u03c0(2((-2(1|x| + 2) - 2)/(3(1|x| + 2) - 1))^2 + 1((-2(1|x| + 2) - 2)/(3(1|x| + 2) - 1)) - 4) - 3) + 1 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "6", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = -3|(2(2cos(1\u03c0(1x^2 + 2x - 3)) - 1) - 2) + 3| where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "76", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = -1sin(3\u03c0(-1(-3|x + 1|) + 1) - 2) where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "180", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = -5(1(-3sin(3\u03c0x - 3) - 1)^2 + 1(-3sin(3\u03c0x - 3) - 1) - 3) + 1 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "120", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = 3|(1(-2cos(3\u03c0x + 1) - 1)^2 + 4(-2cos(3\u03c0x + 1) - 1) + 2)| equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "35", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = 1cos(3\u03c0((1(-5(2x^2 + 4x + 2)) - 3)/(3(-5(2x^2 + 4x + 2)))) - 1) equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "48", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = -1cos(1\u03c0(3(-3|(-2x^2 + 3x + 5) - 1| - 2) + 5) - 3) + 1 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1152", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = 3sin(3\u03c0((-2(3|x + 1|) - 3)/(2(3|x + 1|) - 1)) - 2) + 1 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "75", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = (-3(1(-3|(3sin(1\u03c0x - 2) - 2)| - 1) + 4) - 2)/(-2(1(-3|(3sin(1\u03c0x - 2) - 2)| - 1) + 4) - 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": "How many zeros does the function f(x) = -1(-3sin(2\u03c0((-1(2|x| - 3) - 1)/(-3(2|x| - 3) + 4)) - 3) + 2) + 4 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "58", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = -2sin(1\u03c0(-4(-2|((1x + 2)/(-2x + 1)) + 1| + 2) - 4) + 2) + 2 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "65", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = -3cos(3\u03c0(4(-2|(2x^2 - 1x + 3) - 2|) - 2) - 2) + 3 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1146", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = (-3(-3sin(1\u03c0(1(1x - 1)^2 - 5(1x - 1) - 2) - 3) + 2) + 2)/(-2(-3sin(1\u03c0(1(1x - 1)^2 - 5(1x - 1) - 2) - 3) + 2) - 1) where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "226", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = -2(-2sin(3\u03c0((-1(1|x + 1| - 1) - 2)/(2(1|x + 1| - 1) + 2)) + 3) + 2)^2 + 5(-2sin(3\u03c0((-1(1|x + 1| - 1) - 2)/(2(1|x + 1| - 1) + 2)) + 3) + 2) - 3 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "30", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = -2|(-1sin(2\u03c0(-1((-2x - 1)/(-2x - 2)) + 3) + 3) - 3) + 1| + 2 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "19", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = 2cos(2\u03c0(3((2x - 1)/(-1x - 3)) - 3) - 2) - 2 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "140", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = -3cos(3\u03c0(-5(3((-1x + 2)/(-1x + 3))^2 + 5((-1x + 2)/(-1x + 3)) - 1) - 2) + 3) - 1 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "393", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation 4(2cos(2\u03c0(-3|(5x^2 - 1x + 2) + 1| - 2) - 3)) - 3 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1365", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation 3cos(2\u03c0((1(-5x^2 - 4x + 4) - 3)/(-1(-5x^2 - 4x + 4) - 2)) + 3) = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "71", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = -1(-3sin(3\u03c0((1(-3|x| + 2) - 2)/(-2(-3|x| + 2) - 2)) - 3) - 1)^2 + 3(-3sin(3\u03c0((1(-3|x| + 2) - 2)/(-2(-3|x| + 2) - 2)) - 3) - 1) equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "90", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = -3|(5(-2sin(2\u03c0x - 3) - 1))| + 2 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "80", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = -2sin(2\u03c0((-3(-1(1|x + 1| + 2)^2 + 2(1|x + 1| + 2)) - 2)/(-3(-1(1|x + 1| + 2)^2 + 2(1|x + 1| + 2)) - 3)) - 3) + 2 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "17", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = -1|((-2(3cos(1\u03c0x + 3) - 2) - 3)/(2(3cos(1\u03c0x + 3) - 2) + 2)) + 3| + 2 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "20", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = (-2(-3cos(1\u03c0(-4(1|x - 2|)^2 + 5(1|x - 2|) - 4) - 1) + 1) + 2)/(-2(-3cos(1\u03c0(-4(1|x - 2|)^2 + 5(1|x - 2|) - 4) - 1) + 1) - 1) have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "581", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = 2cos(1\u03c0(3|(5x^2 + 2x + 3) - 3| + 2) - 2) have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1639", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation -3|(-2cos(1\u03c0(5(2x - 3)^2 - 1(2x - 3) - 5) - 2) + 2) - 3| = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "175", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = -3(-1|(5(3sin(1\u03c0x + 1) + 2)^2 - 4(3sin(1\u03c0x + 1) + 2) + 4) - 3| + 3) + 5 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": "How many solutions does the equation 1cos(3\u03c0(4((3x + 1)/(-2x - 1))^2 + 3((3x + 1)/(-2x - 1)) - 1) - 3) = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "85", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = -1(2cos(2\u03c0(1|x - 2| - 2) + 1) + 3) + 4 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "40", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = 5(-5(1sin(2\u03c0((3x + 3)/(-2x)) + 2) + 1)^2 - 1(1sin(2\u03c0((3x + 3)/(-2x)) + 2) + 1) + 4) where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "66", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation (3(3cos(1\u03c0(1(4x^2 - 5) - 1)) - 3) + 3)/(1(3cos(1\u03c0(1(4x^2 - 5) - 1)) - 3) - 2) = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "758", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation (-3(1cos(1\u03c0(5x^2 - 5x - 4) + 1)) - 2)/(2(1cos(1\u03c0(5x^2 - 5x - 4) + 1)) + 2) = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "883", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = 1cos(2\u03c0(3|(-1x - 1) - 2| - 1) + 1) - 1 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "60", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = 5(3cos(3\u03c0(1((1x + 2)/(2x + 1))^2 + 4((1x + 2)/(2x + 1)) + 5) + 2) - 3) + 4 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "85", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = -5(-3sin(2\u03c0((3x - 2)/(2x - 1)) - 1) - 1) + 3 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "27", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = 2|(-4(1(2sin(2\u03c0x + 2) - 1))^2 + 2)| - 2 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "160", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = -4(3(-2sin(1\u03c0(-3|x - 3| - 2) + 2) - 1)^2 - 5(-2sin(1\u03c0(-3|x - 3| - 2) + 2) - 1) - 1) - 1 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "60", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation (-1(1(1sin(1\u03c0x + 2) + 1) + 2) + 3)/(-3(1(1sin(1\u03c0x + 2) + 1) + 2) + 1) = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "20", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = -3((-2(3cos(2\u03c0x - 2) + 1) - 2)/(3(3cos(2\u03c0x - 2) + 1) + 2))^2 + 2 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "80", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation -4(-3cos(2\u03c0(1((-1x - 3)/(-2x - 1))^2 - 4((-1x - 3)/(-2x - 1)) + 3) + 3) + 1) = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "106", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation (1(-3(-4(-3cos(3\u03c0x - 2) - 2)^2 - 5(-3cos(3\u03c0x - 2) - 2) - 2) - 3))/(-1(-3(-4(-3cos(3\u03c0x - 2) - 2)^2 - 5(-3cos(3\u03c0x - 2) - 2) - 2) - 3) + 3) = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "120", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = 2|(-2sin(3\u03c0(1x^2 + 1x - 3) + 3) + 1)| - 3 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "602", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = -4(3((-1(3sin(1\u03c0x - 1)) + 1)/(-1(3sin(1\u03c0x - 1)))) - 2)^2 + 5 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 number of x-intercepts of the function f(x) = -3cos(2\u03c0(3(-1(3|x| + 1) + 1)^2 - 1(-1(3|x| + 1) + 1)) - 2) + 2 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1222", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = -1sin(1\u03c0(2(-2|x| + 2)^2 + 4(-2|x| + 2) + 5) + 3) - 1 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "510", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = 1(2sin(2\u03c0(-1|((-1x)/(-2x - 2)) + 1| - 1) - 1) + 3) - 1 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "23", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = (2(-3sin(2\u03c0(-1|x + 2| - 3) - 3) - 3) + 3)/(1(-3sin(2\u03c0(-1|x + 2| - 3) - 3) - 3) + 3) where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "40", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = (-1(-1(-1|(-1sin(1\u03c0x - 2)) + 2| - 3) - 5))/(-3(-1(-1|(-1sin(1\u03c0x - 2)) + 2| - 3) - 5) - 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 number of x-intercepts of the function f(x) = (3(1(1cos(2\u03c0x + 1))^2 + 2(1cos(2\u03c0x + 1)) - 1) - 2)/(-3(1(1cos(2\u03c0x + 1))^2 + 2(1cos(2\u03c0x + 1)) - 1) + 4) where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "40", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = -1sin(1\u03c0(-4(1x^2 + 2x - 2) + 3) - 1) - 1 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "372", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = 1((-1(-4(3sin(1\u03c0x - 3) + 1)^2 - 1(3sin(1\u03c0x - 3) + 1) + 4) - 3)/(-2(-4(3sin(1\u03c0x - 3) + 1)^2 - 1(3sin(1\u03c0x - 3) + 1) + 4) + 3)) - 5 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "40", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation 1cos(3\u03c0(-2(1|x - 1| - 2) - 1) - 3) + 1 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "60", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation 2cos(2\u03c0(1|(5x^2 - 3x) - 2| + 1) + 3) = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1502", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = (-3(-2(1cos(1\u03c0(-5x + 4)) + 2)^2 + 2(1cos(1\u03c0(-5x + 4)) + 2) + 4) - 1)/(2(-2(1cos(1\u03c0(-5x + 4)) + 2)^2 + 2(1cos(1\u03c0(-5x + 4)) + 2) + 4) - 3) where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "100", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = -5(2|(1cos(2\u03c0((3x - 1)/(3x - 2)) + 3) + 3)| - 3)^2 + 5(2|(1cos(2\u03c0((3x - 1)/(3x - 2)) + 3) + 3)| - 3) + 1 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "19", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = 1(-3cos(3\u03c0(2|x - 2| - 2) + 2) - 1)^2 - 1(-3cos(3\u03c0(2|x - 2| - 2) + 2) - 1) - 5 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "120", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation -3sin(2\u03c0(3(4x + 2)^2 - 3(4x + 2) - 5) - 1) + 1 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1532", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = 3((-2(3(3cos(3\u03c0x + 2) + 1)^2 - 1(3cos(3\u03c0x + 2) + 1) - 4) - 3)/(3(3(3cos(3\u03c0x + 2) + 1)^2 - 1(3cos(3\u03c0x + 2) + 1) - 4) + 3)) + 3 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 number of x-intercepts of the function f(x) = -5(-3sin(2\u03c0(-2|x - 3| - 2) + 3)) - 4 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "80", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = 4(-3cos(1\u03c0(-1|(-5x^2 + 3x - 3) - 3| - 3) + 3) - 3) + 5 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "932", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = 2sin(1\u03c0(3|(1x^2 + 3x - 2) - 3|) + 1) have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "614", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = 1(2|(3sin(1\u03c0x + 3) + 3)| - 1)^2 + 4(2|(3sin(1\u03c0x + 3) + 3)| - 1) + 3 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = (2(3cos(2\u03c0(-1|(3x) + 1| + 3) - 2) + 3))/(1(3cos(2\u03c0(-1|(3x) + 1| + 3) - 2) + 3) - 2) equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "60", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = 2|((-2(-3cos(1\u03c0(5x + 5) - 3) - 1) - 2)/(-3(-3cos(1\u03c0(5x + 5) - 3) - 1) + 2))| - 2 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "100", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = -3cos(1\u03c0(-2(-2|((-3x - 2)/(1x + 2)) + 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": "137", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation -2(2((-3(-2sin(2\u03c0x + 3) - 2) + 1)/(2(-2sin(2\u03c0x + 3) - 2) + 2))^2 - 1((-3(-2sin(2\u03c0x + 3) - 2) + 1)/(2(-2sin(2\u03c0x + 3) - 2) + 2)) - 2) - 4 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "20", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = (3(-3cos(2\u03c0(4x + 2) - 2) - 3) + 3)/(-2(-3cos(2\u03c0(4x + 2) - 2) - 3) + 1) equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "160", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation (3(3cos(3\u03c0(-5x^2 + 3x + 5) - 3) - 1) - 3)/(-2(3cos(3\u03c0(-5x^2 + 3x + 5) - 3) - 1) + 3) = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "523", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = -4(2sin(2\u03c0(3x + 2) - 3) + 1)^2 - 1(2sin(2\u03c0(3x + 2) - 3) + 1) + 4 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "120", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = 2|(-2cos(1\u03c0(3x) - 2) - 1) + 3| - 1 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "60", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = -1cos(3\u03c0(-2|(-5x - 3) - 2| + 3) + 1) - 1 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "297", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = (1(-2|(-5(-3cos(1\u03c0x - 3) + 3)^2 - 3(-3cos(1\u03c0x - 3) + 3) - 2)| + 2) + 3)/(-2(-2|(-5(-3cos(1\u03c0x - 3) + 3)^2 - 3(-3cos(1\u03c0x - 3) + 3) - 2)| + 2) + 3) 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": "How many solutions does the equation 2sin(1\u03c0((-1(-5x - 4) + 1)/(1(-5x - 4) + 1))) + 2 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = 3sin(1\u03c0(-3|((-3(5x^2 - 1x + 1) + 3)/(1(5x^2 - 1x + 1))) + 3| + 1)) + 3 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = -3sin(3\u03c0(2|((-2(-3x^2 + 1x - 4) - 1)/(1(-3x^2 + 1x - 4) - 3)) + 1| + 2) + 1) + 1 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = 3cos(1\u03c0(-3|(-1((-2x - 1)/(-1x))^2 - 5((-2x - 1)/(-1x)) - 3) - 3| - 3) - 1) + 3 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": "Determine the number of values x in [-10, 10] where f(x) = 1(4(2sin(3\u03c0x - 2) - 2) - 5)^2 + 5(4(2sin(3\u03c0x - 2) - 2) - 5) - 4 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "60", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = 2sin(1\u03c0(-2|(-2((3x)/(-1x + 2))^2 + 5((3x)/(-1x + 2)) - 3) - 2| + 3) + 3) - 2 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "275", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation (3(2cos(2\u03c0(4(3|x - 2| + 3)^2 - 3(3|x - 2| + 3) - 1) - 2) - 1) + 2)/(2(2cos(2\u03c0(4(3|x - 2| + 3)^2 - 3(3|x - 2| + 3) - 1) - 2) - 1)) = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "643", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = -3((-1(2sin(3\u03c0(-3|x - 3|) + 2) - 1) - 1)/(1(2sin(3\u03c0(-3|x - 3|) + 2) - 1))) + 1 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "180", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation (-2(3sin(2\u03c0(1(1x^2 - 3x - 5) - 2) + 1) + 1) + 1)/(1(3sin(2\u03c0(1(1x^2 - 3x - 5) - 2) + 1) + 1) + 3) = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "410", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = 5(-3sin(3\u03c0((-2x)/(-1x + 2)) - 1)) + 5 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "122", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation 3sin(1\u03c0(3(2|(3x - 2) - 2| + 2)^2 - 3(2|(3x - 2) - 2| + 2) - 5) + 1) + 2 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1301", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = -3sin(3\u03c0((-2(1(-1|x + 1| - 3) + 5))/(-1(1(-1|x + 1| - 3) + 5) - 3)) + 2) + 2 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "266", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = 3(1(-2cos(1\u03c0((-2x - 3)/(1x + 2)) + 3) - 3)^2 + 3(-2cos(1\u03c0((-2x - 3)/(1x + 2)) + 3) - 3) - 2) - 4 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "35", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = -2(-1|(2sin(1\u03c0x - 3) + 2) + 2| + 2) have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = (-3(-3(2sin(2\u03c0(3|x + 3| + 2) + 2) + 2)^2 - 1(2sin(2\u03c0(3|x + 3| + 2) + 2) + 2) + 4) - 3)/(1(-3(2sin(2\u03c0(3|x + 3| + 2) + 2) + 2)^2 - 1(2sin(2\u03c0(3|x + 3| + 2) + 2) + 2) + 4) + 2) equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "110", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = 2((-2(-3(1sin(1\u03c0x + 1) - 2)^2 + 2(1sin(1\u03c0x + 1) - 2) + 3) - 3)/(3(-3(1sin(1\u03c0x + 1) - 2)^2 + 2(1sin(1\u03c0x + 1) - 2) + 3) + 1)) + 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": "Determine the number of values x in [-10, 10] where f(x) = -2(4((-2(-3cos(2\u03c0x + 3) - 1) - 3)/(2(-3cos(2\u03c0x + 3) - 1) - 1)) - 4)^2 - 1(4((-2(-3cos(2\u03c0x + 3) - 1) - 3)/(2(-3cos(2\u03c0x + 3) - 1) - 1)) - 4) equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "36", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation -1sin(3\u03c0(-1(-1|((-3x + 2)/(-1x - 2)) + 3| - 3)^2 + 3(-1|((-3x + 2)/(-1x - 2)) + 3| - 3) - 5) + 3) = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "705", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = (1(3sin(3\u03c0(-3x^2 - 2x - 3) + 3) + 1))/(-2(3sin(3\u03c0(-3x^2 - 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": "375", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = (-3(-3sin(3\u03c0(2|(4x - 4) - 2| + 3) - 1) + 1))/(-2(-3sin(3\u03c0(2|(4x - 4) - 2| + 3) - 1) + 1) + 3) where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "480", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = 2sin(3\u03c0(1|(-4x + 3)| - 1) - 2) + 2 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "117", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = 2cos(3\u03c0((-3(-4x - 2))/(-3(-4x - 2) + 2)) - 2) + 2 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = (-2(-4(3cos(1\u03c0x + 1) + 3)^2 + 2(3cos(1\u03c0x + 1) + 3) + 2) - 1)/(-3(-4(3cos(1\u03c0x + 1) + 3)^2 + 2(3cos(1\u03c0x + 1) + 3) + 2)) where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "20", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = 1sin(3\u03c0((2(-1x^2 + 3x + 4) + 1)/(2(-1x^2 + 3x + 4) - 3)) - 1) have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "88", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = -2(2cos(3\u03c0(-2|x + 1| + 2) + 2) - 3) - 2 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "60", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation 2cos(1\u03c0(1|(-3((1x + 3)/(-2x + 1)) + 1)| + 2) - 2) + 1 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "80", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation -5(3cos(2\u03c0(-2|x| + 2) + 3) + 2) + 5 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "80", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = -1cos(3\u03c0(3(-3|(-1x + 3) + 3| - 3)^2 - 5(-3|(-1x + 3) + 3| - 3) - 4) - 2) - 1 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1242", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = 2cos(1\u03c0(2(-5x - 5)^2 - 2(-5x - 5) + 1) - 1) + 1 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1424", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation 1sin(3\u03c0((1(-2|x - 2| + 2) - 3)/(1(-2|x - 2| + 2) - 2)) - 2) - 1 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "22", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = (-2(2|(3cos(1\u03c0(4x + 3))) + 1| - 2) + 3)/(2(2|(3cos(1\u03c0(4x + 3))) + 1| - 2)) have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "160", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation -1(3sin(3\u03c0(2((-2x + 2)/(-3x))^2 + 5((-2x + 2)/(-3x)) + 2) + 2) - 1) - 1 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "124", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = 2(3cos(1\u03c0((2x - 1)/(-3x - 2)) + 3)) + 4 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "26", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = -2((-2(-2sin(3\u03c0x - 1) + 1) + 1)/(1(-2sin(3\u03c0x - 1) + 1))) + 4 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "60", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = -2(1cos(1\u03c0((-3(-2|x| + 1) - 2)/(3(-2|x| + 1) - 2)) + 3) + 2)^2 + 2(1cos(1\u03c0((-3(-2|x| + 1) - 2)/(3(-2|x| + 1) - 2)) + 3) + 2) + 4 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "50", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = 2cos(2\u03c0((2(1|x - 1| - 1) + 1)/(-1(1|x - 1| - 1) + 2)) - 3) have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "229", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = -3cos(3\u03c0(-1(-1(-3|x - 2| + 2) + 2)^2 + 2(-1(-3|x - 2| + 2) + 2) + 1)) - 1 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1474", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation -5(-2(-2cos(2\u03c0(1|x + 2| - 1) + 1) + 1)^2 - 5(-2cos(2\u03c0(1|x + 2| - 1) + 1) + 1) - 2) - 3 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "40", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = -1sin(1\u03c0(-5(1(-2|x| + 1) + 1)^2 + 2(1(-2|x| + 1) + 1) - 1) + 1) equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1584", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = 1cos(1\u03c0(-4((-2(2|x + 3| - 1))/(3(2|x + 3| - 1) + 2)) - 5) + 1) - 1 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "30", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = 1|(-3cos(1\u03c0(2x^2 - 2x + 5) + 3) + 2)| where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "197", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = (1(1cos(1\u03c0(1x - 4) - 1)) - 1)/(2(1cos(1\u03c0(1x - 4) - 1))) have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = -2cos(2\u03c0((3(2x + 1) + 3)/(1(2x + 1) + 2))) - 2 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "38", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation -2|(3(1sin(3\u03c0x + 1) + 1) - 4) + 1| = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "36", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = 1|(-1(4(2cos(1\u03c0x) + 1) + 3)^2 + 2(4(2cos(1\u03c0x) + 1) + 3) - 2) + 2| - 3 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "30", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation 2|(2sin(3\u03c0(1x + 4) + 3) - 1) + 3| - 3 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "60", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = 4(-3cos(2\u03c0(3|x - 3| - 3) - 