instruction_seed stringlengths 5 2.9k | response_seed stringlengths 3 9.55k | input stringclasses 1
value | _source stringclasses 1
value |
|---|---|---|---|
Let f(o) = -2*o + 18 - 7 + 3*o - 7*o. Let k(v) = 4*v + 81. Let g be k(-19). Let s(a) = -5*a + 9. Let l(m) = g*s(m) - 4*f(m). Determine l(-6).\n | 7\n | ibivibiv/math_instruct | |
What is 19496.061 milliseconds in hours?\n | 0.0054155725\n | ibivibiv/math_instruct | |
Let d(w) = 156930*w + 1380. Let f be d(-6). What is f rounded to the nearest 10000?\n | -940000\n | ibivibiv/math_instruct | |
Simplify (sqrt(6)/(sqrt(3) + sqrt(27)) - sqrt(2)*-2*1)**2.\n | 81/8\n | ibivibiv/math_instruct | |
Let o(x) = -4*x**2 - 2*x - 1. Suppose 1919 = -11*u - 633. Let q = -233 - u. Give o(q).\n | -3\n | ibivibiv/math_instruct | |
Simplify r**(1/2)/(r*r**(-28)) assuming r is positive.\n | r**(55/2)\n | ibivibiv/math_instruct | |
Let s = -3.09 + 3. Let h = s - 0.01. What is the closest to 0 in 0.4, h, 0.5?\n | h\n | ibivibiv/math_instruct | |
Which is bigger: 283 or 173?\n | 283\n | ibivibiv/math_instruct | |
Let h(j) = j**3 - 19*j**2 + 14*j + 1. Determine h(18).\n | -71\n | ibivibiv/math_instruct | |
Suppose w = -1, 4*a - a - w = -5. Is (-1)/a + (-83727)/(-42) composite?\n | True\n | ibivibiv/math_instruct | |
Solve 370909*v = 371212*v - 7878 for v.\n | 26\n | ibivibiv/math_instruct | |
Suppose -3*h + 28 = -14. Calculate the highest common divisor of 7 and h.\n | 7\n | ibivibiv/math_instruct | |
Let y = 243 - 6073/25. What is the third smallest value in -2/7, y, 6, 0.4?\n | 0.4\n | ibivibiv/math_instruct | |
Suppose 0*x = -x - 5. Let t be (4/x)/(10/(-25)). What is the second derivative of z**3 + z**t - 4*z - 5*z**3 - z**2 wrt z?\n | -24*z\n | ibivibiv/math_instruct | |
Let r(k) = -k**3 - 11*k**2 + 1126*k + 966. Determine r(29).\n | -20\n | ibivibiv/math_instruct | |
Two letters picked without replacement from vlavvyvavvai. Give prob of picking 1 y and 1 l.\n | 1/66\n | ibivibiv/math_instruct | |
Solve 21*n - 10497 = 658*n - 15928 - 23871 for n.\n | 46\n | ibivibiv/math_instruct | |
Which is greater: 376889 or 376892?\n | 376892\n | ibivibiv/math_instruct | |
Calculate 22/(-49280)*-64*(-20)/6.\n | -2/21\n | ibivibiv/math_instruct | |
What is (-470763)/(-44048) - 10/(-32)?\n | 11\n | ibivibiv/math_instruct | |
Let t(w) = 2*w**2. Let p(z) = -58*z**2 + 5*z - 33. Let y(g) = -g**2 + g - 1. Let j(n) = -p(n) + 5*y(n). Determine t(j(x)).\n | 5618*x**4 + 5936*x**2 + 1568\n | ibivibiv/math_instruct | |
Round -1.587212 to one decimal place.\n | -1.6\n | ibivibiv/math_instruct | |
Is 13153993 a composite number?\n | False\n | ibivibiv/math_instruct | |
Calculate the highest common factor of 19 and 2.\n | 1\n | ibivibiv/math_instruct | |
What are the prime factors of 69277?\n | 13, 73\n | ibivibiv/math_instruct | |
Let c = 109 + -109. Solve -5*u + 1 - 26 = c for u.\n | -5\n | ibivibiv/math_instruct | |
Suppose q - 6 = 10. Suppose -s + q = -0*s. Suppose 4*f = 44 + 20. What is the lowest common multiple of f and s?\n | 16\n | ibivibiv/math_instruct | |
How many millennia are there in 13.33551 months?\n | 0.0011112925\n | ibivibiv/math_instruct | |
Simplify (((h**(-2/5)*h)/h*h*h)**(3/35)*(h**(-2/3)/h*h)/h**3)**(-5) assuming h is positive.\n | h**(1853/105)\n | ibivibiv/math_instruct | |
Let f = 65 - 69. What is the closest to -2 in 1/2, f, 2?\n | f\n | ibivibiv/math_instruct | |
Does 16 divide 14592?\n | True\n | ibivibiv/math_instruct | |
Let m(t) be the second derivative of -14*t + 0*t**3 + 0 + 1/3*t**4 + 11/2*t**2. What is the derivative of m(z) wrt z?\n | 8*z\n | ibivibiv/math_instruct | |
Simplify 6*(sqrt(448) + (sqrt(448)*-1)**2 - sqrt(448)) + ((sqrt(28) + -1)*6)**2.\n | -144*sqrt(7) + 3732\n | ibivibiv/math_instruct | |
Work out -114.6 * -0.08172.\n | 9.365112\n | ibivibiv/math_instruct | |
Let p = -1/24 - -19/72. What is the third biggest value in -0.1, p, -0.09?\n | -0.1\n | ibivibiv/math_instruct | |
Calculate the remainder when 5464 is divided by 24.\n | 16\n | ibivibiv/math_instruct | |
What is the third smallest value in 4/3, 1, -2/9, 5/4, -1/64?\n | 1\n | ibivibiv/math_instruct | |
b"What is the rth term of -3886, -3888, -3890, -3892, -3894, -3896?\n" | -2*r - 3884\n | ibivibiv/math_instruct | |
List the prime factors of 262634.\n | 2, 131317\n | ibivibiv/math_instruct | |
What is 4*((-15)/12 + 1)?\n | -1\n | ibivibiv/math_instruct | |
List the prime factors of 425.\n | 5, 17\n | ibivibiv/math_instruct | |
Let p(f) = f**4 + 2*f**3 - 2. Let o(h) = 6*h**4 + 10*h**3 - 11. Let u = -3 - -1. Let n(s) = u*o(s) + 11*p(s). Factor n(i).\n | -i**3*(i - 2)\n | ibivibiv/math_instruct | |
Let b(f) = -f + 1. Suppose 47*a - 1446 + 1164 = 0. Let d(t) = 4*t - 58. Determine a*b(i) + d(i).\n | -2*i - 52\n | ibivibiv/math_instruct | |
Let t(h) be the first derivative of -h**3/3 + 15*h**2 + 559*h - 4402. Factor t(d).\n | -(d - 43)*(d + 13)\n | ibivibiv/math_instruct | |
Let u be 6112/(-60) - 5/((-450)/(-12)). Is u less than -100?\n | True\n | ibivibiv/math_instruct | |
What is 3 take away -49499?\n | 49502\n | ibivibiv/math_instruct | |
Let h = -0.071 - 47.929. Let b = h + 52. Let p = 0.2 - 0.25. Sort 5, b, p in descending order.\n | 5, b, p\n | ibivibiv/math_instruct | |
What is next in -571519, -1143046, -1714573, -2286100, -2857627?\n | -3429154\n | ibivibiv/math_instruct | |
Suppose -12*o - 130 = -17*o. Suppose -2*t + o = -122. Let s = 78 - t. Solve 4 + 0 = s*d for d.\n | 1\n | ibivibiv/math_instruct | |
Four letters picked without replacement from gveevvevevvvvgevve. What is prob of sequence vvee?\n | 5/136\n | ibivibiv/math_instruct | |
Let n(b) = b + 4. Let u(k) = -8*k**3 - 3*k**2 + k + 2. Let j be u(-1). Suppose -3*i - 5*t = -j, i + t + 3 = -i. Calculate n(i).\n | 1\n | ibivibiv/math_instruct | |
Four letters picked without replacement from {a: 4, p: 2, s: 3, u: 1}. Give prob of sequence sppa.\n | 1/210\n | ibivibiv/math_instruct | |