2) - 1)^2 + 3(-3cos(2\u03c0(3|x - 3| - 3) - 2) - 1) - 1 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "240", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = -5(-3sin(3\u03c0(-1x - 3) - 2) + 3)^2 + 5(-3sin(3\u03c0(-1x - 3) - 2) + 3) + 2 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "60", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = -1(-2sin(1\u03c0(-2|x - 3| - 1) + 1) - 3) - 3 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "40", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = 3cos(3\u03c0(3|(2x + 5) - 2| + 3) - 3) - 2 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "360", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = 1(2(3cos(2\u03c0x - 2) - 3) + 1)^2 - 5(2(3cos(2\u03c0x - 2) - 3) + 1) - 1 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "40", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation -3cos(1\u03c0(-1((2x + 1)/(-3x)) + 1)) + 1 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "19", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation -1(2|(-2sin(1\u03c0x + 1) + 2)|) + 4 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "20", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = 3|(-2(2sin(1\u03c0x + 2) + 2) + 1) - 1| - 1 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "20", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = -1cos(3\u03c0(-3(3|x - 3| - 1)^2 + 3(3|x - 3| - 1) + 5)) + 1 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1116", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = (-2(-1(1|(2cos(3\u03c0x - 3) - 2) + 1| - 1) + 1) - 2)/(-3(-1(1|(2cos(3\u03c0x - 3) - 2) + 1| - 1) + 1) + 2) equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "30", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = 3sin(3\u03c0((-3(4x) + 1)/(-2(4x) - 1)) + 1) + 3 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "21", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = 2cos(1\u03c0(-3(5((-2x + 1)/(-3x + 2))^2 + 1((-2x + 1)/(-3x + 2)) + 2) + 5) + 1) - 1 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "51", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = 1cos(2\u03c0(-3(-2x^2 - 5x) + 2) + 3) + 1 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "969", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = -3cos(1\u03c0(2|((1(3x + 3) + 2)/(2(3x + 3) - 3)) + 3|) + 2) + 1 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "36", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation -4(2(3sin(1\u03c0((-2x - 3)/(1x)) + 3) + 2)^2 + 3(3sin(1\u03c0((-2x - 3)/(1x)) + 3) + 2) - 4) - 1 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "65", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = 1|(-2(3cos(1\u03c0((2x + 2)/(-3x - 1)) - 1) - 3) - 3)| where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "7", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = 3cos(3\u03c0(-4(-4x - 4)^2 + 1(-4x - 4) + 5) - 1) + 1 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1508", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation 3cos(2\u03c0(-1(-1((-1x - 3)/(3x)) - 2)^2 + 3(-1((-1x - 3)/(3x)) - 2)) + 2) + 3 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "69", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = -2sin(2\u03c0((-2(-1x - 5) + 3)/(-1(-1x - 5) - 3)) + 1) - 1 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "142", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation -2sin(2\u03c0((3(-4(2|x + 2| + 1)^2 + 1(2|x + 2| + 1) + 3) - 2)/(1(-4(2|x + 2| + 1)^2 + 1(2|x + 2| + 1) + 3))) - 2) = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "20", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = -1((1(-1sin(2\u03c0x + 2) + 1) - 2)/(2(-1sin(2\u03c0x + 2) + 1) - 1))^2 - 3((1(-1sin(2\u03c0x + 2) + 1) - 2)/(2(-1sin(2\u03c0x + 2) + 1) - 1)) - 1 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "80", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = -2|(3(-2cos(2\u03c0(-4x^2 - 3x - 4)) - 1) + 5) + 2| + 2 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "740", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = -2sin(1\u03c0(3(-1(2|x - 2| - 2)^2 + 4(2|x - 2| - 2) - 2) + 1) + 1) - 1 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1178", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = 2(4(2sin(3\u03c0((-3x + 1)/(2x))) - 1))^2 - 1(4(2sin(3\u03c0((-3x + 1)/(2x))) - 1)) equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "16", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = 1|(-4(-3cos(3\u03c0x - 3) - 3) - 5) + 3| - 3 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "60", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = -4(2sin(1\u03c0((3x + 1)/(2x + 1)) - 2) - 1) - 4 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "19", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation -3(1((-1(-3cos(2\u03c0x) + 1) - 2)/(-3(-3cos(2\u03c0x) + 1) - 2)) + 1)^2 + 3(1((-1(-3cos(2\u03c0x) + 1) - 2)/(-3(-3cos(2\u03c0x) + 1) - 2)) + 1) + 1 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "40", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = -5(-3cos(3\u03c0(4x^2 + 2x + 1) + 3) - 1) - 1 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1552", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = -4((-3(-1|(1sin(1\u03c0x - 1) - 3)| + 3) + 2)/(-1(-1|(1sin(1\u03c0x - 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": "10", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = 3sin(3\u03c0(5(-2|x + 2| - 1) - 3)) - 1 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "600", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = -3sin(2\u03c0(-2(-1x - 4)^2 - 5(-1x - 4) - 4) - 2) - 2 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "774", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = -1(-1|(-4(-1cos(1\u03c0x - 2) - 1)^2 - 4(-1cos(1\u03c0x - 2) - 1) - 4) + 3| + 3) - 4 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "20", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = 3cos(2\u03c0(-2|(-3x^2 - 1x + 1) - 1| - 2) - 3) have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1583", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = 3((3(-1cos(3\u03c0(4x - 5) + 1)) + 3)/(-2(-1cos(3\u03c0(4x - 5) + 1))))^2 + 2((3(-1cos(3\u03c0(4x - 5) + 1)) + 3)/(-2(-1cos(3\u03c0(4x - 5) + 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": "How many zeros does the function f(x) = -1|(-3sin(1\u03c0((1(-1x - 5) - 3)/(2(-1x - 5) + 2))) - 1) + 1| + 1 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "63", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = -2sin(3\u03c0(-1(3|x - 2| + 1) + 5)) + 2 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "90", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation -3cos(3\u03c0(-2|((-3(1x^2 - 5x + 2) - 2)/(2(1x^2 - 5x + 2) + 3)) - 2| + 1) + 3) + 2 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "98", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = (2(-1cos(3\u03c0(1|(2x^2 + 5x - 5)|) - 2)) - 1)/(-3(-1cos(3\u03c0(1|(2x^2 + 5x - 5)|) - 2)) - 3) have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1111", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = -2cos(3\u03c0(-3|(-1(-4x + 3)^2 + 4(-4x + 3))| + 2) - 3) have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1606", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = 1(3(1sin(1\u03c0x - 2) + 1) - 2)^2 + 2(3(1sin(1\u03c0x - 2) + 1) - 2) - 3 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "20", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = -3sin(2\u03c0(-5(1|x| + 3)^2 - 2(1|x| + 3) - 1) - 2) - 3 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1259", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = 1(1|(-3cos(2\u03c0(-3x - 2) + 1)) - 3| + 3)^2 - 5(1|(-3cos(2\u03c0(-3x - 2) + 1)) - 3| + 3) - 5 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "120", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation 1sin(1\u03c0(1(1(-2|x + 3|)^2 - 5(-2|x + 3|) + 5)) + 2) + 1 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "481", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = 5(-3cos(3\u03c0(5x^2 + 1x - 2) - 1)) + 4 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1591", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = -2cos(3\u03c0(-2|(5x + 2) - 3| + 2) + 2) - 1 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "600", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = 1(3sin(3\u03c0(3|x + 1| - 3)) + 2) have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "182", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = 1sin(2\u03c0(-3((2(3|x + 2| - 2) - 2)/(-1(3|x + 2| - 2) + 2)) + 3) - 2) + 1 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "80", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation 1(-2|(2cos(3\u03c0x + 1)) + 1|)^2 - 2(-2|(2cos(3\u03c0x + 1)) + 1|) - 2 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "120", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = -2(-1sin(1\u03c0(1|x + 2| - 1) + 2) - 2) - 4 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "20", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = 2sin(2\u03c0(-1|(-1((-3x + 3)/(2x + 2))^2 - 4((-3x + 3)/(2x + 2)) + 2) + 3|)) + 1 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "171", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = (3(1(-2sin(2\u03c0x) - 1)^2 - 4(-2sin(2\u03c0x) - 1)) - 3)/(-1(1(-2sin(2\u03c0x) - 1)^2 - 4(-2sin(2\u03c0x) - 1)) - 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": "How many solutions does the equation 1(2sin(3\u03c0(2|(-3x + 3) + 1| + 2) - 1) - 2)^2 + 4(2sin(3\u03c0(2|(-3x + 3) + 1| + 2) - 1) - 2) + 4 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "337", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = -5(-1sin(2\u03c0(2|((-2x + 2)/(2x - 3)) + 2| - 1) + 1) + 1) + 4 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "55", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = 3sin(2\u03c0(-3|((1(-3x^2 + 2x - 2) + 2)/(3(-3x^2 + 2x - 2) + 3)) + 1|) + 3) + 2 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = -1sin(2\u03c0(-2((1x - 2)/(-2x + 3))^2 - 3) + 2) - 1 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "26", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = -1(2(-3sin(2\u03c0x - 2) + 1)^2 - 4(-3sin(2\u03c0x - 2) + 1) - 4) - 1 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "80", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = -3|((-1(3sin(1\u03c0(-1x + 4) - 3) + 1) + 3)/(-1(3sin(1\u03c0(-1x + 4) - 3) + 1) - 2)) + 1| + 3 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "40", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = -2|(3cos(2\u03c0(3(-1x^2 - 4)) + 1) - 1)| where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "439", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = 1cos(2\u03c0(-1(3(-3|x - 3| - 1) - 2)^2 + 1(3(-3|x - 3| - 1) - 2) - 5) + 1) + 1 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1280", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = (3(-3(3sin(1\u03c0(-2|x + 1| + 3)) + 3)^2 + 3(3sin(1\u03c0(-2|x + 1| + 3)) + 3) + 2) + 3)/(-2(-3(3sin(1\u03c0(-2|x + 1| + 3)) + 3)^2 + 3(3sin(1\u03c0(-2|x + 1| + 3)) + 3) + 2) - 1) have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "40", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = 2cos(3\u03c0(-2|(-1(-1x - 3)^2 + 5(-1x - 3) + 2) - 1| + 1)) - 2 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "649", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = 3sin(1\u03c0(4(3|(-4x^2 + 4x + 3) - 2| + 3) - 5) + 3) - 2 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1272", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = 3cos(1\u03c0(-4(-3|x + 1| - 1)^2 + 1(-3|x + 1| - 1))) - 1 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1530", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation -3sin(2\u03c0(4((2(1|x - 3| - 3) - 3)/(-1(1|x - 3| - 3) + 3)) - 3) - 1) + 3 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "186", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = 1sin(1\u03c0(1|(-4((3x)/(2x - 3))^2 + 1((3x)/(2x - 3)) + 3) - 3| + 2) + 1) have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "196", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = -3(3cos(3\u03c0(2|x| - 1) + 3) - 1) - 4 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "120", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation -3|(1sin(2\u03c0(4x) + 2) + 1) - 2| + 2 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "160", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = 2|(-1cos(2\u03c0((1(-4x^2 - 2x + 3) + 3)/(2(-4x^2 - 2x + 3) + 3))) + 2) - 2| where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation (-2(3cos(2\u03c0(-1x^2 + 1x - 4) - 2) + 3) + 3)/(-1(3cos(2\u03c0(-1x^2 + 1x - 4) - 2) + 3) + 2) = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "229", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = 1((1(-3sin(2\u03c0x + 1)))/(-3(-3sin(2\u03c0x + 1)) + 2))^2 + 4((1(-3sin(2\u03c0x + 1)))/(-3(-3sin(2\u03c0x + 1)) + 2)) + 4 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "36", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = (1(-2(-3sin(1\u03c0(4x^2 + 3x - 3) - 1) - 3) - 3) + 2)/(3(-2(-3sin(1\u03c0(4x^2 + 3x - 3) - 1) - 3) - 3)) where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "550", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation 2sin(1\u03c0(5(-3|((1x - 2)/(-1x)) + 3| - 3)^2 - 1(-3|((1x - 2)/(-1x)) + 3| - 3) - 4) - 1) + 1 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "716", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = -1cos(3\u03c0(1|((-3x)/(2x - 1)) + 3| - 2) - 2) where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "56", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = 2cos(2\u03c0((-3(-1(-4x - 5)^2 + 2(-4x - 5) + 4) + 3)/(-2(-1(-4x - 5)^2 + 2(-4x - 5) + 4) - 1)) - 2) - 2 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "17", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = 3cos(2\u03c0(-1(-3x - 4)^2 - 5(-3x - 4) - 4) - 3) - 2 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1325", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation 1cos(3\u03c0(2((-2x)/(1x - 2))^2 + 5((-2x)/(1x - 2)) + 5) - 1) - 1 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "213", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = (-2(3(1|(-3cos(2\u03c0x - 3)) - 3| - 2) + 4) - 2)/(1(3(1|(-3cos(2\u03c0x - 3)) - 3| - 2) + 4)) where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "40", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation 3sin(1\u03c0((-1(-2(2x^2) + 1) + 1)/(-1(-2(2x^2) + 1) - 2)) - 3) = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "48", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation 2sin(3\u03c0(1(1|x - 2| + 1)^2 - 3(1|x - 2| + 1) + 4) + 2) + 1 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "564", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation 4(3((1(-3sin(1\u03c0x - 1) + 1) - 2)/(2(-3sin(1\u03c0x - 1) + 1))) - 4)^2 + 2(3((1(-3sin(1\u03c0x - 1) + 1) - 2)/(2(-3sin(1\u03c0x - 1) + 1))) - 4) - 2 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "30", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation (3(-3sin(3\u03c0(-2|x + 2| + 3) - 1) + 2) - 1)/(-2(-3sin(3\u03c0(-2|x + 2| + 3) - 1) + 2) + 3) = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "120", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = 4(5((-2(-2sin(3\u03c0x + 1)) + 1)/(3(-2sin(3\u03c0x + 1)) + 2))^2 + 3((-2(-2sin(3\u03c0x + 1)) + 1)/(3(-2sin(3\u03c0x + 1)) + 2)) - 2) + 1 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "60", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation -2|(3cos(3\u03c0((2x - 2)/(-3x - 3)) + 2) + 3)| + 2 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "66", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = -1sin(3\u03c0(-5(-1x^2 + 3x) + 3)) equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1651", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = 3(-1(-1sin(1\u03c0x + 2) + 3)^2 + 1(-1sin(1\u03c0x + 2) + 3) + 4) + 5 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "20", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = -2|((-1(-1(-2sin(3\u03c0x) - 1) - 3) - 1)/(-2(-1(-2sin(3\u03c0x) - 1) - 3)))| have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "34", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = (1(-3|(3cos(1\u03c0(-5x + 1) + 3)) - 2| + 2))/(-3(-3|(3cos(1\u03c0(-5x + 1) + 3)) - 2| + 2) - 1) equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "166", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = 1(-2|(-1cos(1\u03c0(5x^2 - 5x + 2) - 2) - 1) - 2| + 1) + 4 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "942", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = -3|(1cos(1\u03c0(2(-1x^2 + 5x + 2) - 5) + 1) + 2) - 2| + 2 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "849", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation -1((-2(2e^(2(-5x)) - 1) + 2)/(1(2e^(2(-5x)) - 1) - 3))^2 - 2((-2(2e^(2(-5x)) - 1) + 2)/(1(2e^(2(-5x)) - 1) - 3)) = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "25", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = -1(-4(-2sin(2\u03c0((-3x - 1)/(-2x - 1)) - 3) + 1) - 3)^2 + 4(-4(-2sin(2\u03c0((-3x - 1)/(-2x - 1)) - 3) + 1) - 3) + 2 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "17", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation 2sin(2\u03c0(-2|((-3x + 1)/(-1x - 1)) - 2| - 3) - 1) - 1 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "130", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation -1(-3|(-1sin(3\u03c0x + 2)) + 1| + 1) = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "60", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation -3(-1sin(1\u03c0((-1(3|x + 1| - 2) - 3)/(1(3|x + 1| - 2) + 1)) - 1) - 1)^2 - 1(-1sin(1\u03c0((-1(3|x + 1| - 2) - 3)/(1(3|x + 1| - 2) + 1)) - 1) - 1) + 4 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "53", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = (3(3sin(1\u03c0(-5x^2 + 2x - 1) + 2) - 2) + 1)/(1(3sin(1\u03c0(-5x^2 + 2x - 1) + 2) - 2) - 3) equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "927", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = (-2(2cos(3\u03c0(3x + 5))) - 3)/(-2(2cos(3\u03c0(3x + 5))) - 1) equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "180", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = -3sin(3\u03c0(5(1x^2 + 2x - 3))) where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1645", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = -2(-1|(1cos(2\u03c0((-2x - 2)/(3x - 2)) - 3) + 3) - 1| + 3)^2 + 1(-1|(1cos(2\u03c0((-2x - 2)/(3x - 2)) - 3) + 3) - 1| + 3) + 2 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "55", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = -4(-1(2cos(3\u03c0x - 2) + 2) + 4)^2 - 3(-1(2cos(3\u03c0x - 2) + 2) + 4) + 2 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "60", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation 2|((2(-1cos(3\u03c0x - 3)) + 3)/(1(-1cos(3\u03c0x - 3)))) + 3| = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "34", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = 2cos(2\u03c0(3((1x - 3)/(2x + 1))^2 - 2) + 3) + 1 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "167", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = -2|((2(2(2sin(1\u03c0x)) + 2) + 2)/(2(2(2sin(1\u03c0x)) + 2))) - 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": "How many zeros does the function f(x) = -1sin(1\u03c0((-1(-1|x - 1| - 1) - 3)/(-3(-1|x - 1| - 1) - 3)) - 3) - 1 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "19", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation -2sin(1\u03c0((1(1x + 2) + 2)/(-3(1x + 2) - 2)) - 1) - 1 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "22", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = -2cos(2\u03c0(1((3(-2x^2 + 1x + 4) + 1)/(2(-2x^2 + 1x + 4) + 3)) + 3)) equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "53", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = -3cos(3\u03c0(1|(5x + 2) - 1| + 2) - 3) + 2 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "300", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = 3sin(3\u03c0(2|(-4((-3x + 2)/(2x - 1)) + 2) - 2| + 3) + 1) + 2 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "73", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = 2(-2|(-2sin(1\u03c0(5x^2 + 5x - 1) + 1) + 3)| + 3) - 2 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "439", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = 4(5(1cos(2\u03c0x + 3))^2 + 5(1cos(2\u03c0x + 3)) - 2) equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "40", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = -2cos(2\u03c0(4((-3(-5x^2 + 3x) + 2)/(-1(-5x^2 + 3x))) - 4)) - 1 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "96", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = -5(-3sin(2\u03c0(-3x^2 + 5x - 3) - 1) - 2) + 5 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "513", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = (1(3|(3cos(1\u03c0x - 2) + 2) - 3| + 1) - 1)/(1(3|(3cos(1\u03c0x - 2) + 2) - 3| + 1) + 1) where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "9", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = -2|((2(-5(3sin(3\u03c0x + 3) + 1) - 1) + 1)/(3(-5(3sin(3\u03c0x + 3) + 1) - 1) - 2)) - 2| + 3 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "120", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = 1((-2(2cos(3\u03c0(-5x - 5) - 2) - 1) - 2)/(-2(2cos(3\u03c0(-5x - 5) - 2) - 1) + 1))^2 - 4((-2(2cos(3\u03c0(-5x - 5) - 2) - 1) - 2)/(-2(2cos(3\u03c0(-5x - 5) - 2) - 1) + 1)) - 2 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "600", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = -2sin(2\u03c0((2(-3x^2 - 1x + 2))/(-1(-3x^2 - 1x + 2) - 1)) + 1) + 1 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "56", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = 1((1(-2(-2sin(2\u03c0x + 1) + 1)^2 + 4(-2sin(2\u03c0x + 1) + 1) + 4) - 1)/(-3(-2(-2sin(2\u03c0x + 1) + 1)^2 + 4(-2sin(2\u03c0x + 1) + 1) + 4))) + 5 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "36", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = 1cos(1\u03c0(5(2((1x - 2)/(-2x + 1)) - 4)^2 - 4(2((1x - 2)/(-2x + 1)) - 4) - 5) + 1) - 1 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "178", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation 3sin(2\u03c0(-3|(-2x) - 3| - 1)) + 2 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "240", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = 3sin(1\u03c0(5(2(-3|x - 3|)^2 - 2) - 2) + 3) + 2 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1279", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = (-1(-2sin(3\u03c0(5x + 2) - 1)) + 2)/(1(-2sin(3\u03c0(5x + 2) - 1))) where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "150", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation (-2(-4(1(1sin(3\u03c0x) - 2) + 3)^2 - 2(1(1sin(3\u03c0x) - 2) + 3) + 1))/(3(-4(1(1sin(3\u03c0x) - 2) + 3)^2 - 2(1(1sin(3\u03c0x) - 2) + 3) + 1) + 1) = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "60", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = -4(-3cos(1\u03c0(2(-3|x - 2| - 3)^2 + 5(-3|x - 2| - 3) - 4) + 1) - 3) - 1 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "754", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = -2(-3|(-2sin(1\u03c0((-3x - 3)/(-1x + 3)) + 2) + 2) - 2|)^2 + 3(-3|(-2sin(1\u03c0((-3x - 3)/(-1x + 3)) + 2) + 2) - 2|) have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "19", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = -2((1(-4(1sin(1\u03c0x - 3)) - 1) + 3)/(3(-4(1sin(1\u03c0x - 3)) - 1) + 3))^2 - 1((1(-4(1sin(1\u03c0x - 3)) - 1) + 3)/(3(-4(1sin(1\u03c0x - 3)) - 1) + 3)) + 4 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 number of x-intercepts of the function f(x) = (-2(-1(-3cos(3\u03c0x - 2))^2 + 3(-3cos(3\u03c0x - 2)) + 1))/(-3(-1(-3cos(3\u03c0x - 2))^2 + 3(-3cos(3\u03c0x - 2)) + 1) + 4) where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "60", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = 2cos(1\u03c0((-2(-3|x + 1| + 1) + 2)/(-2(-3|x + 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": "64", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = (-1(-2cos(2\u03c0(3x + 4) - 2) - 3) - 1)/(2(-2cos(2\u03c0(3x + 4) - 2) - 3) - 1) have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "60", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = -1|(-3sin(1\u03c0((1(5x - 3) + 3)/(-2(5x - 3) + 3))) - 1) + 1| + 1 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "25", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = (-2(5(2cos(1\u03c0(2x^2 - 5x - 3) - 2)) + 3) + 2)/(3(5(2cos(1\u03c0(2x^2 - 5x - 3) - 2)) + 3) + 3) equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "275", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = -3|((-3(-1(2sin(2\u03c0x + 2) + 2)^2 - 3(2sin(2\u03c0x + 2) + 2)))/(-1(-1(2sin(2\u03c0x + 2) + 2)^2 - 3(2sin(2\u03c0x + 2) + 2)) + 2)) - 1| + 2 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "80", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation -1(-1sin(2\u03c0((3(-4x + 2) - 2)/(2(-4x + 2))) - 3) + 1)^2 - 3(-1sin(2\u03c0((3(-4x + 2) - 2)/(2(-4x + 2))) - 3) + 1) + 1 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "21", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = -2sin(1\u03c0(2(1|x| + 1) - 5) - 1) equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "40", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = -2(2sin(1\u03c0((1(-5x) + 2)/(-2(-5x) - 2)) - 3) - 3)^2 + 3 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "9", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = 2sin(1\u03c0(-2|(4(-1x + 1)^2 - 4(-1x + 1) + 2)|) - 1) have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1376", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = -3cos(1\u03c0(3(-3((1x - 2)/(-2x + 3))^2 - 1((1x - 2)/(-2x + 3))) + 2) + 2) - 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": "How many solutions does the equation (3(-2cos(1\u03c0(-4(-2|x + 3| + 1)^2 + 1(-2|x + 3| + 1) + 4) + 3) - 3) + 3)/(-3(-2cos(1\u03c0(-4(-2|x + 3| + 1)^2 + 1(-2|x + 3| + 1) + 4) + 3) - 3) + 4) = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1023", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation 2cos(2\u03c0((-2(4(-1|x + 1| + 3) - 5) - 1)/(-1(4(-1|x + 1| + 3) - 5) + 3)) - 1) - 1 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "118", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = 5(-2cos(3\u03c0(2|((-1x - 1)/(1x)) - 3| - 3)) - 1) - 1 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "79", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = 4(-2sin(2\u03c0(3(-2|x + 2| - 3) - 5) - 3) + 3)^2 - 1(-2sin(2\u03c0(3(-2|x + 2| - 3) - 5) - 3) + 3) - 4 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "240", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = (2(-1sin(2\u03c0(3(-1|x - 2| + 3) + 1) - 3)))/(-2(-1sin(2\u03c0(3(-1|x - 2| + 3) + 1) - 3)) + 3) equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "120", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = 1(3sin(3\u03c0(3(-2|x + 2| - 2)^2 - 2(-2|x + 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": "1359", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = 3cos(2\u03c0(-1(3|x - 2| - 2)^2 - 2(3|x - 2| - 2) + 4)) - 3 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1063", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = 3(5((-1(-2sin(3\u03c0x - 1) + 3) + 3)/(3(-2sin(3\u03c0x - 1) + 3) + 2))^2 - 4((-1(-2sin(3\u03c0x - 1) + 3) + 3)/(3(-2sin(3\u03c0x - 1) + 3) + 2)) + 1) - 2 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "60", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation 1(-2cos(2\u03c0((-1(-5x^2 - 2x - 4) + 2)/(-1(-5x^2 - 2x - 4) - 2)) + 2) - 2) + 3 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = 1((-2(5(2cos(1\u03c0x + 3) - 1) + 4) - 1)/(2(5(2cos(1\u03c0x + 3) - 1) + 4) - 1))^2 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "20", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = (-3(2|(3sin(3\u03c0(-1x - 2) - 3) + 2) - 1| + 1) + 3)/(-2(2|(3sin(3\u03c0(-1x - 2) - 3) + 2) - 1| + 1) - 1) where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "32", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = -5((2(3sin(1\u03c0x + 3) - 3) + 3)/(2(3sin(1\u03c0x + 3) - 3) + 1)) - 5 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": "Determine the number of values x in [-10, 10] where f(x) = -2|(4(2sin(2\u03c0(3x + 3) - 1))^2 - 2(2sin(2\u03c0(3x + 3) - 1)) - 5) + 2| equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "89", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation 2((-2(-3|(2sin(1\u03c0x) + 1) - 3| + 3) + 3)/(-3(-3|(2sin(1\u03c0x) + 1) - 3| + 3) + 2)) + 2 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "20", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = 3cos(2\u03c0(5(-1(1|x - 2| - 2)^2 - 4(1|x - 2| - 2) - 5)) + 2) - 2 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1264", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation 2sin(3\u03c0(-3((2(-3x^2 - 1x + 5) + 3)/(-1(-3x^2 - 1x + 5) + 3)) - 5) - 2) + 1 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "221", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = -1cos(2\u03c0(2((3x + 1)/(1x))^2 - 5((3x + 1)/(1x)) - 1) + 3) - 1 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "74", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = -3((-2(2|(1sin(1\u03c0x + 3) + 3) - 3|) + 3)/(3(2|(1sin(1\u03c0x + 3) + 3) - 3|) - 2))^2 - 5((-2(2|(1sin(1\u03c0x + 3) + 3) - 3|) + 3)/(3(2|(1sin(1\u03c0x + 3) + 3) - 3|) - 2)) where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "80", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = (-3(-2cos(3\u03c0(-1|x + 3| + 3) - 3) - 2) - 1)/(3(-2cos(3\u03c0(-1|x + 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": "60", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = 2sin(2\u03c0(-1|(1(-1x - 3)^2 - 1(-1x - 3) - 4) - 2| + 2) - 3) + 2 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "211", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = 1(-3|(2cos(1\u03c0x + 1) - 2) + 3| + 3) + 1 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "20", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = 3|((2(2sin(2\u03c0x + 1)))/(2(2sin(2\u03c0x + 1)) - 1)) - 3| - 3 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "80", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = (-1(4(3cos(1\u03c0(3|x - 1| + 2) + 3) + 1)^2 + 4(3cos(1\u03c0(3|x - 1| + 2) + 3) + 1) - 5) - 3)/(3(4(3cos(1\u03c0(3|x - 1| + 2) + 3) + 1)^2 + 4(3cos(1\u03c0(3|x - 1| + 2) + 3) + 1) - 5) + 2) equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "120", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = 3cos(1\u03c0(-2(3|(1x^2 - 5x - 3) - 3| - 1) + 3) + 1) + 2 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1043", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = 2|((2(-1sin(1\u03c0(5x + 2) + 2) + 1) - 3)/(-2(-1sin(1\u03c0(5x + 2) + 2) + 1))) + 1| - 2 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "100", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = 2(2((3(-3sin(3\u03c0x + 3) - 1) + 1)/(-2(-3sin(3\u03c0x + 3) - 1) - 3)) - 1)^2 + 2(2((3(-3sin(3\u03c0x + 3) - 1) + 1)/(-2(-3sin(3\u03c0x + 3) - 1) - 3)) - 1) - 1 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "120", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation -2cos(1\u03c0(-2|(2(-4x - 4)^2 + 4(-4x - 4) + 5) + 1| + 2) - 1) + 2 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1179", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = -3|(-1cos(3\u03c0(-1x^2 - 4x - 3) - 3))| + 3 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "542", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = 2sin(2\u03c0(-1|(4(-5x^2 - 5x - 5) - 5) - 3| - 2) + 2) have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1613", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = 3cos(2\u03c0(1(-3|x + 2| + 3) - 3) + 1) + 1 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "120", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = 2cos(3\u03c0(-3|(3x^2 + 2) - 1| + 3) - 1) + 1 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1286", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = (-2(2(-4(1cos(2\u03c0x + 2) - 1)^2 + 3) - 1) + 2)/(-1(2(-4(1cos(2\u03c0x + 2) - 1)^2 + 3) - 1) - 1) where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "40", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation -4(-2sin(1\u03c0(-4(-3|x| + 1)^2 + 5(-3|x| + 1)) - 1) - 2) - 3 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1304", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = -1|(1cos(3\u03c0(-1x) + 2) - 2)| + 2 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "60", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation 3|((-3(4(3sin(2\u03c0x - 2) - 1)) + 1)/(2(4(3sin(2\u03c0x - 2) - 1)) + 3))| = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "18", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = 2(-1cos(2\u03c0(1|(-3x^2 - 4x - 2) - 2| + 1) - 3) - 2) + 3 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1086", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation -3sin(2\u03c0((-2(-1|x + 2| + 2) + 3)/(1(-1|x + 2| + 2) + 2)) + 3) - 2 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "231", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation 2cos(1\u03c0(-1|(1x - 1) + 1| + 3)) - 1 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "20", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation -1((-1(2cos(3\u03c0(3|x + 3| + 1) - 2) - 1) + 1)/(-2(2cos(3\u03c0(3|x + 3| + 1) - 2) - 1) + 1)) - 4 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "80", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation -2(-3cos(1\u03c0((-2x - 3)/(2x - 1))) + 3) + 1 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "46", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation 4((2(1sin(3\u03c0(2x^2 + 4x + 5) - 3) + 1) - 2)/(-2(1sin(3\u03c0(2x^2 + 4x + 5) - 3) + 1) + 3)) - 3 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "482", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = 3sin(3\u03c0(1|(3(-2x^2 - 5x + 2) + 5) - 2| + 3)) - 3 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1145", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = -3sin(3\u03c0(-3(3|x|) + 2) - 1) + 3 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "267", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation 3sin(3\u03c0((-1(4(3x^2 + 4x - 2) - 3) - 1)/(-3(4(3x^2 + 4x - 2) - 3) + 1)) + 1) - 2 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation -3sin(2\u03c0(3|((-2(-5x^2 - 1x + 4) + 3)/(-2(-5x^2 - 1x + 4) + 1)) - 2| - 3) + 3) + 1 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "58", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation -2sin(3\u03c0(1(2|(3x^2 - 5x - 4) + 3| - 2) - 1) + 1) + 2 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1159", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = 2cos(2\u03c0(-2|(-1x - 1) + 3| + 3) - 2) - 1 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "80", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = (-3(-1|(-3sin(2\u03c0(5x^2 - 4x + 4) - 2) - 1) + 2| + 1) + 2)/(-2(-1|(-3sin(2\u03c0(5x^2 - 4x + 4) - 2) - 1) + 2| + 1) + 3) equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "487", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = 3(-4(-2cos(2\u03c0x + 1) - 2) - 3)^2 + 5(-4(-2cos(2\u03c0x + 1) - 2) - 3) - 5 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "80", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = (1(2|(-3(2sin(2\u03c0x + 1) - 2)^2 + 4(2sin(2\u03c0x + 1) - 2) - 4) + 2| - 1) - 3)/(3(2|(-3(2sin(2\u03c0x + 1) - 2)^2 + 4(2sin(2\u03c0x + 1) - 2) - 4) + 2| - 1) - 2) equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "20", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = -2|(-4((3(-3cos(1\u03c0x - 1) - 3) + 2)/(-1(-3cos(1\u03c0x - 1) - 3) - 1)) + 1) - 2| + 2 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "40", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = -2|((3(-1sin(2\u03c0x + 2)) - 1)/(3(-1sin(2\u03c0x + 2)))) + 1| + 1 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "80", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = 1(1cos(1\u03c0(3x^2 - 2) - 2) + 3) - 3 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "600", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = 2sin(1\u03c0(-1(-3|x| + 2)^2 + 3(-3|x| + 2) + 1) - 2) have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1412", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = 3cos(1\u03c0(-3(-2|x - 2| - 2)^2 + 2(-2|x - 2| - 2) + 5) + 3) - 1 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1694", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = -4(-3|(-5(-1sin(2\u03c0x + 2))^2 - 3(-1sin(2\u03c0x + 2)) - 2) + 3| + 2) have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "160", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = 3sin(1\u03c0((2(-1x - 4) + 3)/(2(-1x - 4) - 3)) - 3) - 3 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "36", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation -2cos(1\u03c0(-5(-2|x + 3|) + 4)) - 2 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "100", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = -2sin(3\u03c0(-3|((1(-5x + 5))/(-3(-5x + 5) + 2)) + 3| - 1) - 2) + 1 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "23", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = -2|(1cos(2\u03c0((-3x)/(3x - 2)) - 3) - 1) + 1| + 2 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "36", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation 3(1cos(2\u03c0(-5x + 1) - 3) + 1)^2 - 4 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "200", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = 1((-3(1(3cos(1\u03c0x - 2) + 3) - 3) - 3)/(3(1(3cos(1\u03c0x - 2) + 3) - 3) - 2))^2 + 2((-3(1(3cos(1\u03c0x - 2) + 3) - 3) - 3)/(3(1(3cos(1\u03c0x - 2) + 3) - 3) - 2)) - 3 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "40", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation -4(1sin(3\u03c0(-4x^2 - 1x - 2) + 2)) + 4 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "942", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation 2sin(1\u03c0(2(3|x + 2| - 2) - 3)) - 1 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "120", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation 3cos(1\u03c0(5((3x - 2)/(2x - 1)) + 3) + 2) = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "41", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = 3|(-3(3cos(2\u03c0x) - 3)^2 - 5(3cos(2\u03c0x) - 3) + 2) + 2| - 2 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "40", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = (1(-2sin(1\u03c0(4(-2|x + 3| + 3) + 2) - 2) + 3) - 3)/(2(-2sin(1\u03c0(4(-2|x + 3| + 3) + 2) - 2) + 3) - 1) have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "160", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = 5(-3(-1sin(3\u03c0x + 3) + 1) + 2)^2 - 2(-3(-1sin(3\u03c0x + 3) + 1) + 2) - 2 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": "How many zeros does the function f(x) = -2cos(2\u03c0(-4(-2|(-3x - 5) + 1| + 1)^2 - 5(-2|(-3x - 5) + 1| + 1) - 3) - 2) + 1 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1418", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation 2sin(3\u03c0(5(1x^2 + 5x - 2) - 4) - 1) + 2 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1065", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = (-3(3(-2cos(1\u03c0(-3|x + 1| - 1) + 3)) + 3))/(2(3(-2cos(1\u03c0(-3|x + 1| - 1) + 3)) + 3) - 1) equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "60", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = 1cos(1\u03c0((-1(1|x + 3| - 1) - 3)/(1(1|x + 3| - 1))) - 3) have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "127", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = 2(-1sin(1\u03c0(-3x + 3) + 2) - 1)^2 - 2(-1sin(1\u03c0(-3x + 3) + 2) - 1) - 1 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "60", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation 3cos(2\u03c0(5((-3(5x + 1) + 1)/(3(5x + 1) + 1))^2 - 3((-3(5x + 1) + 1)/(3(5x + 1) + 1)) + 5) + 3) - 1 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "63", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = (-2(-2|(5(2sin(3\u03c0x - 1) - 1) + 2) + 2| + 1) - 2)/(-1(-2|(5(2sin(3\u03c0x - 1) - 1) + 2) + 2| + 1) + 3) 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 number of x-intercepts of the function f(x) = 2cos(3\u03c0(5((-1x - 2)/(-3x + 1)) + 1)) - 2 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "75", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = 1(-1sin(2\u03c0(4(1|x - 2| + 1) + 1) + 3) + 1)^2 + 2(-1sin(2\u03c0(4(1|x - 2| + 1) + 1) + 3) + 1) - 5 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "160", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = -1sin(1\u03c0((-2(3|x + 2| - 3) + 1)/(-2(3|x + 2| - 3) - 1)) + 2) + 1 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "21", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = -3sin(2\u03c0(1|(3((-2x - 1)/(3x + 3)) + 1) + 1| + 1) - 2) have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "55", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = (-3(1(2cos(1\u03c0(1x + 5) - 3))^2 - 1(2cos(1\u03c0(1x + 5) - 3)) - 5) + 3)/(3(1(2cos(1\u03c0(1x + 5) - 3))^2 - 1(2cos(1\u03c0(1x + 5) - 3)) - 5) + 2) where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = 3sin(1\u03c0(2(-3|x| + 1)^2 - 3(-3|x| + 1) - 5)) - 3 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1126", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = -3sin(1\u03c0(4((1(1|x - 2|) - 1)/(-2(1|x - 2|) - 1)) - 3) + 2) - 3 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "6", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = -2|(2cos(3\u03c0((1(2x^2 - 3x - 4) + 1)/(-3(2x^2 - 3x - 4))) - 3) - 1) + 3| + 3 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "24", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation (-1(2cos(1\u03c0(5(1x - 3)^2 + 3(1x - 3) + 1) - 2)) - 1)/(2(2cos(1\u03c0(5(1x - 3)^2 + 3(1x - 3) + 1) - 2)) - 1) = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "813", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = 3sin(1\u03c0(4(-1|(5x + 1) + 1| - 1)^2 - 4(-1|(5x + 1) + 1| - 1) + 3) + 2) + 1 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1556", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = 4(1cos(1\u03c0((3(-3x^2 - 2x + 3) + 2)/(2(-3x^2 - 2x + 3) + 3)) - 1) - 1) + 2 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "27", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation -3|(-2sin(3\u03c0(5((2x + 2)/(-1x + 3)) - 1) - 3) - 2)| + 2 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "337", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = (-2(3|(-4(3sin(1\u03c0x) + 2) - 1) - 3| - 2) - 3)/(-3(3|(-4(3sin(1\u03c0x) + 2) - 1) - 3| - 2) - 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": "How many solutions does the equation -3sin(3\u03c0(-2|(1x^2 - 5x - 1)| - 1) - 2) + 3 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "537", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = -3sin(1\u03c0((1(-2|(-1x - 5) + 1| + 1))/(2(-2|(-1x - 5) + 1| + 1) - 1)) - 2) - 2 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "24", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = 1sin(1\u03c0(-1(3|((-1x + 1)/(3x)) - 1| - 3)^2 + 1(3|((-1x + 1)/(3x)) - 1| - 3) - 3) + 1) equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "77", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = -3((-2(-3sin(2\u03c0(3|x + 3|) + 3) - 1) + 3)/(3(-3sin(2\u03c0(3|x + 3|) + 3) - 1) + 1))^2 + 5((-2(-3sin(2\u03c0(3|x + 3|) + 3) - 1) + 3)/(3(-3sin(2\u03c0(3|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": "170", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = (1(-1cos(2\u03c0(-1|(-3x^2 + 2x + 2) + 3| + 2) + 1)) - 1)/(-2(-1cos(2\u03c0(-1|(-3x^2 + 2x + 2) + 3| + 2) + 1)) + 3) equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "523", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = -3|(3cos(3\u03c0(5x^2 - 5x - 2)) + 1) - 1| + 1 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "479", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = 3cos(1\u03c0(3|(1(-1x + 4)^2 + 4(-1x + 4) + 5) + 2| - 3) + 1) have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "816", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = 1(3sin(1\u03c0((3x + 1)/(1x - 3)) - 2) + 3)^2 - 2(3sin(1\u03c0((3x + 1)/(1x - 3)) - 2) + 3) - 3 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "114", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation -4(1(2cos(2\u03c0(-3|x - 1|) - 2) + 2)^2 - 4) - 5 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "120", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation (1(-2sin(2\u03c0(5x^2 + 4x - 3) - 3) + 1) - 3)/(-1(-2sin(2\u03c0(5x^2 + 4x - 3) - 3) + 1)) = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "980", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = -1cos(1\u03c0((-1(-1x^2 - 2x - 1) + 2)/(-2(-1x^2 - 2x - 1) - 3)) - 2) - 1 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "34", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = (1(2cos(1\u03c0(-1x^2 + 2x + 5) + 1) + 1) - 1)/(-2(2cos(1\u03c0(-1x^2 + 2x + 5) + 1) + 1) + 3) where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "201", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation (2(3|(-1(-3sin(2\u03c0x - 3) - 1) + 2)| - 2) - 2)/(-3(3|(-1(-3sin(2\u03c0x - 3) - 1) + 2)| - 2)) = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "40", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = 1sin(3\u03c0(2(2x - 1)^2 - 1(2x - 1) + 2)) + 1 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1095", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = 4(-2cos(1\u03c0(5((-1x - 1)/(-3x + 4))^2 - 1((-1x - 1)/(-3x + 4)) - 1) - 1) + 3) - 5 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "59", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation (-2(-3|(-1sin(1\u03c0x) + 2) - 3|) - 2)/(3(-3|(-1sin(1\u03c0x) + 2) - 3|) - 2) = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "20", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = -4(2cos(3\u03c0(-5(-1|x + 2| + 3)^2 + 3) + 3) - 2) - 3 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1144", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = -3((1(1sin(2\u03c0(2|x - 1| - 3) - 1) - 1) - 2)/(1(1sin(2\u03c0(2|x - 1| - 3) - 1) - 1) + 2)) - 3 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "40", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = 2sin(1\u03c0(-3|((2x + 2)/(2x - 1)) + 1| + 2) + 2) equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "77", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation -2sin(2\u03c0(2((3(1|x|) - 3)/(1(1|x|) + 1)) + 5) - 3) + 1 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "44", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = -1(-3sin(1\u03c0((-3x + 1)/(-2x - 3)) - 2) - 2) + 1 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "34", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = -2cos(1\u03c0(2|(-1x^2 + 4x - 3) + 3|) + 3) - 1 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "416", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = (3(3sin(3\u03c0(4x^2 - 5x + 4) - 3) + 3) - 1)/(2(3sin(3\u03c0(4x^2 - 5x + 4) - 3) + 3) + 3) where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "825", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = 2cos(1\u03c0(-1|(-3((-1x + 2)/(1x - 3))^2 + 2((-1x + 2)/(1x - 3))) - 3| - 1) + 3) - 1 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 number of x-intercepts of the function f(x) = 1cos(3\u03c0(4(-2x^2 + 1x - 5)) + 1) - 1 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1077", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation (-1(-3cos(3\u03c0(2x - 2) - 1) + 1))/(3(-3cos(3\u03c0(2x - 2) - 1) + 1) + 2) = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "120", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = -4(-3|(2cos(3\u03c0x - 3) - 1) + 3| + 2) + 4 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "60", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = -2((2(3sin(2\u03c0x - 2)))/(2(3sin(2\u03c0x - 2)) - 1))^2 + 3((2(3sin(2\u03c0x - 2)))/(2(3sin(2\u03c0x - 2)) - 1)) equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "80", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation 2sin(1\u03c0(-1|((-2(-1x - 1) - 3)/(-1(-1x - 1) + 3))|)) + 1 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "107", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation -2(3cos(2\u03c0((-1(1|x| - 1) + 1)/(-2(1|x| - 1) - 3))) - 1) - 3 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation -2sin(2\u03c0(5(3((2x + 3)/(-3x - 3)) - 2)^2 - 1(3((2x + 3)/(-3x - 3)) - 2) + 4) - 2) - 2 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "180", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation -3sin(2\u03c0((-3(-2|x + 3| - 2) + 3)/(-2(-2|x + 3| - 2) - 2)) - 2) + 2 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = -1((3(-2sin(3\u03c0x + 2) - 3) - 3)/(2(-2sin(3\u03c0x + 2) - 3) + 3))^2 + 3((3(-2sin(3\u03c0x + 2) - 3) - 3)/(2(-2sin(3\u03c0x + 2) - 3) + 3)) - 1 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "60", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation (-2(-1cos(1\u03c0(3|x + 2|) + 2) - 1) - 1)/(-2(-1cos(1\u03c0(3|x + 2|) + 2) - 1) + 3) = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "60", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation 3((-3(-2cos(2\u03c0(-1|x + 2| + 3))) + 1)/(3(-2cos(2\u03c0(-1|x + 2| + 3))))) - 2 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "40", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = -2sin(1\u03c0(2(-1|x - 1| - 1)^2 + 5) + 2) - 2 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "230", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = -3(-3|(-1sin(2\u03c0(3x + 2) + 3)) - 2| + 3)^2 - 4(-3|(-1sin(2\u03c0(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": "120", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = (-3(2|(2(-1sin(2\u03c0x - 3) + 2)^2 - 4) + 2| - 3) - 3)/(-1(2|(2(-1sin(2\u03c0x - 3) + 2)^2 - 4) + 2| - 3) - 3) where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "40", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation 2cos(3\u03c0(4(3x^2 - 3x - 2) - 2)) - 2 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1062", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = (-2(-2|(4(-2cos(1\u03c0x - 3) + 2) - 3) - 2| - 1) - 2)/(-2(-2|(4(-2cos(1\u03c0x - 3) + 2) - 3) - 2| - 1) + 3) where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "9", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = -3|(2sin(1\u03c0(4(-3x^2 - 1x + 2) - 2) - 3)) + 1| + 1 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "676", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = 1cos(1\u03c0(-1|(-3x + 4) - 1| + 2) + 1) - 1 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "31", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation 3(3|(-3sin(3\u03c0x + 2) + 3) - 1| - 2)^2 + 3(3|(-3sin(3\u03c0x + 2) + 3) - 1| - 2) - 2 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "240", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = -4(1|(-2sin(2\u03c0((-3x - 3)/(-1x - 3)) - 2) + 2) - 2|) + 1 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "93", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = 2cos(1\u03c0(2(-1|x - 2| - 2) - 3) + 3) + 2 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": "How many solutions does the equation -3cos(2\u03c0(2|((-3(-1x - 4) + 1)/(-2(-1x - 4) - 1)) - 1| - 2) - 2) + 3 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "50", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = -1(-3cos(3\u03c0(1|((1x + 2)/(-1x + 2)) + 1| + 1) + 3) + 2) + 4 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "117", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation (2(3cos(1\u03c0(1|(-2x - 2) - 2| - 3)) + 1) + 2)/(-1(3cos(1\u03c0(1|(-2x - 2) - 2| - 3)) + 1) + 3) = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "40", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = 5((-2(1|(-2sin(1\u03c0x - 2) - 1) - 3| - 1) + 2)/(2(1|(-2sin(1\u03c0x - 2) - 1) - 3| - 1) - 1)) + 4 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "20", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = -2sin(3\u03c0(1((2(4x - 3))/(-1(4x - 3) + 3))^2 - 5((2(4x - 3))/(-1(4x - 3) + 3)) - 4) - 2) equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "206", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = 1cos(2\u03c0(-4(-1x^2 - 2x - 4) + 4) - 3) - 1 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "684", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = -2cos(1\u03c0(2|(-3(-1x^2 + 4x - 2) + 5) + 1| + 3) + 1) equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1167", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = (-1(-5(-3cos(1\u03c0x + 1) - 1)^2 + 5(-3cos(1\u03c0x + 1) - 1) + 3) + 3)/(1(-5(-3cos(1\u03c0x + 1) - 1)^2 + 5(-3cos(1\u03c0x + 1) - 1) + 3)) where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "40", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = 3|((-1(-4(-3cos(2\u03c0x - 2) + 2)^2 - 5(-3cos(2\u03c0x - 2) + 2) - 5) + 2)/(-1(-4(-3cos(2\u03c0x - 2) + 2)^2 - 5(-3cos(2\u03c0x - 2) + 2) - 5) - 3)) - 3| equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "28", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation -2sin(3\u03c0(-2((1x - 2)/(2x - 1))^2 + 3) - 1) - 2 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "61", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation -2|(-1(-2sin(3\u03c0x + 1) + 3)^2 + 3(-2sin(3\u03c0x + 1) + 3) + 3) + 2| + 3 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "120", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = 5(3sin(1\u03c0((1(-1x + 2))/(3(-1x + 2) - 2)) + 2) + 1)^2 + 2(3sin(1\u03c0((1(-1x + 2))/(3(-1x + 2) - 2)) + 2) + 1) - 4 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "19", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = -3|(-1(-2sin(1\u03c0((2x + 3)/(2x - 3))) + 3)^2 + 5(-2sin(1\u03c0((2x + 3)/(2x - 3))) + 3) - 3) + 2| where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = 2|(-1cos(2\u03c0(-5(3x^2 + 1x - 5) + 1)) + 2) - 3| - 2 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1475", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = (-2(-1(1(-3cos(2\u03c0x - 1))^2 + 1(-3cos(2\u03c0x - 1)) - 1)) - 3)/(1(-1(1(-3cos(2\u03c0x - 1))^2 + 1(-3cos(2\u03c0x - 1)) - 1))) equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "80", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = -2(-3cos(2\u03c0((3x + 3)/(3x + 1))) + 1) + 2 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "44", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = 5(1(3cos(3\u03c0x) - 1)^2 - 4(3cos(3\u03c0x) - 1) + 2) - 5 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "60", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = 5(1sin(3\u03c0((-3x)/(-1x + 2)) + 1) - 1)^2 - 4(1sin(3\u03c0((-3x)/(-1x + 2)) + 1) - 1) - 4 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "145", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = 2sin(3\u03c0((-2(-1x - 3) + 3)/(2(-1x - 3) + 1)) + 3) - 1 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "86", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = -2cos(2\u03c0((-1(-1x^2 + 5x - 4) - 3)/(-1(-1x^2 + 5x - 4) + 2)) - 2) have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "170", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = -3sin(3\u03c0(3|((1x - 3)/(2x - 3)) - 1| - 3) + 3) - 2 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "75", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = -3sin(3\u03c0(1(-3((-3x + 1)/(3x - 2)))^2 - 5(-3((-3x + 1)/(3x - 2))) + 4) + 2) + 3 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "59", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = (3(-4(3sin(2\u03c0x - 1) - 1) + 3) + 1)/(-3(-4(3sin(2\u03c0x - 1) - 1) + 3) + 2) have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "40", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = -3sin(3\u03c0(5((-2(-3|x + 2| - 1) - 3)/(2(-3|x + 2| - 1))) - 4) - 2) + 1 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "42", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = 1|(3cos(2\u03c0(-2x^2 + 2x - 5) + 1) - 3)| - 2 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "800", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = -5(3cos(3\u03c0((-1x + 2)/(-1x - 1)) - 2) - 2)^2 + 3(3cos(3\u03c0((-1x + 2)/(-1x - 1)) - 2) - 2) + 5 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "103", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation -2cos(2\u03c0((2(1(2x^2 - 5x) + 3) - 1)/(-2(1(2x^2 - 5x) + 3))) + 1) + 2 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "34", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = 5(1sin(1\u03c0(-4x^2 + 2x + 4) + 3) - 1) + 3 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "796", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = (3(-1sin(1\u03c0(-2|x - 1| - 2) + 2) + 1) - 3)/(-2(-1sin(1\u03c0(-2|x - 1| - 2) + 2) + 1) - 3) equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "40", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = 1((1(-3sin(3\u03c0x + 1) + 1) + 1)/(2(-3sin(3\u03c0x + 1) + 1) - 1))^2 - 4((1(-3sin(3\u03c0x + 1) + 1) + 1)/(2(-3sin(3\u03c0x + 1) + 1) - 1)) - 5 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "120", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation (1(-2|(-2cos(2\u03c0(-1x^2 - 4x + 3) - 2) + 1) - 1|))/(1(-2|(-2cos(2\u03c0(-1x^2 - 4x + 3) - 2) + 1) - 1|) + 3) = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "382", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = -1(2cos(3\u03c0(-3|x + 1| - 1) - 3) + 2) equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "89", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation -1sin(2\u03c0(-1|(4x - 2) + 1| - 3) - 2) + 1 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "80", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation -1(-3cos(1\u03c0(1((2x - 1)/(-2x - 3)) - 1) + 1) + 3)^2 + 3 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "48", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = (-3(3sin(1\u03c0(1|x| + 3) + 1)) + 3)/(-3(3sin(1\u03c0(1|x| + 3) + 1)) - 3) 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": "How many zeros does the function f(x) = (3(-3cos(1\u03c0(-5(4x - 5)^2 + 4(4x - 5) - 4)) - 1) + 1)/(3(-3cos(1\u03c0(-5(4x - 5)^2 + 4(4x - 5) - 4)) - 1)) have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "213", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation -5(-3|((2(3cos(2\u03c0x - 2) + 2) - 3)/(-1(3cos(2\u03c0x - 2) + 2)))| + 3) + 2 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "80", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = -5(3(-2cos(1\u03c0(-3|x + 2| - 1)) - 3) + 3)^2 - 4(3(-2cos(1\u03c0(-3|x + 2| - 1)) - 3) + 3) + 1 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "60", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation 3cos(2\u03c0(5(-1|((-3x - 1)/(-2x - 1))| + 1) + 5) - 2) - 3 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "33", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = -2cos(1\u03c0(1(-1((3x - 1)/(1x - 2))^2 + 1((3x - 1)/(1x - 2)) + 4) + 4) - 2) - 2 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "126", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation -2sin(1\u03c0(2((2(1x) - 3)/(1(1x) + 1))^2 + 2((2(1x) - 3)/(1(1x) + 1))) - 1) - 2 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "171", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation -4((-2(4(2cos(1\u03c0x + 1) + 2) - 1) - 2)/(3(4(2cos(1\u03c0x + 1) + 2) - 1) - 2))^2 + 5((-2(4(2cos(1\u03c0x + 1) + 2) - 1) - 2)/(3(4(2cos(1\u03c0x + 1) + 2) - 1) - 2)) + 5 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "20", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation (-1(2|(4(-2cos(3\u03c0x + 1) - 1)^2 - 5) + 1| - 3) - 2)/(-3(2|(4(-2cos(3\u03c0x + 1) - 1)^2 - 5) + 1| - 3) - 2) = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "160", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = 3(3(-2sin(2\u03c0((2x + 3)/(-2x - 1)) + 3) - 3) + 3)^2 - 5 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "43", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = -2|((2(1cos(3\u03c0(-2x + 2) + 2) - 1) - 3)/(1(1cos(3\u03c0(-2x + 2) + 2) - 1) + 1)) + 2| + 3 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "120", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = -1sin(2\u03c0(-5(3|x - 3| + 1) + 5) - 1) - 1 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "296", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = 2cos(3\u03c0(2|(4x^2 - 4) - 2| + 1) - 1) - 1 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1453", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation (2(-3sin(1\u03c0(5x^2 + 4x + 5) - 1) + 2))/(-3(-3sin(1\u03c0(5x^2 + 4x + 5) - 1) + 2) + 2) = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "428", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = -3(2(-1sin(3\u03c0(-3|x - 1| + 2) - 3) + 2)^2 - 5(-1sin(3\u03c0(-3|x - 1| + 2) - 3) + 2) - 3) where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "75", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = -3cos(2\u03c0(1(3|x + 3| - 3)^2 - 2(3|x + 3| - 3) - 2) - 3) + 1 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1426", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation 3cos(3\u03c0(-1(-2|((-2x + 3)/(-3x))| + 2) + 4)) + 2 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "80", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = 3sin(1\u03c0(3((1x + 2)/(1x - 3))^2 - 4((1x + 2)/(1x - 3)) + 1) + 1) + 2 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "240", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = -1(3sin(2\u03c0((-3(4x^2 - 1x + 4))/(-1(4x^2 - 1x + 4) + 2)) - 3) + 3) + 3 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = -1|((-2(2sin(2\u03c0(-2x + 3)) + 1))/(3(2sin(2\u03c0(-2x + 3)) + 1) - 1)) + 3| + 2 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "155", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = -2sin(3\u03c0(2|(5((1x + 1)/(1x - 3)) - 5) + 2| - 1) - 3) - 2 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "224", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = 3sin(2\u03c0(1|((-3(4x^2 - 2x + 1) - 2)/(1(4x^2 - 2x + 1) - 3)) + 1| - 1) + 2) - 2 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "113", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = 1sin(2\u03c0((1(-1|x + 2| + 2) + 1)/(-1(-1|x + 2| + 2) + 2)) - 1) equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "89", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation 3cos(3\u03c0(4(-4((-2x + 1)/(-3x - 2)) - 1)^2 - 5(-4((-2x + 1)/(-3x - 2)) - 1) + 4) - 1) - 2 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "499", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = -2|(-2sin(2\u03c0((3x + 1)/(2x + 1)) + 3) + 2) - 3| + 1 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "34", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = -2|(-1(-3cos(2\u03c0((-1x + 2)/(-3x - 2)) - 2) - 2)^2 - 4(-3cos(2\u03c0((-1x + 2)/(-3x - 2)) - 2) - 2)) + 3| + 2 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "68", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation 5(2sin(2\u03c0(-4x^2 + 4x - 3) + 2) + 1) + 5 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "682", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = -1sin(1\u03c0((2(2|x| - 1) - 1)/(-3(2|x| - 1) - 3)) - 1) + 1 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation -1(2sin(2\u03c0(3((-3x - 3)/(-1x + 3)) - 4) + 2) - 1)^2 + 2(2sin(2\u03c0(3((-3x - 3)/(-1x + 3)) - 4) + 2) - 1) + 3 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "294", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = 3sin(1\u03c0(-1|((-1x + 1)/(-3x - 2)) + 1| + 2)) - 3 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = -1sin(2\u03c0(-1((-2(-3x + 4) - 1)/(-3(-3x + 4) + 4))^2 - 1)) + 1 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "29", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = -3cos(2\u03c0(-1(-2|x - 3| - 3) - 4) + 2) + 1 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "80", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = (1(-3sin(1\u03c0(2(2x^2 + 5x + 4)) - 3)) + 3)/(2(-3sin(1\u03c0(2(2x^2 + 5x + 4)) - 3)) + 1) where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "399", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = -3sin(2\u03c0(5(4(-1|x|) - 1)^2 - 1(4(-1|x|) - 1) + 5) - 1) - 3 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1217", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation 3cos(2\u03c0(3|((-2x - 3)/(-3x - 3)) - 2| - 3) - 3) = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "56", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = (2(4(3sin(3\u03c0(-5x^2 - 3x - 5) + 3)) + 3) + 3)/(2(4(3sin(3\u03c0(-5x^2 - 3x - 5) + 3)) + 3) - 1) have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "349", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = 1(-2sin(3\u03c0(-2(-1|x - 2| + 2) - 3) - 1) + 1)^2 + 5(-2sin(3\u03c0(-2(-1|x - 2| + 2) - 3) - 1) + 1) - 4 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "120", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = (1(3|(-2sin(2\u03c0x + 1) - 3) + 1| - 1))/(3(3|(-2sin(2\u03c0x + 1) - 3) + 1| - 1) + 1) equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "40", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation (-2(1(2cos(1\u03c0x - 2))^2 + 5(2cos(1\u03c0x - 2)) - 2) - 3)/(2(1(2cos(1\u03c0x - 2))^2 + 5(2cos(1\u03c0x - 2)) - 2) - 3) = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "20", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = 1((2(3(1cos(2\u03c0x - 3) + 1)^2 + 3(1cos(2\u03c0x - 3) + 1) - 3) - 2)/(-3(3(1cos(2\u03c0x - 3) + 1)^2 + 3(1cos(2\u03c0x - 3) + 1) - 3) + 2)) + 2 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "39", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = 4(-3cos(3\u03c0(-2|x + 2| + 1) - 2) - 3)^2 + 4(-3cos(3\u03c0(-2|x + 2| + 1) - 2) - 3) - 3 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "120", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = 3sin(2\u03c0(-1(-3(3|x|) + 2)^2 - 5(-3(3|x|) + 2) + 4)) + 2 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1234", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = -2sin(3\u03c0(2(-1|(-2x) + 2| - 1)^2 - 5(-1|(-2x) + 2| - 1) - 5) + 3) - 2 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1094", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = 3|(4(-3cos(1\u03c0x + 1) - 3)^2 + 4(-3cos(1\u03c0x + 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": "50", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = -5(1|(-2sin(3\u03c0((1x - 1)/(3x + 1))) + 1) - 2| - 1) - 1 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "55", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation 2cos(2\u03c0(5((1x)/(2x - 1)) + 5)) + 2 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "30", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = -1cos(1\u03c0(3|((1x - 3)/(1x))| - 2) + 3) + 1 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "61", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = 1(3sin(2\u03c0(-1|x + 2| + 3) + 1) + 3)^2 - 1(3sin(2\u03c0(-1|x + 2| + 3) + 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": "How many zeros does the function f(x) = (-3(-2cos(3\u03c0(-1(-2|x - 1| + 2)^2 + 5(-2|x - 1| + 2) + 1) + 1) + 1) + 3)/(-1(-2cos(3\u03c0(-1(-2|x - 1| + 2)^2 + 5(-2|x - 1| + 2) + 1) + 1) + 1) - 1) have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1628", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = -3cos(2\u03c0((1(-1|x + 2| + 2) - 1)/(-2(-1|x + 2| + 2) - 2)) - 1) + 3 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "57", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = 1|(1sin(3\u03c0(1x^2 + 3x + 1) + 3) - 3) + 1| - 1 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "287", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = -5(-5(1sin(3\u03c0(-1|x - 3| - 2) - 3) - 1)^2 + 2(1sin(3\u03c0(-1|x - 3| - 2) - 3) - 1) + 2) - 5 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "62", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = 1(1|(-1cos(2\u03c0(1x - 2) - 2) - 1) - 1| - 1)^2 + 2(1|(-1cos(2\u03c0(1x - 2) - 2) - 1) - 1| - 1) - 3 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "40", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = (-1(-1(2|(2sin(3\u03c0x) + 3) + 1| - 1) + 5) - 3)/(-2(-1(2|(2sin(3\u03c0x) + 3) + 1| - 1) + 5)) equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "60", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = (-1(-5(3sin(1\u03c0(-2|x - 1| + 3) + 1) - 3)^2 - 2(3sin(1\u03c0(-2|x - 1| + 3) + 1) - 3) + 1) - 1)/(-1(-5(3sin(1\u03c0(-2|x - 1| + 3) + 1) - 3)^2 - 2(3sin(1\u03c0(-2|x - 1| + 3) + 1) - 3) + 1)) equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "40", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = 2|((-3(-1cos(2\u03c0x + 3) - 1) - 1)/(1(-1cos(2\u03c0x + 3) - 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": "Determine the number of values x in [-10, 10] where f(x) = 3sin(3\u03c0((-1(4x - 1) - 3)/(1(4x - 1) + 2)) - 2) - 3 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "18", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation -4((-2(3|(-2cos(1\u03c0x - 1) + 2) - 3| - 2) + 3)/(3(3|(-2cos(1\u03c0x - 1) + 2) - 3| - 2) + 3))^2 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "20", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = -1cos(2\u03c0(-2|((1x - 1)/(1x - 2)) - 1|) + 3) + 1 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 zeros does the function f(x) = -1(-2cos(1\u03c0(2x + 2) - 2) - 1)^2 + 5(-2cos(1\u03c0(2x + 2) - 2) - 1) + 4 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": "How many solutions does the equation -3cos(2\u03c0(-4(3|((-1x + 2)/(1x))| - 2)^2 - 5(3|((-1x + 2)/(1x))| - 2) + 2) - 2) = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "428", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = -3sin(2\u03c0(-3|(-3x + 5)| - 2) + 2) - 3 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "178", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = (-2(4(3cos(3\u03c0(-1x^2 + 1x + 4) - 1) + 1) + 2))/(-1(4(3cos(3\u03c0(-1x^2 + 1x + 4) - 1) + 1) + 2) + 2) where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "267", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = -1cos(1\u03c0(2|(-1(-3x^2 + 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": "511", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = -2sin(1\u03c0(-1((-1x)/(2x + 1)) - 2) - 1) - 1 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "18", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = 1sin(2\u03c0((-3(1(-2x + 2)^2 + 2(-2x + 2) + 1) + 1)/(-2(1(-2x + 2)^2 + 2(-2x + 2) + 1))) + 1) have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "42", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = -5(-1sin(1\u03c0(3|x - 3| + 1) - 2) + 1) + 2 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "60", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = -3(-3sin(1\u03c0(2|(-4x - 4) + 1|)))^2 + 5(-3sin(1\u03c0(2|(-4x - 4) + 1|))) + 1 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "319", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = 2cos(1\u03c0((-2(1x^2 + 5x - 2) - 2)/(-1(1x^2 + 5x - 2) + 2)) + 3) + 1 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "68", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation -1(-3cos(2\u03c0(-3|x|) - 3)) + 2 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "120", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = -1sin(3\u03c0(-3|(-1x^2 - 4x + 3) - 2|) - 1) + 1 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "767", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = 3sin(1\u03c0(1(-1((1x - 2)/(-3x + 2))^2 + 3((1x - 2)/(-3x + 2)) + 3) + 3) + 2) - 1 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "47", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = (-1(-4(3cos(3\u03c0(3|x| + 2) + 3) + 3)^2 + 4) - 2)/(1(-4(3cos(3\u03c0(3|x| + 2) + 3) + 3)^2 + 4) - 2) have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "180", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = 2sin(2\u03c0(-1(3x - 3)^2 - 3(3x - 3)) + 3) where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1709", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = 3cos(1\u03c0(5((1x)/(-1x + 2))) - 2) - 1 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "112", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation 4(2sin(1\u03c0(3x - 4) + 2) + 1)^2 + 1(2sin(1\u03c0(3x - 4) + 2) + 1) - 5 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "60", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation -3(-2((3(-3sin(1\u03c0x - 2) - 3) + 1)/(-3(-3sin(1\u03c0x - 2) - 3) - 3)) + 2)^2 + 1(-2((3(-3sin(1\u03c0x - 2) - 3) + 1)/(-3(-3sin(1\u03c0x - 2) - 3) - 3)) + 2) + 5 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "40", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = 2sin(2\u03c0(1|(-2((-2x + 2)/(2x + 1)) + 5) + 2| - 3) - 1) equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "93", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = (-3(-5(1cos(2\u03c0(1|x - 1| - 3) + 2) + 1) + 4) - 2)/(-3(-5(1cos(2\u03c0(1|x - 1| - 3) + 2) + 1) + 4) - 3) equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "40", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = 1(-5(3|(-1cos(3\u03c0x + 1) - 2) + 1|)^2 + 4(3|(-1cos(3\u03c0x + 1) - 2) + 1|) - 2) + 4 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "60", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation 2(3sin(3\u03c0(-4x^2 + 2x + 1) + 3) + 1) + 4 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "940", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = 5((1(-1cos(1\u03c0x)) - 3)/(3(-1cos(1\u03c0x)) + 1))^2 + 4((1(-1cos(1\u03c0x)) - 3)/(3(-1cos(1\u03c0x)) + 1)) - 5 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "20", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation (-1(3(2cos(2\u03c0(-2|x + 2| - 2) + 2) - 1) + 2))/(2(3(2cos(2\u03c0(-2|x + 2| - 2) + 2) - 1) + 2) - 3) = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "80", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = -1|(-1(2sin(1\u03c0x + 3) - 1) + 3) + 1| + 3 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation -3sin(2\u03c0(2(-4((-2x + 3)/(-2x - 2))^2 + 4((-2x + 3)/(-2x - 2)) + 2) - 1) - 2) = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "327", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation -3|(-4(-3cos(1\u03c0(1x - 3)) - 1)^2 + 5) - 2| + 3 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "80", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = 1|(-1cos(2\u03c0((-1x)/(2x + 2)) - 2) + 3) + 1| - 3 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation (-3(1(3cos(3\u03c0x + 3) - 2) + 2) - 2)/(2(1(3cos(3\u03c0x + 3) - 2) + 2) + 2) = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "60", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = -3cos(2\u03c0(3(-5(1|x + 3| + 2) + 2)^2 + 4) - 2) have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1571", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation 3sin(1\u03c0(-2|(-4x + 3) + 1| - 3) - 2) + 2 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "160", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = -1(-3|((3(-3cos(2\u03c0x - 3) - 2))/(3(-3cos(2\u03c0x - 3) - 2) + 3)) + 2| - 3)^2 - 2(-3|((3(-3cos(2\u03c0x - 3) - 2))/(3(-3cos(2\u03c0x - 3) - 2) + 3)) + 2| - 3) + 5 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "30", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = -1(-2(-2sin(1\u03c0((2x + 3)/(2x - 1)) + 1) - 1)^2 + 2(-2sin(1\u03c0((2x + 3)/(2x - 1)) + 1) - 1)) - 3 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "50", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = -2(4(-1|(-2cos(1\u03c0x + 3) + 1) + 1| + 1) + 3)^2 + 3(4(-1|(-2cos(1\u03c0x + 3) + 1) + 1| + 1) + 3) + 1 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "40", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = (-1(3sin(1\u03c0(-2|x + 2| + 2) + 2)) + 1)/(-1(3sin(1\u03c0(-2|x + 2| + 2) + 2)) + 3) equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "40", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = -2cos(1\u03c0((1(2|(2x) - 1| - 1) + 3)/(-3(2|(2x) - 1| - 1) + 1)) + 1) + 1 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "34", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation -3sin(2\u03c0(3(3|x + 1|)^2 - 2(3|x + 1|) + 4)) + 3 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1099", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = -3cos(3\u03c0(1(-2|((-1x - 2)/(-1x + 2)) - 1| - 1)^2 + 5) + 2) + 3 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "290", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = -3cos(2\u03c0(-1|(-1(1x^2 - 3) + 4) + 1|) + 1) - 3 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "191", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = (1(3sin(3\u03c0(-4x^2 + 2x - 1) - 3) + 3) - 2)/(-2(3sin(3\u03c0(-4x^2 + 2x - 1) - 3) + 3) + 3) have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "429", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = -2sin(3\u03c0(-2|(-5(-1x + 5)^2 + 4(-1x + 5) + 3) - 2| - 1)) + 2 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1161", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation 1|(2(2sin(3\u03c0x - 2) + 2)^2 - 2(2sin(3\u03c0x - 2) + 2) + 5) - 3| - 3 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "60", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = (1(1(1cos(2\u03c0(5x + 5) - 1) + 3)^2 - 1(1cos(2\u03c0(5x + 5) - 1) + 3) - 5))/(-3(1(1cos(2\u03c0(5x + 5) - 1) + 3)^2 - 1(1cos(2\u03c0(5x + 5) - 1) + 3) - 5) + 2) where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "200", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation 3sin(2\u03c0(-1(-2|((-2x + 2)/(3x - 1)) - 2| + 3) + 4) - 2) = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "46", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = -1|(-2(-1sin(2\u03c0x + 3) + 2)^2 + 3(-1sin(2\u03c0x + 3) + 2) - 4) + 1| + 3 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "40", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = -2(-3(2sin(2\u03c0(-1|x - 2| + 3)) + 1) + 2)^2 - 3(-3(2sin(2\u03c0(-1|x - 2| + 3)) + 1) + 2) + 4 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": "Determine the number of values x in [-10, 10] where f(x) = -1(-5(-3cos(3\u03c0x - 2)) + 4)^2 + 3(-5(-3cos(3\u03c0x - 2)) + 4) - 2 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "100", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation 2sin(1\u03c0(-4(1((-2x + 3)/(3x - 1)) - 1)^2 + 1(1((-2x + 3)/(3x - 1)) - 1) + 2)) + 2 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "65", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation (1(5(3cos(3\u03c0x + 3) - 3)^2 - 2(3cos(3\u03c0x + 3) - 3)) - 2)/(1(5(3cos(3\u03c0x + 3) - 3)^2 - 2(3cos(3\u03c0x + 3) - 3)) + 1) = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "60", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation -1((3(-2sin(1\u03c0x + 3) + 1) - 2)/(-3(-2sin(1\u03c0x + 3) + 1) - 2))^2 + 3((3(-2sin(1\u03c0x + 3) + 1) - 2)/(-3(-2sin(1\u03c0x + 3) + 1) - 2)) + 5 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "20", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation (-1(-3|(-2sin(1\u03c0(-3x^2 - 2x) + 2) - 2) + 2|) - 1)/(-1(-3|(-2sin(1\u03c0(-3x^2 - 2x) + 2) - 2) + 2|) - 3) = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "528", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = 3sin(1\u03c0(1((2x + 3)/(-1x - 1))^2 + 4((2x + 3)/(-1x - 1)) - 4) - 1) - 3 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "39", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = -3cos(1\u03c0(-5(-2|((3x + 1)/(-1x - 3)) - 1| + 1) + 4) + 1) + 1 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "302", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = (1(-5(-2cos(3\u03c0x - 3) + 1)^2 + 3(-2cos(3\u03c0x - 3) + 1) + 5) - 1)/(-1(-5(-2cos(3\u03c0x - 3) + 1)^2 + 3(-2cos(3\u03c0x - 3) + 1) + 5)) where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "120", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = -1(2|(3(-2cos(3\u03c0x + 3) + 1)^2 + 4(-2cos(3\u03c0x + 3) + 1) + 1) - 2| + 3) + 3 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "41", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = -2cos(3\u03c0(-1((2x - 2)/(-1x - 1)) - 2) + 2) - 1 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "114", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = -3(-2cos(3\u03c0((-1x - 1)/(1x - 2)) + 1) - 1) - 2 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "105", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = (-2(3(2sin(1\u03c0(-5x + 4) + 1))^2 - 3(2sin(1\u03c0(-5x + 4) + 1)) + 1) + 3)/(-1(3(2sin(1\u03c0(-5x + 4) + 1))^2 - 3(2sin(1\u03c0(-5x + 4) + 1)) + 1) + 3) equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "200", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = 3cos(3\u03c0(-1(3(-2|x - 3| + 2) - 4)^2 - 2(3(-2|x - 3| + 2) - 4)) - 1) - 2 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1290", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = 5(2cos(2\u03c0(-1|x - 1| + 1) + 2) + 2)^2 - 3(2cos(2\u03c0(-1|x - 1| + 1) + 2) + 2) - 2 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "40", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = -2(-3sin(3\u03c0(2x^2 - 5x + 2) + 2) + 1) - 3 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "881", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation -2(-1|(-3sin(1\u03c0x - 2)) + 1| + 3)^2 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "20", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation 3(-3(1cos(1\u03c0((3x)/(3x + 2)) - 2) - 2)^2 - 4(1cos(1\u03c0((3x)/(3x + 2)) - 2) - 2)) + 5 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "30", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = -5(-2|(1sin(3\u03c0x + 2) + 1)|) - 3 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "60", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = -1cos(3\u03c0(2|(4((3x - 2)/(3x + 1)) + 4) - 1| + 1) + 2) - 1 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "99", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = -2|(2sin(1\u03c0(1((-3x)/(1x + 2)) + 4) - 1) + 2) + 1| + 2 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "48", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = 2sin(1\u03c0((2(4x^2 - 1x - 1) + 1)/(-2(4x^2 - 1x - 1) + 3)) - 1) - 2 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "20", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation -2|((-1(1cos(1\u03c0(-3x^2 - 3x - 2) + 3) + 3) + 2)/(-1(1cos(1\u03c0(-3x^2 - 3x - 2) + 3) + 3) - 2)) + 1| + 2 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "278", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation -1sin(1\u03c0(-1|(-1x^2 + 2x) - 1| + 2) + 2) + 1 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "102", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = 2cos(1\u03c0((-2(-1|x - 1| - 1) - 2)/(1(-1|x - 1| - 1) + 3)) - 1) + 1 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "135", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = (1(2|(-1(2sin(1\u03c0x + 1) + 3) + 3)| + 1) - 3)/(-1(2|(-1(2sin(1\u03c0x + 1) + 3) + 3)| + 1) - 1) have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "40", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation -4(2cos(2\u03c0(1(-2|x + 1| - 3) + 5) - 1) - 1)^2 - 4(2cos(2\u03c0(1(-2|x + 1| - 3) + 5) - 1) - 1) + 1 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "160", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation 4(-3sin(1\u03c0(2|(-3x + 3)| - 2) + 2) + 2)^2 + 5(-3sin(1\u03c0(2|(-3x + 3)| - 2) + 2) + 2) - 3 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "120", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation -3sin(1\u03c0(-3(2|x + 3| - 3) + 2) - 3) + 3 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "60", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = 3sin(2\u03c0(-2(3(3|x + 2| - 3)^2 + 3(3|x + 2| - 3) + 2) - 3) - 1) equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1579", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation (2(2|(-3sin(3\u03c0x + 2)) - 2| + 1) - 2)/(-1(2|(-3sin(3\u03c0x + 2)) - 2| + 1) + 2) = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "50", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation 3cos(2\u03c0(4((-1x + 3)/(-3x - 1))^2 - 5((-1x + 3)/(-3x - 1)) + 1) + 3) - 1 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "146", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = -1|(-5(3sin(2\u03c0x + 3) - 2) + 3) + 3| + 2 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "40", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = 5(-3sin(2\u03c0((3x)/(3x + 3)) - 2)) + 3 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "54", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = -1|(-2sin(3\u03c0((-3(-2x^2 - 5x + 2) - 1)/(3(-2x^2 - 5x + 2) + 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": "27", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = -3(1|(-1sin(3\u03c0(-2x^2 + 1x - 2) + 3) + 2) - 1|) + 4 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1143", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = 1cos(1\u03c0(3(2|((3x + 1)/(3x)) - 1| - 1)^2 + 4(2|((3x + 1)/(3x)) - 1| - 1) + 3) + 2) have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "73", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = (3(-3(-1sin(2\u03c0(2|x - 3| - 1) + 2) - 2)^2 - 1(-1sin(2\u03c0(2|x - 3| - 1) + 2) - 2) + 4))/(1(-3(-1sin(2\u03c0(2|x - 3| - 1) + 2) - 2)^2 - 1(-1sin(2\u03c0(2|x - 3| - 1) + 2) - 2) + 4) + 2) equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "80", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = -2cos(2\u03c0(-1|((-3x - 2)/(-3x - 3))|) - 1) equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "32", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = (-3(2cos(1\u03c0(-1(-3|x + 3| + 3) - 1) - 2)) - 2)/(2(2cos(1\u03c0(-1(-3|x + 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": "60", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation 2cos(1\u03c0(-3|((2x - 1)/(-1x - 1))| + 2) + 1) - 2 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "65", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation -3cos(1\u03c0((1(-2|(-3x^2 + 2x + 3) + 2| + 3) + 2)/(3(-2|(-3x^2 + 2x + 3) + 2| + 3) + 3)) + 3) + 2 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "23", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = 3sin(3\u03c0((-2(-3|x + 1| + 2))/(-2(-3|x + 1| + 2) - 1)) - 3) - 1 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "54", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = -3cos(3\u03c0(5(1(-2|x - 2| - 1)^2 - 4(-2|x - 2| - 1) + 4) - 5) - 3) - 1 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1504", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation 1((-2(2cos(3\u03c0x) + 1) + 2)/(2(2cos(3\u03c0x) + 1) - 1))^2 - 2 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "120", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation 1((-1(3cos(1\u03c0(-5x^2 + 4x - 3)) - 2))/(3(3cos(1\u03c0(-5x^2 + 4x - 3)) - 2) + 1)) - 4 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "19", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = (-2(-2(3cos(1\u03c0x - 3) + 2)^2 + 4(3cos(1\u03c0x - 3) + 2) + 4))/(-2(-2(3cos(1\u03c0x - 3) + 2)^2 + 4(3cos(1\u03c0x - 3) + 2) + 4) - 1) where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "40", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation (2(5(1cos(1\u03c0x - 3) - 1) + 5) + 1)/(-2(5(1cos(1\u03c0x - 3) - 1) + 5)) = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "20", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation -3sin(3\u03c0(-1|((1(-4x + 5))/(1(-4x + 5) - 2)) + 1| - 2)) - 1 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "45", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = 2((3(-4(-3cos(2\u03c0x + 1) + 2) - 1) + 2)/(-2(-4(-3cos(2\u03c0x + 1) + 2) - 1) + 3))^2 - 1((3(-4(-3cos(2\u03c0x + 1) + 2) - 1) + 2)/(-2(-4(-3cos(2\u03c0x + 1) + 2) - 1) + 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": "How many zeros does the function f(x) = 3cos(1\u03c0(5(-2x^2 + 3x + 3) - 1) - 3) + 2 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1291", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = 2sin(2\u03c0(-1(2|(-2x^2 + 2x - 1) - 2| + 1) + 3) - 2) + 2 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "676", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = -1(-3sin(2\u03c0((2(1|x + 1|) - 3)/(1(1|x + 1|))) + 3) + 3) + 4 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "89", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = -1|(5(1(-1cos(3\u03c0x + 1) - 3)^2 + 1(-1cos(3\u03c0x + 1) - 3) - 5) + 1)| + 2 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": "Determine the number of values x in [-10, 10] where f(x) = 1cos(2\u03c0(1|(4(-4x - 5)^2 + 2(-4x - 5) - 1) + 1| - 3) - 3) equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1589", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = -2|(-3(3cos(3\u03c0x - 1))^2 - 1(3cos(3\u03c0x - 1)) + 1) + 2| have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "63", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = 3sin(1\u03c0(-4((1(-1|x - 2| + 3) - 1)/(-2(-1|x - 2| + 3) - 2)) + 2) + 3) + 1 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "148", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = 3sin(3\u03c0(5(-1|(2x + 4) - 2| - 1)^2 + 1(-1|(2x + 4) - 2| - 1)) + 3) - 2 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1320", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation -3((1(3sin(3\u03c0x + 3) + 1) - 1)/(2(3sin(3\u03c0x + 3) + 1) - 1)) + 5 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "60", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = -1(-2(2cos(3\u03c0((-2x + 3)/(-1x + 2)) - 1) - 1) + 1)^2 + 3(-2(2cos(3\u03c0((-2x + 3)/(-1x + 2)) - 1) - 1) + 1) + 3 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "84", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = -1cos(3\u03c0(1((2(2|x + 1| - 3) + 1)/(-1(2|x + 1| - 3) + 2))^2 - 1((2(2|x + 1| - 3) + 1)/(-1(2|x + 1| - 3) + 2)) + 4) - 1) - 1 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "248", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = -3sin(3\u03c0(-3(1|((-1x + 3)/(-1x - 3)) + 3| + 3)^2 + 4(1|((-1x + 3)/(-1x - 3)) + 3| + 3) - 3) + 2) - 2 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "669", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = -3|(-3cos(3\u03c0((2x + 1)/(3x - 1)) - 3)) - 3| + 1 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "36", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation -2((-1(3cos(1\u03c0x + 1) + 2) - 3)/(-2(3cos(1\u03c0x + 1) + 2) + 3))^2 + 4((-1(3cos(1\u03c0x + 1) + 2) - 3)/(-2(3cos(1\u03c0x + 1) + 2) + 3)) + 3 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "40", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation 4(2sin(3\u03c0(-3|((-3x + 1)/(2x - 1)) + 1| - 3) + 1) + 1) - 2 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "55", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = (-3(4(3cos(2\u03c0(2x^2 + 3x + 3) - 1)) + 1) + 2)/(1(4(3cos(2\u03c0(2x^2 + 3x + 3) - 1)) + 1) + 2) equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "342", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = -1cos(3\u03c0(-1(-3|x + 1| - 3) + 1) - 1) + 1 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "91", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = 3((-3(-1|(3cos(3\u03c0x - 3) + 2) - 3| + 3))/(2(-1|(3cos(3\u03c0x - 3) + 2) - 3| + 3) - 3))^2 + 4((-3(-1|(3cos(3\u03c0x - 3) + 2) - 3| + 3))/(2(-1|(3cos(3\u03c0x - 3) + 2) - 3| + 3) - 3)) - 5 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "60", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = (-2(-1cos(2\u03c0(2|(-1x^2 + 3x - 2) - 2| + 1) - 3) - 2) - 3)/(3(-1cos(2\u03c0(2|(-1x^2 + 3x - 2) - 2| + 1) - 3) - 2) + 3) equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "800", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = (3(-2|(2sin(3\u03c0(-1x - 3) + 1)) + 2| + 3) + 3)/(-2(-2|(2sin(3\u03c0(-1x - 3) + 1)) + 2| + 3) + 1) where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "60", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = 2(3sin(3\u03c0(-1x + 3) - 2) - 2)^2 - 4(3sin(3\u03c0(-1x + 3) - 2) - 2) - 5 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "60", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = -3sin(1\u03c0(-2(-5((-2x - 3)/(-1x - 1))^2 + 5((-2x - 3)/(-1x - 1)) - 1) + 2) - 2) + 2 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "156", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = -5(3cos(1\u03c0(-4((-2x - 2)/(1x))^2 + 5((-2x - 2)/(1x)) + 3) - 3)) + 3 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "207", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = -1|(3cos(1\u03c0(-5x) - 1) - 1) - 2| have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "50", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = -2|(-1((-1(-2cos(1\u03c0x - 2) + 3) - 1)/(1(-2cos(1\u03c0x - 2) + 3) - 2)) + 3) + 1| equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = 2(3cos(2\u03c0(2x^2 - 1x) - 3) - 1) + 5 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "789", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = (-3(4(-2sin(1\u03c0(-1|x - 2| + 1) - 1) - 1) + 5) + 1)/(-2(4(-2sin(1\u03c0(-1|x - 2| + 1) - 1) - 1) + 5) - 1) where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "20", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = 3(3sin(2\u03c0((3x + 3)/(-2x - 3)) - 3))^2 + 1(3sin(2\u03c0((3x + 3)/(-2x - 3)) - 3)) - 3 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "48", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = -5(-2(3cos(1\u03c0(-1|x - 1| - 1)) + 2) + 2)^2 + 1(-2(3cos(1\u03c0(-1|x - 1| - 1)) + 2) + 2) + 4 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "40", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation -1sin(3\u03c0(-2|(-3x - 4) + 1| + 1) - 2) = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "360", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation 2(2cos(2\u03c0(4((-1x + 3)/(3x + 1))^2 + 5((-1x + 3)/(3x + 1)) - 1) - 3) + 2) - 3 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "152", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = 4(3|(-2sin(3\u03c0(1x^2 - 5) + 2) + 1) - 1| - 1) + 1 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "430", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = -3sin(2\u03c0(1|(-4(-1x^2 + 4x) - 4) + 1|) - 3) + 2 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1189", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation -3cos(3\u03c0(5(3|((-1x)/(2x + 1)) + 3| + 2)^2 + 5(3|((-1x)/(2x + 1)) + 3| + 2) - 1) + 2) - 2 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "449", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation 4(-2|(3sin(1\u03c0x - 1) - 2) + 2| + 2) - 2 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "40", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = -3cos(1\u03c0(-2((3x)/(-1x - 1))^2 + 5((3x)/(-1x - 1)) - 2) + 1) - 2 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "190", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = -1sin(1\u03c0((2(-1x + 2) - 1)/(1(-1x + 2) - 2)) - 3) - 1 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "38", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = 1cos(1\u03c0((3(-1(-5x - 5)^2 - 3(-5x - 5) - 1) + 3)/(2(-1(-5x - 5)^2 - 3(-5x - 5) - 1))) + 2) have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "27", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = 2|(1sin(1\u03c0((1x + 1)/(1x)) - 2) + 3) - 3| - 1 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "53", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation 2cos(3\u03c0(-1(1(1|x + 2| + 3)^2 - 3(1|x + 2| + 3) - 4) + 1) - 1) + 2 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "365", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = -2cos(3\u03c0((3(1x^2 + 5x - 4) - 1)/(-3(1x^2 + 5x - 4) - 2)) + 3) - 1 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "51", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = -3cos(2\u03c0((-1(5x + 3) + 3)/(-3(5x + 3) + 2))) - 3 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = (2(-2cos(1\u03c0(1x + 3) + 3) - 1) + 3)/(1(-2cos(1\u03c0(1x + 3) + 3) - 1) + 2) 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": "Determine the number of values x in [-10, 10] where f(x) = (1(-1sin(3\u03c0(-4x - 2) + 1) + 2) - 2)/(-1(-1sin(3\u03c0(-4x - 2) + 1) + 2)) equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "240", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = -3sin(2\u03c0(2(-1|x| - 1) + 5) + 3) + 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 solutions does the equation 3(1cos(1\u03c0(2|x - 1| + 1) - 2) - 2)^2 + 1(1cos(1\u03c0(2|x - 1| + 1) - 2) - 2) - 4 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "40", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = 1|(-3sin(3\u03c0(-3x^2 + 5x + 2)) + 3) + 3| - 3 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "753", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = -1cos(2\u03c0(1(-5((1x + 2)/(-1x + 2)) + 1)^2 - 1(-5((1x + 2)/(-1x + 2)) + 1) - 4) + 1) - 1 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "404", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = (3(-3|(-3sin(2\u03c0x - 2) + 2)| + 2) + 2)/(2(-3|(-3sin(2\u03c0x - 2) + 2)| + 2) + 1) equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "72", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = -1(-2(2cos(2\u03c0x - 1) - 2)^2 - 4(2cos(2\u03c0x - 1) - 2) + 2) - 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 number of x-intercepts of the function f(x) = -3cos(2\u03c0((2(-2(-5x + 4)^2 - 5(-5x + 4) + 4) + 2)/(2(-2(-5x + 4)^2 - 5(-5x + 4) + 4) - 1)) - 1) where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "24", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = 1cos(2\u03c0(-2(-4x^2 + 1x + 3) - 1) + 2) have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1663", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation -3sin(2\u03c0(2|(2x + 2)| + 1)) - 2 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "160", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = (1(1sin(2\u03c0(-3x^2 - 5x + 5) - 2) - 2) + 2)/(-2(1sin(2\u03c0(-3x^2 - 5x + 5) - 2) - 2) - 1) where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1166", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation (2(4(-3sin(3\u03c0(-3x^2 + 4x - 2) - 2) + 3) - 4) - 3)/(1(4(-3sin(3\u03c0(-3x^2 + 4x - 2) - 2) + 3) - 4) + 3) = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "807", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = 3((-1(-3sin(1\u03c0(4x^2 + 5x + 1) + 1) + 3) + 3)/(-1(-3sin(1\u03c0(4x^2 + 5x + 1) + 1) + 3) + 2)) + 4 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "266", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = 3(-3sin(1\u03c0((-3(1|x - 1|))/(-2(1|x - 1|) + 3)) - 1) + 2) - 5 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "104", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation 3sin(3\u03c0(2(3(2|x + 2|)^2 - 3(2|x + 2|) + 1) + 3) - 2) - 3 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1090", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = 4(2sin(1\u03c0(-2|(-4x^2 + 2) - 1| - 3)) - 1) - 4 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "675", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = -2sin(1\u03c0((-2(3|x - 2| - 1))/(2(3|x - 2| - 1) - 1)) - 3) + 1 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "29", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation 3(3(-1cos(2\u03c0((-2x + 2)/(-1x + 2)) - 1) - 1)^2 + 1(-1cos(2\u03c0((-2x + 2)/(-1x + 2)) - 1) - 1) + 1) - 5 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "69", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = 2cos(3\u03c0(-1(1(-2|x - 2| + 2) + 1)^2 - 4(1(-2|x - 2| + 2) + 1) - 5) + 1) + 2 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "667", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = -1|(-4((1(-3cos(2\u03c0x - 2) + 3) - 3)/(3(-3cos(2\u03c0x - 2) + 3) + 1)) - 1) - 1| + 1 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "80", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = 2|((1(4(2sin(2\u03c0x - 3)) + 4) - 1)/(2(4(2sin(2\u03c0x - 3)) + 4) - 1)) + 1| - 3 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "36", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = 2cos(2\u03c0((-1(4x - 1) + 1)/(-3(4x - 1) - 1)) - 2) where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "19", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation (-3(-2sin(1\u03c0(-5x + 2) - 1) - 2))/(1(-2sin(1\u03c0(-5x + 2) - 1) - 2) + 2) = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "50", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = 4((3(-1(-2cos(3\u03c0x + 3) - 2) - 3) - 1)/(-2(-1(-2cos(3\u03c0x + 3) - 2) - 3) + 3))^2 + 2((3(-1(-2cos(3\u03c0x + 3) - 2) - 3) - 1)/(-2(-1(-2cos(3\u03c0x + 3) - 2) - 3) + 3)) - 5 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "60", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = (2(-2sin(3\u03c0(-4x - 5) + 3) + 1) - 2)/(-3(-2sin(3\u03c0(-4x - 5) + 3) + 1) + 2) where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "240", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = -2cos(1\u03c0(1((-3(3|x + 1| - 3) + 2)/(-1(3|x + 1| - 3) + 2)) + 3) + 1) + 1 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "79", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation 3(3cos(2\u03c0(2(-1|x + 3| + 1)^2 - 4(-1|x + 3| + 1) - 5) + 2)) - 5 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "825", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation -1cos(1\u03c0(2|(-4x + 2) + 1| + 2) - 3) + 1 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "80", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = -2cos(1\u03c0(4(4(-3|x - 2| - 1) + 1)^2 + 4(4(-3|x - 2| - 1) + 1) - 5) + 2) + 1 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1395", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = 2|(1cos(3\u03c0(-4((-3x + 2)/(1x))^2 - 1((-3x + 2)/(1x)) + 2) - 1)) + 1| where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "215", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = 3(3cos(1\u03c0(4((2x - 1)/(-1x + 2))) - 2) + 2)^2 - 3(3cos(1\u03c0(4((2x - 1)/(-1x + 2))) - 2) + 2) - 4 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "165", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = (-3(-3(3cos(1\u03c0x + 1) + 2)^2 - 5(3cos(1\u03c0x + 1) + 2) + 1) + 2)/(-2(-3(3cos(1\u03c0x + 1) + 2)^2 - 5(3cos(1\u03c0x + 1) + 2) + 1) - 2) where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "20", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = 5(1|(1cos(2\u03c0x)) - 2| - 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 number of x-intercepts of the function f(x) = (1(-4(-1cos(3\u03c0(2|x + 1| - 1) + 2) + 1) + 2) + 2)/(-3(-4(-1cos(3\u03c0(2|x + 1| - 1) + 2) + 1) + 2) - 2) where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "120", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = -2sin(2\u03c0(-1|(-3x^2 - 2x + 4)|) - 3) + 1 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1077", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = -4((1(3sin(3\u03c0x + 2) + 2) - 3)/(-2(3sin(3\u03c0x + 2) + 2) - 3))^2 - 3((1(3sin(3\u03c0x + 2) + 2) - 3)/(-2(3sin(3\u03c0x + 2) + 2) - 3)) + 4 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "60", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation -3(-1sin(3\u03c0(5x - 1) - 3) - 2)^2 - 5(-1sin(3\u03c0(5x - 1) - 3) - 2) - 2 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "150", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = (-3(-2sin(1\u03c0(3|(-3x - 1) + 2|)) - 2))/(-3(-2sin(1\u03c0(3|(-3x - 1) + 2|)) - 2) - 2) where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "89", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation -1cos(3\u03c0(5(3x + 5)^2 - 3(3x + 5) - 4) - 1) = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1580", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation 5((2(1(3cos(2\u03c0x - 2) + 2)^2 + 3(3cos(2\u03c0x - 2) + 2) + 1) - 1)/(-2(1(3cos(2\u03c0x - 2) + 2)^2 + 3(3cos(2\u03c0x - 2) + 2) + 1) + 3)) - 3 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "40", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation -2sin(2\u03c0(-2|(5((1x - 2)/(3x - 2)) + 2) + 2| + 2)) - 1 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "99", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = (-3(2|(-2sin(3\u03c0(-2x^2 + 2x - 4) - 2) + 3) - 3| - 1) + 2)/(1(2|(-2sin(3\u03c0(-2x^2 + 2x - 4) - 2) + 3) - 3| - 1) - 3) have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1326", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = 1|(3cos(3\u03c0(4((2x - 2)/(3x + 1)) + 4) - 2) + 3)| - 2 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "116", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = -1(-1(2cos(1\u03c0(2|x| + 1) + 1) + 1) + 2)^2 + 5 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": "How many zeros does the function f(x) = -2cos(2\u03c0(-3(3|(-5x + 1) + 2| + 3)^2 + 5(3|(-5x + 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": "1211", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = -3sin(2\u03c0(-1|(5x + 4) + 1| + 3) + 2) - 3 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "100", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = -3sin(2\u03c0(-1|(5x - 3) - 1| + 1)) + 1 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "200", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = -5(-3cos(2\u03c0(5(-1|x - 2| - 1)^2 + 1(-1|x - 2| - 1) + 1) + 3)) + 2 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1647", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = -2sin(3\u03c0(-1((-1(-4x) + 3)/(2(-4x) - 3))^2 - 4((-1(-4x) + 3)/(2(-4x) - 3)) + 1) - 2) - 2 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "24", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = 1(-2(1sin(3\u03c0((3x + 1)/(-2x - 2)) + 3) + 3) + 3)^2 + 4(-2(1sin(3\u03c0((3x + 1)/(-2x - 2)) + 3) + 3) + 3) - 3 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "46", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation -4(3(-1sin(1\u03c0((1x - 1)/(2x + 1)) + 1) + 2)^2 - 4(-1sin(1\u03c0((1x - 1)/(2x + 1)) + 1) + 2) - 3) - 4 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "32", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = 2sin(3\u03c0(5((2x)/(-2x - 3))^2 - 1((2x)/(-2x - 3)) - 3) - 3) - 2 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "152", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = -3sin(3\u03c0(1(-3|(1x + 4) + 1| - 2)^2 - 1(-3|(1x + 4) + 1| - 2) + 4)) - 3 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1215", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation (3(-1(-3cos(3\u03c0(2|x - 1|) + 2) + 2) + 2) + 3)/(-1(-1(-3cos(3\u03c0(2|x - 1|) + 2) + 2) + 2) + 2) = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "120", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = -1sin(2\u03c0((2(-5x^2 + 3x + 1))/(-1(-5x^2 + 3x + 1) - 1)) - 2) have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "55", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation -4(3(2sin(3\u03c0x + 1) + 1)^2 + 4(2sin(3\u03c0x + 1) + 1) - 1) - 4 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "60", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = -3(-5(2cos(3\u03c0x - 1) - 2) - 2)^2 - 5(-5(2cos(3\u03c0x - 1) - 2) - 2) 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 number of x-intercepts of the function f(x) = 3cos(2\u03c0(3|((1x + 2)/(-3x + 2)) + 3| + 1) - 2) + 2 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "75", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = 3(2sin(1\u03c0(-3x) + 1) + 2)^2 + 1(2sin(1\u03c0(-3x) + 1) + 2) - 1 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "60", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = (2(-2sin(3\u03c0(-4(4x - 4)^2 + 3(4x - 4) + 2)) + 2) - 1)/(1(-2sin(3\u03c0(-4(4x - 4)^2 + 3(4x - 4) + 2)) + 2)) have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1082", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = -2(-2cos(2\u03c0(-4((-1x + 3)/(3x + 3)) + 1) + 3) - 2)^2 - 4(-2cos(2\u03c0(-4((-1x + 3)/(3x + 3)) + 1) + 3) - 2) + 4 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "107", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation 3|(-2cos(1\u03c0(1x^2 - 1x + 4) + 3) - 3) + 2| - 2 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "402", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = (-1(-3cos(3\u03c0(3(-1|x + 1| - 3)^2 + 2) + 1)) - 2)/(2(-3cos(3\u03c0(3(-1|x + 1| - 3)^2 + 2) + 1)) - 3) have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1276", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation -3sin(2\u03c0(1(1|x - 1| + 2) - 1) + 3) - 3 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "20", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation 3(1|(-2sin(2\u03c0(4x + 3) + 2) + 1) + 3| - 3)^2 + 5(1|(-2sin(2\u03c0(4x + 3) + 2) + 1) + 3| - 3) - 1 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "160", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = 3|((1(-3sin(1\u03c0(5x - 1) + 2) - 1) + 3)/(-2(-3sin(1\u03c0(5x - 1) + 2) - 1) - 1)) + 2| have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "58", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = -1(-1cos(1\u03c0(-2|x - 2| - 3) + 3) - 1)^2 + 5(-1cos(1\u03c0(-2|x - 2| - 3) + 3) - 1) + 5 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "40", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = (-1(5(-3cos(1\u03c0(-1x^2 - 1x + 2) + 1) - 2) + 4) + 2)/(-3(5(-3cos(1\u03c0(-1x^2 - 1x + 2) + 1) - 2) + 4) - 2) have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "194", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = -2sin(2\u03c0(3((-2(5x - 5) - 3)/(2(5x - 5)))^2 + 2((-2(5x - 5) - 3)/(2(5x - 5))) + 5) - 3) + 2 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "34", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = -1sin(1\u03c0(-2|(5((2x + 1)/(1x - 3))^2) - 3| + 2) + 3) - 1 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "354", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation (2(2cos(1\u03c0(-3x - 2) + 1) + 2))/(-1(2cos(1\u03c0(-3x - 2) + 1) + 2) + 3) = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "30", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = 3cos(2\u03c0(1(1|x - 2| + 2) + 5) + 1) - 1 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "40", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = -1cos(3\u03c0(3(5x^2 + 2x + 4) - 3) + 3) + 1 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1164", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation 1sin(1\u03c0(5((-2(2|x + 1| - 2) - 3)/(-3(2|x + 1| - 2) + 1)) - 4) - 3) - 1 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "75", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = -1sin(1\u03c0(2(5(3|x - 1| - 3)^2 + 3(3|x - 1| - 3) + 1) + 2) - 1) where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1584", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = -3|(-3(2cos(1\u03c0x + 1))^2 + 3(2cos(1\u03c0x + 1)) + 2) + 2| + 1 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "80", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = 1cos(2\u03c0((3(-3(-2|x - 1| + 1) - 3) - 3)/(2(-3(-2|x - 1| + 1) - 3) + 3)) - 1) + 1 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "44", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = -3cos(3\u03c0(-5(-3(-1|x + 3| + 2)^2 - 1(-1|x + 3| + 2) + 3) - 1) + 2) - 1 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1544", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = 1cos(3\u03c0((2(3x) - 3)/(-1(3x) - 2)) + 2) - 1 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "54", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = 5(-1sin(1\u03c0(3|(5x^2 + 1x + 1) + 1| - 3) - 1)) - 4 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1033", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = 1cos(1\u03c0(-4(3|x - 3| + 2)^2 + 2(3|x - 3| + 2) - 5) + 3) - 1 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1137", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = -4((3(3cos(2\u03c0(3x^2 - 5x - 4) + 2) + 2) + 1)/(3(3cos(2\u03c0(3x^2 - 5x - 4) + 2) + 2) + 3)) + 3 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1168", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = 3cos(3\u03c0(1|((3x - 3)/(2x - 3)) - 1| - 3) + 2) - 1 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "57", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = 1|(3sin(3\u03c0(-1x) - 1) + 1) - 1| - 3 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "60", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = -3(-2sin(1\u03c0(-3|(-3x^2 - 5x + 4)|) - 2) - 1) - 1 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1423", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = 3(-3cos(3\u03c0(2x^2 + 4x - 2) + 1) - 3) + 1 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "750", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = 1(5(-2cos(2\u03c0((1x)/(3x + 2)) - 3) - 1)^2 - 3(-2cos(2\u03c0((1x)/(3x + 2)) - 3) - 1) + 3) - 3 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "26", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = (3(-1cos(3\u03c0(5(3|x + 2|) - 5) - 2)) + 2)/(2(-1cos(3\u03c0(5(3|x + 2|) - 5) - 2)) - 3) where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "900", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = (-3(-3cos(1\u03c0(-2x^2 + 5x + 4) + 2) + 2) - 2)/(2(-3cos(1\u03c0(-2x^2 + 5x + 4) + 2) + 2) - 1) have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "393", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = 1sin(2\u03c0(3((2x + 2)/(3x + 2))^2 - 4((2x + 2)/(3x + 2)) + 2) + 1) + 1 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "29", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation -1|(3(2cos(3\u03c0x + 3) + 