Subtract 0.5 from -81020431012.\n | -81020431012.5\n | ibivibiv/math_instruct | |
Let k = 12 - 7. Let o be (-2)/(-9) + (k/(-9) - 0). Let f = 2/21 - -55/84. Which is the nearest to f? (a) 3/4 (b) o (c) -5\n | a\n | ibivibiv/math_instruct | |
Simplify ((t/((t*t/((t/(t/((t/(t**(-4)/t*t))/t)))/t))/t))/t)**(2/49) assuming t is positive.\n | t**(4/49)\n | ibivibiv/math_instruct | |
Solve 0*v + 5*h - 1 = 4*v, 2*h - 6 = -4*v for v.\n | 1\n | ibivibiv/math_instruct | |
Four letters picked without replacement from {b: 8, m: 5}. Give prob of sequence mbbm.\n | 28/429\n | ibivibiv/math_instruct | |
How many centimeters are there in 177.2955um?\n | 0.01772955\n | ibivibiv/math_instruct | |
Let c = 187 + -116. Suppose 0 = -2*z + b + c, 0*z = -2*z + 5*b + 91. Let u = z + -5. What is the remainder when u is divided by 10?\n | 8\n | ibivibiv/math_instruct | |
Is 2936147 prime?\n | False\n | ibivibiv/math_instruct | |
What is 12959520 divided by -1120?\n | -11571\n | ibivibiv/math_instruct | |
Evaluate (-3 + -9 - (-4 - 4)) + 6.\n | 2\n | ibivibiv/math_instruct | |
What is next in -596, -1135, -1686, -2255, -2848, -3471, -4130?\n | -4831\n | ibivibiv/math_instruct | |
Let s(w) be the first derivative of w**4/4 + w**3/3 + w**2/2 + w - 102. Let h(g) = -12*g**3 - 3*g**2 - 3*g - 3. What is h(i) + 3*s(i)?\n | -9*i**3\n | ibivibiv/math_instruct | |
Simplify (((sqrt(228)*-2 + sqrt(228))*6)/(sqrt(588) - sqrt(588)*2))**2.\n | 684/49\n | ibivibiv/math_instruct | |
What is the result of the following expression?
90.931 / -0.6 | -151.5517 | ibivibiv/math_instruct | |
Let c be (9 - 1) + -1 + 2. Let h = c - 4. Let y(f) = -4*f**3 - 2*f + 6*f + 1 + 4*f**2 + 3*f**3. Determine y(h).\n | -4\n | ibivibiv/math_instruct | |
What is the nearest to -2/19 in 18, 2, -3, -0.1?\n | -0.1\n | ibivibiv/math_instruct | |
Does 41 divide 75645?\n | True\n | ibivibiv/math_instruct | |
Calculate the highest common factor of 35262 and 732.\n | 6\n | ibivibiv/math_instruct | |
Let s = 3 + 0. Let t be (-12 - (-18)/2)/((-6)/(-8)). Put s, 5, t in decreasing order.\n | 5, s, t\n | ibivibiv/math_instruct | |
What is the closest to -1 in 23.31, 2, 9593, -2/11, 4?\n | -2/11\n | ibivibiv/math_instruct | |
Write an educational piece suited for college students related to the following text snippet:
"# Urysohn’s lemma
A normal space is a topological space $X$ such that whenever $A$ and $B$ are disjoint closed subsets of $X$, then there are disjoint open subsets $U$ and $V$ of $X$ such that $A\subseteq U$ and $B\subseteq ... | Topological spaces are fundamental structures in mathematics, used to provide a general framework for analyzing the properties of geometric objects. A key concept within this field is normality, which pertains to how sets within a topology interact with one another. Specifically, a topological space $X$ is considered ... | ibivibiv/math_instruct | |
Find the third derivative of -172020228*p**3 + 3*p**2 + 22909*p + 5.\n | -1032121368\n | ibivibiv/math_instruct | |