3) - 4) + 1| + 1 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "60", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = -2|(4(2sin(2\u03c0x + 1) + 1)^2 - 3(2sin(2\u03c0x + 1) + 1)) - 3| + 3 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "160", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = (-2(3(1|(2sin(3\u03c0x - 1) - 1) + 2|)^2 + 2(1|(2sin(3\u03c0x - 1) - 1) + 2|) - 1) - 1)/(1(3(1|(2sin(3\u03c0x - 1) - 1) + 2|)^2 + 2(1|(2sin(3\u03c0x - 1) - 1) + 2|) - 1)) where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "120", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation -3cos(1\u03c0((3(-1x^2 - 2x - 1) + 2)/(-3(-1x^2 - 2x - 1) - 1)) + 1) - 2 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "37", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation 1((-1(-3cos(1\u03c0x + 1) + 2) + 3)/(1(-3cos(1\u03c0x + 1) + 2) - 2)) - 1 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "20", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = (1(2(3sin(3\u03c0(5x^2 + 4x + 5) + 1) + 1) + 2) - 2)/(-1(2(3sin(3\u03c0(5x^2 + 4x + 5) + 1) + 1) + 2) - 1) have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "987", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = 3sin(1\u03c0(4(1|x - 1| - 3)^2 - 2(1|x - 1| - 3) + 4) + 1) + 2 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "452", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = 2(-2sin(2\u03c0(-1|((2x + 3)/(-1x - 1)) + 2| + 2) - 2) + 1) - 2 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "55", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation -3cos(3\u03c0(3(3(2|x - 3|) - 3)^2 - 5(3(2|x - 3|) - 3) + 3) + 3) + 3 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1213", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = -3cos(2\u03c0(4(-4((1x + 3)/(2x + 2)) - 5)^2 + 5(-4((1x + 3)/(2x + 2)) - 5) + 4) + 1) + 3 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "364", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = -2sin(2\u03c0(-2|((-1x + 2)/(3x + 2)) + 3| + 1) - 1) equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "68", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = -3cos(1\u03c0(5(1|x + 1| - 1)^2 + 1(1|x + 1| - 1) + 2) + 3) - 1 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "820", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = 1cos(2\u03c0(2|((2x + 1)/(-1x + 3)) + 2| - 1) - 2) - 1 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "109", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = 3cos(1\u03c0(-2|(-1(3x^2 + 2x + 2) - 4) - 1| + 2) - 2) where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1167", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation 1|(1sin(2\u03c0(4((3x - 2)/(-3x - 3)) - 3) - 2) - 3) + 1| - 1 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "74", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation 1(-2sin(3\u03c0(-4x - 5) - 2))^2 + 2(-2sin(3\u03c0(-4x - 5) - 2)) - 5 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "240", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = -1cos(1\u03c0(3(-2|x - 2| - 3)^2 + 4(-2|x - 2| - 3) - 4) + 3) + 1 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1129", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = 2(3sin(2\u03c0(2((-3x + 2)/(-2x + 3))^2 - 3) - 3)) + 4 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "123", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = 1(4(-3sin(2\u03c0x) + 1)^2 - 1(-3sin(2\u03c0x) + 1) - 2) - 5 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 number of x-intercepts of the function f(x) = -2cos(3\u03c0(1|(-5((2x - 1)/(1x + 3)) - 2) + 3| - 3) + 3) + 2 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "209", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = 3cos(2\u03c0(4(3(3|x - 2| - 2) + 2)^2 - 1(3(3|x - 2| - 2) + 2) + 2) - 2) + 2 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1210", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = 3|(5(-2cos(2\u03c0((2x + 1)/(-1x + 2)) + 2) - 2)^2 + 5(-2cos(2\u03c0((2x + 1)/(-1x + 2)) + 2) - 2) - 2) - 1| - 3 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "52", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = (2(3sin(1\u03c0(5(-2|x - 3| + 3) + 5) + 1) + 1) - 1)/(-1(3sin(1\u03c0(5(-2|x - 3| + 3) + 5) + 1) + 1) - 3) equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "200", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = 1(1cos(2\u03c0((-2x + 2)/(1x + 3)) + 2) + 2) - 1 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "83", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = -1cos(3\u03c0(-4(-2x^2 + 5x) + 1) - 3) + 1 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1064", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = (-1(-3sin(2\u03c0(2|(4x^2 + 4x + 3) - 2| + 1) + 2) - 2) - 2)/(1(-3sin(2\u03c0(2|(4x^2 + 4x + 3) - 2| + 1) + 2) - 2)) where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "986", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = -1|((2(2sin(3\u03c0(-1x + 1) - 2) - 2) + 3)/(3(2sin(3\u03c0(-1x + 1) - 2) - 2))) + 3| + 3 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 number of x-intercepts of the function f(x) = -3sin(3\u03c0(2|(1((1x + 3)/(1x)) - 4) - 3| + 1) + 2) - 2 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "134", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = 1|(2cos(2\u03c0(2x + 4) - 3) + 2) + 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 number of x-intercepts of the function f(x) = 1|(2((2(-1cos(1\u03c0x + 3) + 1))/(3(-1cos(1\u03c0x + 3) + 1) - 2))^2 + 2((2(-1cos(1\u03c0x + 3) + 1))/(3(-1cos(1\u03c0x + 3) + 1) - 2)) - 4) + 2| - 3 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "40", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = -1(-1sin(1\u03c0(-1(-1|x + 2| - 3)^2 - 4(-1|x + 2| - 3) + 4)) + 1) + 2 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "123", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = 2|(-2cos(1\u03c0(3x + 1) + 2) + 2) - 1| have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "38", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = 3|(1sin(1\u03c0(3x^2 - 1x - 5) + 2) + 2) - 1| - 2 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "600", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = -3sin(2\u03c0(1(4(1|x - 1| + 3)^2 + 1(1|x - 1| + 3)) + 5) + 3) - 3 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1047", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = -1|(-3cos(3\u03c0(5((-2x - 3)/(3x - 1)) - 3) - 1) + 2) - 3| equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "51", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation -2|((-2(5(-1cos(2\u03c0x + 3))^2 + 5(-1cos(2\u03c0x + 3)) - 5) + 1)/(-1(5(-1cos(2\u03c0x + 3))^2 + 5(-1cos(2\u03c0x + 3)) - 5) - 3)) - 2| + 3 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "40", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = -2sin(3\u03c0(-1((-2x + 1)/(-2x))^2 - 5((-2x + 1)/(-2x)) - 2) - 3) + 1 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "103", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = 4(-3sin(3\u03c0((-1(2|x - 3| - 3) + 3)/(-1(2|x - 3| - 3))) + 1) + 2)^2 + 4(-3sin(3\u03c0((-1(2|x - 3| - 3) + 3)/(-1(2|x - 3| - 3))) + 1) + 2) have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "166", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = 1cos(1\u03c0((3(-1x^2 + 4x) + 3)/(-3(-1x^2 + 4x) + 2)) - 2) + 1 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "26", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation (1(-4(-2sin(2\u03c0(-1x^2 + 4x) + 3) + 3) + 4))/(2(-4(-2sin(2\u03c0(-1x^2 + 4x) + 3) + 3) + 4) + 3) = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "205", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = -3|(4(1sin(2\u03c0x + 3)) + 2) - 2| + 2 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "80", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation (-3(1cos(2\u03c0(-3|x| + 2) + 3)))/(-1(1cos(2\u03c0(-3|x| + 2) + 3)) + 2) = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "120", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation 3(2cos(3\u03c0(-2|(1x + 5) + 1| - 1) - 2) + 3)^2 - 4 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "120", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation 3sin(1\u03c0(-5((-1(4x - 4))/(-2(4x - 4) + 3))^2 - 3((-1(4x - 4))/(-2(4x - 4) + 3)) - 4) + 3) - 1 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "39", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = -1sin(1\u03c0(2|((-3(1x + 3) + 3)/(2(1x + 3) - 3)) - 1| + 3) - 3) - 1 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "26", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = (2(2|(2cos(1\u03c0x - 1)) - 2| - 3) + 3)/(-1(2|(2cos(1\u03c0x - 1)) - 2| - 3) + 2) 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": "How many zeros does the function f(x) = -3sin(3\u03c0(3((-2(-1x^2 + 5x - 4) + 3)/(3(-1x^2 + 5x - 4) + 2)) - 5) + 3) + 1 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "130", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation 3cos(3\u03c0(1(3((-1x + 2)/(1x + 1)) - 3)^2 - 5(3((-1x + 2)/(1x + 1)) - 3) - 3) - 3) - 3 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "371", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = -2sin(2\u03c0(-4(-1|x - 3|) - 1) - 3) + 2 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "80", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = (-2(-1sin(2\u03c0(2(3|x - 3| + 2)^2 - 2(3|x - 3| + 2) + 4) - 2) - 1) - 3)/(3(-1sin(2\u03c0(2(3|x - 3| + 2)^2 - 2(3|x - 3| + 2) + 4) - 2) - 1) + 2) have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1098", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = 4(-1sin(2\u03c0((-3(1|x + 2|) - 3)/(1(1|x + 2|))) - 2) - 2)^2 + 4(-1sin(2\u03c0((-3(1|x + 2|) - 3)/(1(1|x + 2|))) - 2) - 2) equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "51", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = -2cos(1\u03c0(-3(1|(-2x - 3) + 2| - 3)^2 - 4(1|(-2x - 3) + 2| - 3) + 1) + 2) - 1 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1302", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = (2(2sin(2\u03c0(5x - 1) + 3) + 2) - 3)/(-1(2sin(2\u03c0(5x - 1) + 3) + 2) + 2) where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "200", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = (3(1|(1sin(1\u03c0x - 3)) + 1| - 1) + 2)/(3(1|(1sin(1\u03c0x - 3)) + 1| - 1) - 1) equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "20", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = (-2(-2cos(3\u03c0(4x - 4) - 3) + 1) + 1)/(1(-2cos(3\u03c0(4x - 4) - 3) + 1) - 2) where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "240", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = -1(-3sin(2\u03c0((1x - 1)/(3x - 1)) + 1)) + 2 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "22", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = 1(-3sin(3\u03c0((2x - 3)/(-1x - 2)) - 2))^2 + 1(-3sin(3\u03c0((2x - 3)/(-1x - 2)) - 2)) - 3 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "228", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = -1|(-1(-1(-2cos(1\u03c0x - 1)) - 3)^2 + 5(-1(-2cos(1\u03c0x - 1)) - 3) + 5) + 1| + 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": "How many zeros does the function f(x) = 1(1sin(2\u03c0(2|((2x + 1)/(-1x + 2)) - 2|) - 2) - 2)^2 + 2(1sin(2\u03c0(2|((2x + 1)/(-1x + 2)) - 2|) - 2) - 2) - 1 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "154", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation -5(-1((-2(-2cos(2\u03c0x) - 2) - 3)/(-1(-2cos(2\u03c0x) - 2) - 3))^2 - 1((-2(-2cos(2\u03c0x) - 2) - 3)/(-1(-2cos(2\u03c0x) - 2) - 3)) + 1) - 1 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "80", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = -3|(-4(-3sin(1\u03c0x + 2))^2 + 3(-3sin(1\u03c0x + 2))) + 3| + 2 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "80", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = (3(-4(-1sin(3\u03c0(-5x^2 + 4x + 3) + 1)) + 4) - 1)/(1(-4(-1sin(3\u03c0(-5x^2 + 4x + 3) + 1)) + 4) - 2) have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "824", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = 3cos(2\u03c0(4(-3|(4x - 3) - 3| + 1)^2 - 1(-3|(4x - 3) - 3| + 1) - 4) + 2) - 2 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1110", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = 1(2cos(3\u03c0((-1x + 3)/(3x - 1)) + 1) - 1)^2 + 5(2cos(3\u03c0((-1x + 3)/(3x - 1)) + 1) - 1) + 5 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "59", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation 1sin(2\u03c0(1(5((-3x)/(3x - 2)) + 2)^2 - 2(5((-3x)/(3x - 2)) + 2) + 4) - 2) + 1 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "143", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = -1|(-2(3cos(2\u03c0x - 1) - 3) + 1) - 1| where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "20", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = (1(1(3sin(2\u03c0x + 3) + 1)^2 - 5) - 1)/(1(1(3sin(2\u03c0x + 3) + 1)^2 - 5) + 2) equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "40", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = -1|(5(-2sin(2\u03c0x + 3) - 1)^2 - 1(-2sin(2\u03c0x + 3) - 1) - 4) - 1| equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "19", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation 2(1sin(2\u03c0(2x - 2) - 3))^2 - 2(1sin(2\u03c0(2x - 2) - 3)) - 1 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "80", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = (3(-2sin(3\u03c0(-5(2|x - 1| + 2)^2 - 2(2|x - 1| + 2) - 4) + 3) - 2))/(-1(-2sin(3\u03c0(-5(2|x - 1| + 2)^2 - 2(2|x - 1| + 2) - 4) + 3) - 2) - 3) equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1645", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = 5(-3cos(3\u03c0(1x - 5)))^2 + 3(-3cos(3\u03c0(1x - 5))) - 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": "Determine the number of values x in [-10, 10] where f(x) = 1cos(1\u03c0(2(-3|((2x)/(-1x - 2)) + 3| - 3)^2 + 3(-3|((2x)/(-1x - 2)) + 3| - 3) - 1) + 2) equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "564", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = -3cos(1\u03c0((3(1x - 3) + 3)/(3(1x - 3) - 2)) - 2) - 3 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "25", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = 1|(-2cos(3\u03c0((3x - 1)/(3x + 3)) - 1) + 2) - 3| - 1 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "91", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = -1cos(1\u03c0((1(3x - 1) - 3)/(3(3x - 1) - 1)) - 3) + 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 zeros does the function f(x) = -1|(-4(3cos(3\u03c0(4x - 3)) + 2)^2 - 3(3cos(3\u03c0(4x - 3)) + 2) + 4) + 1| have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "132", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = (1(3cos(3\u03c0(-2|x - 3| + 3) + 1) - 2) - 1)/(3(3cos(3\u03c0(-2|x - 3| + 3) + 1) - 2) - 2) where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "60", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation 1sin(2\u03c0(1((-2x)/(2x - 1)) + 5) + 1) = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "38", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = (2(2sin(2\u03c0(-1x + 1)) - 1) - 1)/(1(2sin(2\u03c0(-1x + 1)) - 1) + 2) equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "40", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = -1|(-2e^(2(2x + 4)) + 1) - 3| + 2 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "52", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation 2sin(2\u03c0((2(1(-1|x - 3| - 2)^2 + 1(-1|x - 3| - 2) - 2) + 3)/(1(1(-1|x - 3| - 2)^2 + 1(-1|x - 3| - 2) - 2))) + 1) = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "52", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = 5(-2sin(1\u03c0(2x - 5) + 3) - 2)^2 + 5(-2sin(1\u03c0(2x - 5) + 3) - 2) + 1 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "80", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = 2|((-2(2sin(1\u03c0(1x^2 + 2x + 2) + 1)) + 2)/(3(2sin(1\u03c0(1x^2 + 2x + 2) + 1)) + 3)) - 3| - 3 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "279", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = 3cos(2\u03c0((-2(-4x - 5))/(2(-4x - 5) - 3)) + 1) + 3 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "16", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = (1(1sin(2\u03c0(-3x^2 - 3x - 2) + 1) - 2) + 1)/(-3(1sin(2\u03c0(-3x^2 - 3x - 2) + 1) - 2) + 4) have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "561", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation -5(-1cos(2\u03c0(-2|x| - 2)))^2 + 3(-1cos(2\u03c0(-2|x| - 2))) + 1 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "160", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation (1(-5(2sin(2\u03c0x - 1)) + 5))/(-1(-5(2sin(2\u03c0x - 1)) + 5) - 2) = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "40", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation 4(1cos(1\u03c0(-1|(-4x - 2) - 2| + 2) - 1))^2 - 2(1cos(1\u03c0(-1|(-4x - 2) - 2| + 2) - 1)) = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "159", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation 3sin(3\u03c0((-3(-2x^2 + 1x - 5) - 1)/(1(-2x^2 + 1x - 5) + 2)) - 3) + 3 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "6", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = 2cos(3\u03c0(1(-1x^2 - 5) + 2) + 2) equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "600", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation 3cos(3\u03c0(5(-1|((-1x + 3)/(2x)) + 1| + 3)^2 + 1(-1|((-1x + 3)/(2x)) + 1| + 3) - 4) + 1) + 3 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "169", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = 2(-3|(-2cos(3\u03c0(-3x - 2) - 3) - 2)| + 1)^2 + 5(-3|(-2cos(3\u03c0(-3x - 2) - 3) - 2)| + 1) where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "360", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = -2cos(2\u03c0(2(-3|((-3x + 3)/(3x + 1)) + 2| + 3) - 4) - 2) + 1 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "140", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation 3(-2cos(1\u03c0(4((1x - 1)/(-1x - 3))^2 - 2((1x - 1)/(-1x - 3)) + 3)) + 1) - 4 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "276", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = -2|((-3(-3cos(3\u03c0x - 2) - 3) + 1)/(1(-3cos(3\u03c0x - 2) - 3))) + 2| + 3 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "60", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = 3|(1cos(1\u03c0((-3(-5x^2 - 1x + 1) + 2)/(3(-5x^2 - 1x + 1) + 1)) + 1) - 2)| - 3 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = 3|(2cos(3\u03c0(-5((2x)/(2x + 3))^2 + 2((2x)/(2x + 3)) + 3) + 2))| equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "43", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation 3sin(3\u03c0(-1|((2x - 1)/(1x + 1)) - 2| - 3) - 1) - 3 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "68", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = -1|(1sin(3\u03c0((1x + 2)/(-2x - 3))) + 2) - 1| + 1 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "33", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = (-3(1sin(2\u03c0(-4x^2 + 5x - 5) - 1)) - 3)/(-1(1sin(2\u03c0(-4x^2 + 5x - 5) - 1))) equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "778", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = -4(1cos(3\u03c0(1((2x + 3)/(3x + 2))^2) - 2) - 2) - 5 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "56", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = 2(-1cos(3\u03c0((-2x + 2)/(2x - 1))) + 1) - 3 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "47", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = -3cos(1\u03c0(-5(2((1x + 3)/(-2x - 3))^2 - 2((1x + 3)/(-2x - 3)) - 4) - 1) - 1) - 3 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "86", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation -3((-3(2|(-2cos(2\u03c0x - 3) - 3) + 1| - 2))/(-2(2|(-2cos(2\u03c0x - 3) - 3) + 1| - 2) + 3))^2 - 3((-3(2|(-2cos(2\u03c0x - 3) - 3) + 1| - 2))/(-2(2|(-2cos(2\u03c0x - 3) - 3) + 1| - 2) + 3)) + 5 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "40", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = 3sin(2\u03c0(2|(-5x - 5) + 3|) - 1) - 3 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "200", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation 2sin(3\u03c0(3|((-2x)/(-3x + 2)) - 1| + 1)) + 2 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "41", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = (3(1(-3sin(2\u03c0(-2|x + 3| - 1) + 1) + 3)^2 - 2(-3sin(2\u03c0(-2|x + 3| - 1) + 1) + 3) - 3) - 3)/(1(1(-3sin(2\u03c0(-2|x + 3| - 1) + 1) + 3)^2 - 2(-3sin(2\u03c0(-2|x + 3| - 1) + 1) + 3) - 3)) equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "80", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = (2(3sin(1\u03c0(2x + 3) - 3) + 1) + 1)/(-1(3sin(1\u03c0(2x + 3) - 3) + 1) - 3) equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "40", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation -5(-3sin(2\u03c0(-3|x + 2| - 1) + 1) - 2) - 3 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "120", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = 2(1cos(3\u03c0(-3|((1x + 2)/(-1x)) - 1|) - 2) - 3) + 5 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "155", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation 3sin(1\u03c0((2(4x^2 - 5x - 3) + 1)/(1(4x^2 - 5x - 3))) + 1) + 3 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = (-2(5(-3sin(3\u03c0x - 3) + 3)^2 - 5(-3sin(3\u03c0x - 3) + 3) - 4) - 1)/(-2(5(-3sin(3\u03c0x - 3) + 3)^2 - 5(-3sin(3\u03c0x - 3) + 3) - 4)) where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "32", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = 3(2|(3cos(1\u03c0x + 3) + 3) + 1| - 1)^2 - 1(2|(3cos(1\u03c0x + 3) + 3) + 1| - 1) - 4 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "20", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = -3|(2((-1(1cos(2\u03c0x + 3)) + 3)/(-3(1cos(2\u03c0x + 3)) - 2))^2 - 2) - 2| + 2 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "80", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = 3(-3(3cos(1\u03c0x + 2) - 3) - 5)^2 - 5(-3(3cos(1\u03c0x + 2) - 3) - 5) + 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": "How many zeros does the function f(x) = -2sin(2\u03c0((2(1(1|x - 3| + 2)^2 - 1(1|x - 3| + 2) - 4) + 1)/(-1(1(1|x - 3| + 2)^2 - 1(1|x - 3| + 2) - 4))) + 1) - 2 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "29", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = -2|(-1cos(1\u03c0((2x - 1)/(-3x + 1)) + 1)) + 2| + 3 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = (-2(1(-3sin(3\u03c0x - 2) + 1)) - 2)/(-3(1(-3sin(3\u03c0x - 2) + 1)) - 2) where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "60", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = 2sin(2\u03c0(2(1|(4x^2 + 5x - 3) - 1| + 2) - 2) - 3) - 1 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1473", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = -4(-3sin(1\u03c0(1(-1|x - 2| - 2)^2 + 5(-1|x - 2| - 2) - 1) + 1) - 2) - 5 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "192", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation 1|(-1cos(3\u03c0(-4(3x^2 + 1x - 3) + 1) - 2) + 1) - 1| - 1 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1232", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = 2sin(3\u03c0((-1(4(-1x^2 + 5x + 3) + 5) + 3)/(3(4(-1x^2 + 5x + 3) + 5) + 3))) - 2 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "16", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = 3sin(3\u03c0((2(-2|x - 2|) + 1)/(-2(-2|x - 2|) + 3)) - 2) - 1 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = 3sin(2\u03c0(-1|(2x^2 - 4x - 3) + 1| - 3) + 1) - 2 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "766", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = -2sin(3\u03c0(1((-1(3|x - 1| - 3) - 2)/(1(3|x - 1| - 3) - 2))^2 - 3((-1(3|x - 1| - 3) - 2)/(1(3|x - 1| - 3) - 2)) - 2) - 1) + 2 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "165", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = 3sin(3\u03c0(-2|(-3(-2x^2 + 4x + 2) + 2) - 1| + 3) + 3) + 3 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1043", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = 2sin(1\u03c0(-4((3(4x^2 + 5x - 1) + 1)/(1(4x^2 + 5x - 1) - 3))) + 1) + 2 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "83", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = 1sin(2\u03c0(3(-1|(-3x - 4) - 3| + 2)^2 + 5(-1|(-3x - 4) - 3| + 2) + 3) - 2) - 1 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1058", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = -1cos(1\u03c0(-2(-1x^2 + 3x - 3) - 4) - 1) + 1 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "199", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = -1sin(1\u03c0(3((1x - 3)/(-2x - 2)) + 1) - 3) - 1 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "50", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = (-3(-3cos(2\u03c0(1|x - 3| - 3) + 1) - 1))/(-3(-3cos(2\u03c0(1|x - 3| - 3) + 1) - 1) - 2) equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "40", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = -4(-2sin(3\u03c0(-1|x - 1| - 3) - 3) + 1) where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "58", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation -2cos(3\u03c0(-3|(-3((2x - 3)/(-1x + 3)) + 5) - 3| - 3) - 2) = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "322", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = 1cos(2\u03c0(2|(4(-5x^2) - 3) - 1| + 3)) have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1536", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = -1((-3(-3|(-5x^2 - 3x - 1) - 1| + 1) - 3)/(1(-3|(-5x^2 - 3x - 1) - 1| + 1) + 1)) - 3 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "826", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = 3cos(1\u03c0((2(-5x^2 + 5x - 2) - 3)/(-3(-5x^2 + 5x - 2) - 1)) + 1) + 2 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation 5(3sin(2\u03c0(-4((2x + 2)/(-3x + 2)) - 2) + 1) - 3)^2 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "74", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = -5(2cos(1\u03c0(-4(2|x + 1| + 1)^2 + 1(2|x + 1| + 1) + 5) + 2) + 1) - 1 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1425", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = 1|(-4(1cos(2\u03c0x - 2) - 1)^2 - 3(1cos(2\u03c0x - 2) - 1) + 3) + 3| - 2 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "80", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = 2sin(2\u03c0(-1(-3|x| - 2)^2 - 5(-3|x| - 2) - 2) - 1) - 1 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1440", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = (3(2(3cos(2\u03c0(-3|x + 3| - 1) + 1) + 3)^2 - 3(3cos(2\u03c0(-3|x + 3| - 1) + 1) + 3) - 4) - 2)/(3(2(3cos(2\u03c0(-3|x + 3| - 1) + 1) + 3)^2 - 3(3cos(2\u03c0(-3|x + 3| - 1) + 1) + 3) - 4)) have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "53", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = -5((2(-3cos(3\u03c0x - 2) - 2) + 2)/(1(-3cos(3\u03c0x - 2) - 2) + 3)) - 5 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "60", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = 2(2cos(1\u03c0(-2(-3|x + 2| + 3) + 3) + 3) + 3)^2 - 2 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "60", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation -3sin(1\u03c0(-2(-3x)^2 - 2(-3x) + 5)) = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1700", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = (-3(2sin(2\u03c0(4x^2 + 4x - 2) - 3) - 1) - 1)/(-3(2sin(2\u03c0(4x^2 + 4x - 2) - 3) - 1) - 2) where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "359", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation 2cos(2\u03c0(4((-1x - 1)/(1x))) + 2) - 2 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "58", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation -3cos(1\u03c0(2(4x^2 - 2x + 5) - 5) - 1) + 2 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1214", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = -3sin(1\u03c0(-5(2|x + 3| - 1) + 5) - 1) - 1 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "200", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = 3((2(2sin(2\u03c0x - 3) + 2) - 3)/(1(2sin(2\u03c0x - 3) + 2))) + 4 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "40", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = 4(-3sin(3\u03c0(-1|x - 1| + 3) - 3) - 3) + 4 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "62", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = -4(-3cos(3\u03c0(2|x + 2| - 2) + 2)) + 5 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "118", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = -1sin(1\u03c0(5((-1(4x + 4) + 3)/(-1(4x + 4) + 2))^2 - 2((-1(4x + 4) + 3)/(-1(4x + 4) + 2)) + 1) + 2) where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "52", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = -3sin(3\u03c0(-3(5x + 3)^2 - 2(5x + 3) - 1) + 2) + 3 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1219", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = 3sin(1\u03c0(-5(3x - 3)^2 + 4(3x - 3) + 1) - 3) + 3 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1135", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = -3cos(1\u03c0(2((2x + 3)/(3x)) + 4) - 1) - 2 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "45", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = 2cos(2\u03c0((-1(-2|x| + 3) - 3)/(-3(-2|x| + 3) - 3)) + 3) + 1 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "46", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation 3|((1(-3sin(3\u03c0x + 2) + 1) + 3)/(1(-3sin(3\u03c0x + 2) + 1))) + 2| - 2 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "120", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation (2(-1sin(1\u03c0(4x^2 + 1x - 3) - 2)) + 1)/(-2(-1sin(1\u03c0(4x^2 + 1x - 3) - 2)) + 3) = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "794", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = 3(-2|(2(-2sin(2\u03c0x - 1) + 1)^2 + 4(-2sin(2\u03c0x - 1) + 1) - 2) + 2| + 2) - 1 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "80", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = (-1(3cos(1\u03c0(3(-2|x + 2|) + 5) + 3)) - 2)/(3(3cos(1\u03c0(3(-2|x + 2|) + 5) + 3)) - 1) have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "120", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = 3cos(1\u03c0(2|(3(1x^2 + 2x) - 2) + 1| + 3) - 2) + 3 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "516", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = -2sin(2\u03c0(-3((3(3x^2 - 5x - 1) + 3)/(-1(3x^2 - 5x - 1) - 2)) - 4) - 3) + 1 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "125", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = (1(-1(2cos(1\u03c0x - 3) - 1)) + 1)/(3(-1(2cos(1\u03c0x - 3) - 1)) - 1) where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation 3cos(3\u03c0(-3(-3|x - 1| - 1)^2 + 1(-3|x - 1| - 1)) + 3) + 1 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1550", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation -3|(5((2(2sin(1\u03c0x + 2) + 3) - 3)/(-3(2sin(1\u03c0x + 2) + 3) + 2)) - 1) - 2| + 2 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "40", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = -1(1(3|(-2cos(3\u03c0x + 2) - 1) + 1|)^2 - 3(3|(-2cos(3\u03c0x + 2) - 1) + 1|) - 4) + 1 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "120", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = 3cos(3\u03c0((2(-2x^2 - 1x + 1) - 3)/(2(-2x^2 - 1x + 1) + 1)) + 1) - 3 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "47", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = -3sin(2\u03c0(2|(-3x^2 - 1x + 1) - 3| - 1) + 3) + 3 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "959", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = 2sin(1\u03c0(-2|(-1x + 4) + 1| - 3)) equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "40", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = -1|(3sin(2\u03c0((2(5x - 3))/(-2(5x - 3) - 1)))) + 1| + 3 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = 4(-2sin(1\u03c0(-3|((-1x + 1)/(2x - 1)) - 2| + 1)) + 1) - 4 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "33", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = -3sin(3\u03c0((2(1x^2 + 3x + 2) - 3)/(3(1x^2 + 3x + 2) + 3)) + 2) + 2 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation -2(5(3|(2cos(2\u03c0x - 3) + 2) - 3| - 2) + 1)^2 + 4(5(3|(2cos(2\u03c0x - 3) + 2) - 3| - 2) + 1) + 3 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "160", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation 2|(4(2sin(1\u03c0x + 3) + 2)^2 + 2(2sin(1\u03c0x + 3) + 2) - 2) + 3| - 3 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "20", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation 2cos(3\u03c0(4(1x^2 + 3x - 2) + 2) - 2) + 1 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1424", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = -1cos(2\u03c0(-3|(5x^2 + 1x + 1) + 2| + 2) - 1) - 1 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1005", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation 2(5(1sin(1\u03c0x + 3))^2 + 2(1sin(1\u03c0x + 3)) + 1) - 5 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "40", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation 3sin(2\u03c0((3(-2x + 5) - 1)/(2(-2x + 5)))) - 3 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = 3cos(2\u03c0(-3(1|x| - 2) + 4) - 3) + 2 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": "Determine the number of values x in [-10, 10] where f(x) = -2sin(3\u03c0(-1|(1x + 1)|) - 2) + 1 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "60", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation 3|(-2cos(1\u03c0(-4(2x^2 - 5) + 2) + 1) + 2) - 1| - 2 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1196", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = -2sin(2\u03c0(1(2|x + 3| + 3)^2 + 2(2|x + 3| + 3) + 1) + 2) - 1 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1582", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = (3(2cos(2\u03c0(2|(3x + 5) - 3| - 1) - 3)) - 2)/(3(2cos(2\u03c0(2|(3x + 5) - 3| - 1) - 3)) - 1) where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "240", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation -2sin(3\u03c0(-1|(1x - 5) + 3| - 1)) + 2 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "30", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = 2sin(3\u03c0(1(2x^2 - 3x - 2) - 4) + 1) + 1 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1076", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation 1(-1(2|(2cos(2\u03c0x - 3) + 2) - 3| - 2))^2 + 3(-1(2|(2cos(2\u03c0x - 3) + 2) - 3| - 2)) - 2 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "120", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation -1|(-1sin(1\u03c0(1x + 2))) - 2| + 1 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = -1(2cos(2\u03c0(-2|x + 3| - 2) - 2) - 3) - 4 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "80", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = 3cos(3\u03c0((2(5x - 2) - 2)/(-1(5x - 2) + 2)) - 1) + 3 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "23", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = 1cos(1\u03c0(4((3(3|x - 1| - 2) + 1)/(1(3|x - 1| - 2) - 3))^2 + 5((3(3|x - 1| - 2) + 1)/(1(3|x - 1| - 2) - 3)) + 4) + 3) + 1 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "341", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = -2sin(2\u03c0(-2(-4x^2 + 1x - 1)) + 1) where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1658", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = -3sin(2\u03c0(2|(-5(-1x - 2)^2 + 3(-1x - 2) + 4) + 1| - 3) - 3) where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1615", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = -3sin(1\u03c0((-1(2(-5x + 2)^2 + 2(-5x + 2) - 3) - 3)/(-3(2(-5x + 2)^2 + 2(-5x + 2) - 3))) - 1) - 2 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = (-2(3cos(1\u03c0(2|x + 1| - 2) + 3) - 2) + 1)/(-1(3cos(1\u03c0(2|x + 1| - 2) + 3) - 2) + 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 number of x-intercepts of the function f(x) = 1(-2sin(3\u03c0(-4((2x + 2)/(-1x))^2 + 4((2x + 2)/(-1x)) + 3) - 1) + 1) - 3 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "190", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = 1(1sin(1\u03c0((1x)/(3x + 2)) + 2) + 3) - 3 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "19", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = 3((-3(-2(-1cos(2\u03c0x) + 2) + 4) - 3)/(3(-2(-1cos(2\u03c0x) + 2) + 4) + 2))^2 + 5((-3(-2(-1cos(2\u03c0x) + 2) + 4) - 3)/(3(-2(-1cos(2\u03c0x) + 2) + 4) + 2)) - 5 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 number of x-intercepts of the function f(x) = -2cos(3\u03c0((2(-3|x - 3| + 2) + 2)/(2(-3|x - 3| + 2))) - 1) where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "73", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = (3(-1(-3sin(1\u03c0(1|x - 2|) + 3)) - 2) - 2)/(-2(-1(-3sin(1\u03c0(1|x - 2|) + 3)) - 2) + 3) equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "20", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = (2(3sin(2\u03c0(2|(-2x + 2) - 3| + 1)) + 2) - 2)/(-1(3sin(2\u03c0(2|(-2x + 2) - 3| + 1)) + 2) - 3) have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "160", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation -1cos(1\u03c0(-5(3|x - 3|)^2 + 3(3|x - 3|) - 5) - 2) + 1 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1068", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = -1sin(3\u03c0(4(-1|x + 2|) - 5) + 3) + 1 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "120", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = 5(-3|(-3cos(3\u03c0x) + 1) - 3| + 2) + 2 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": "Determine the number of values x in [-10, 10] where f(x) = -4(3sin(2\u03c0(-4((-1x - 3)/(-3x + 4)) - 4) - 2) + 2)^2 - 4(3sin(2\u03c0(-4((-1x - 3)/(-3x + 4)) - 4) - 2) + 2) + 2 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "108", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = -2sin(3\u03c0(3((3x + 3)/(1x - 2)) - 5) - 2) - 1 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "294", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = 3cos(1\u03c0(-3(-3|x - 3| + 1)^2 - 5(-3|x - 3| + 1) - 2) - 2) + 3 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "981", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = -3cos(3\u03c0(1|(5(-5x - 4)^2 - 3(-5x - 4) - 3) - 1| + 3) + 2) - 3 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1237", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation (2(-2|(-3cos(2\u03c0x - 2)) + 3| - 1) + 3)/(1(-2|(-3cos(2\u03c0x - 2)) + 3| - 1) + 1) = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "40", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = -2|(-1(3sin(2\u03c0(5x - 2) + 1) + 3)^2 + 3(3sin(2\u03c0(5x - 2) + 1) + 3) - 2) + 3| + 2 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "400", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = -2|(4(-1cos(2\u03c0x - 3) + 1)^2 - 1(-1cos(2\u03c0x - 3) + 1) - 5) + 2| + 2 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "80", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = 5(3cos(1\u03c0(4x^2 - 3x - 2) + 2) + 3) where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "350", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = (-3(1sin(3\u03c0(2|(-5x + 5) - 3| - 3)) - 1))/(-1(1sin(3\u03c0(2|(-5x + 5) - 3| - 3)) - 1) - 2) equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "288", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation (2(-2cos(3\u03c0(-4x^2 - 2x + 2) + 1) - 3) + 2)/(2(-2cos(3\u03c0(-4x^2 - 2x + 2) + 1) - 3) - 1) = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "956", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = -2|((3(1cos(3\u03c0x - 1) - 1) - 1)/(2(1cos(3\u03c0x - 1) - 1) + 1)) - 2| + 3 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "60", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation (-2(3|(2sin(2\u03c0x + 2) - 1) + 3| - 1) - 1)/(1(3|(2sin(2\u03c0x + 2) - 1) + 3| - 1) + 3) = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "40", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = 1(-1(2sin(3\u03c0x) - 1)^2 + 3(2sin(3\u03c0x) - 1) + 3) - 2 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "60", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = 1cos(3\u03c0(3|(-1x^2 + 1x + 1) - 1|) - 2) - 1 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "763", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation (-2(1(1sin(2\u03c0(-3x + 5) + 1) + 1)^2 + 5(1sin(2\u03c0(-3x + 5) + 1) + 1) - 3) - 2)/(-3(1(1sin(2\u03c0(-3x + 5) + 1) + 1)^2 + 5(1sin(2\u03c0(-3x + 5) + 1) + 1) - 3) + 4) = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "120", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = (-1(-1|(-2(-3cos(1\u03c0x - 2) + 1)^2 + 5(-3cos(1\u03c0x - 2) + 1) + 2) - 3| - 1) - 2)/(1(-1|(-2(-3cos(1\u03c0x - 2) + 1)^2 + 5(-3cos(1\u03c0x - 2) + 1) + 2) - 3| - 1) + 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 number of x-intercepts of the function f(x) = 2sin(3\u03c0(-3|(-3x^2 - 1x - 4) + 2| + 3) + 1) where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1499", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation (-3(4(2sin(1\u03c0x + 2) - 1) + 4) - 1)/(-1(4(2sin(1\u03c0x + 2) - 1) + 4) - 2) = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "20", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation -2cos(3\u03c0(3(1x - 3)^2 - 5(1x - 3) - 3) - 1) + 2 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "838", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = -5(1cos(2\u03c0(2|x + 2| - 1) - 2))^2 + 1(1cos(2\u03c0(2|x + 2| - 1) - 2)) + 3 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "160", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = -3cos(2\u03c0(1(-1|((-1x + 3)/(-1x + 2)) + 3|) - 5) - 2) - 3 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "29", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = 2cos(1\u03c0(-3|(5x - 1) + 1| - 3)) - 2 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "149", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = 3sin(2\u03c0((2(5(2|x + 3| - 2) - 3) - 1)/(-1(5(2|x + 3| - 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": "68", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = -4(-3|((3(2sin(1\u03c0x - 2)) - 3)/(3(2sin(1\u03c0x - 2)) + 3)) - 3|)^2 + 5(-3|((3(2sin(1\u03c0x - 2)) - 3)/(3(2sin(1\u03c0x - 2)) + 3)) - 3|) + 2 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "20", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = 5((-1(3sin(2\u03c0x - 3) + 3) + 2)/(3(3sin(2\u03c0x - 3) + 3) + 2)) - 5 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "20", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = -3|(2((-3(1sin(3\u03c0x + 3)) - 1)/(-2(1sin(3\u03c0x + 3))))) - 3| + 3 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "60", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = -2cos(2\u03c0(-1((1x + 2)/(2x + 3)) + 2) + 1) + 1 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "26", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = 3cos(2\u03c0(3(5x - 1)^2 - 1(5x - 1) + 3) + 3) + 1 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1518", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation (2(-3sin(1\u03c0(1x^2 - 5x - 3) + 2) - 1) + 1)/(-1(-3sin(1\u03c0(1x^2 - 5x - 3) + 2) - 1) + 2) = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "212", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation 3cos(1\u03c0((-2(1x^2 + 3x - 4) + 1)/(-1(1x^2 + 3x - 4) - 2)) - 1) - 1 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "77", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = 1((1(-2sin(1\u03c0(2x^2 - 3x - 4) + 1) - 2) - 2)/(3(-2sin(1\u03c0(2x^2 - 3x - 4) + 1) - 2) + 2)) - 4 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "224", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation -3cos(2\u03c0((-2(3|x| - 3) + 1)/(3(3|x| - 3) + 1))) = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "46", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = -3(-3sin(2\u03c0(-3x^2 + 4x + 5) - 1) + 1) - 1 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1101", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = -3sin(3\u03c0(-1((-1x + 2)/(3x - 2)) - 4) - 1) - 1 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "37", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation -3cos(3\u03c0(-3((3x - 1)/(-3x - 1)) - 5)) - 2 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "84", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = -2cos(3\u03c0(-5(-2|(-1x - 1) - 3| + 3)^2 - 1(-2|(-1x - 1) - 3| + 3) + 3) - 1) + 2 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1052", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = 4(2(-2cos(3\u03c0x - 3) - 3)^2 + 5(-2cos(3\u03c0x - 3) - 3) - 3) where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "60", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation -1((-2(-2(3sin(3\u03c0x - 2) - 3) - 5))/(-2(-2(3sin(3\u03c0x - 2) - 3) - 5) + 1))^2 - 2((-2(-2(3sin(3\u03c0x - 2) - 3) - 5))/(-2(-2(3sin(3\u03c0x - 2) - 3) - 5) + 1)) = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "94", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = 1sin(2\u03c0(-1(3((-1x - 3)/(1x + 1)) + 1)^2 + 1(3((-1x - 3)/(1x + 1)) + 1) - 4) - 3) - 1 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "194", "dataset": "MATH"}