What is the ten thousands digit of 122202284?\n | 0\n | ibivibiv/math_instruct | |
Evaluate -4*(-12)/(-32)*(-8)/30.\n | 2/5\n | ibivibiv/math_instruct | |
Suppose 0 = -16*y - 1404 + 348. Let q be (-4)/6 + 2672956/y. Round q to the nearest one thousand.\n | -41000\n | ibivibiv/math_instruct | |
What is the first derivative of 194*v**3 - 171 wrt v?\n | 582*v**2\n | ibivibiv/math_instruct | |
Suppose -9 = -2*s + s. Let p(b) = 5*b**2 - s*b - 5 + 0 - 6*b**2. Let u be p(-8). Solve -4*j - 1 = u*z - 0*z, -4*z + 2*j = -28 for z.\n | 5\n | ibivibiv/math_instruct | |
What is the highest common factor of 650 and 200?\n | 50\n | ibivibiv/math_instruct | |
Suppose 0 = 15*s - 40 - 1475. Let o = s + -96. Suppose 8 = o*k - 7. What is the units digit of k?\n | 3\n | ibivibiv/math_instruct | |
What is the square root of 7236509 to the nearest integer?\n | 2690\n | ibivibiv/math_instruct | |
Let n be (-2)/(-4)*4 - -2. Suppose 6 = n*r + 2*g, r + 10*g + 21 = 5*g. Let d be 31 - -2*1/2. What is the greatest common factor of d and r?\n | 4\n | ibivibiv/math_instruct | |
Let p(s) = -27*s**2. Let a(z) = -z**2. Give a(p(f)).\n | -729*f**4\n | ibivibiv/math_instruct | |
Product of 5 and 2613.\n | 13065\n | ibivibiv/math_instruct | |
Suppose 4*a + 11 = 3*s, -2*s - 4*a + 5 = 11. Suppose -3*w + 2*r = 2, 4*w - 3*w = -r - 4. Sort w, s, 3 in descending order.\n | 3, s, w\n | ibivibiv/math_instruct | |
Is 1215800 a multiple of 4?\n | True\n | ibivibiv/math_instruct | |
Find the common denominator of -27/13405 and -89/15320.\n | 107240\n | ibivibiv/math_instruct | |
Let g(u) = -u + 6. Let z be g(5). Suppose 2*x = 3*x + z. List the prime factors of 2 + -1 + x + 2.\n | 2\n | ibivibiv/math_instruct | |
Let o = -17 - -17. Let q be (-2 - o)/(2/(-5)). Solve -2*h + 10 = 0, x + 3*h - q = -4*x for x.\n | -2\n | ibivibiv/math_instruct | |
Let f(a) = -a**3 + 4*a**2. Suppose 0 = -0*u + 2*u - 20. Suppose 4 = -0*r - 4*r + 4*q, -5*q - 49 = 4*r. Let i = u + r. What is f(i)?\n | 0\n | ibivibiv/math_instruct | |
Let w = -59 - -56. Let j(o) = -2*o**3 - 2*o**2 - 2*o - 1. Let f be j(w). Suppose f = 3*u - 142. Is 17 a factor of u?\n | False\n | ibivibiv/math_instruct | |
What is the highest common factor of 23 and 150167?\n | 23\n | ibivibiv/math_instruct | |
Let x = -43 + 21. Let a = -22.00000013 - x. Round a to 7 decimal places.\n | -0.0000001\n | ibivibiv/math_instruct | |
Find the common denominator of 69/198232 and -3/24779.\n | 198232\n | ibivibiv/math_instruct | |
What is the common denominator of 39/4 and 4/(-10) - (-13 - (-18692)/1520)?\n | 76\n | ibivibiv/math_instruct | |
b"What is the qth term of 5077, 4780, 4465, 4132?\n" | -9*q**2 - 270*q + 5356\n | ibivibiv/math_instruct | |
Let h = -49 - -48. Suppose 63*s = -282 + 30. Which is the second biggest value? (a) h (b) -1/5 (c) 4 (d) s\n | b\n | ibivibiv/math_instruct | |
Let g(u) = u**3 + 7*u**2 - 2*u - 1. Let f be g(-7). Suppose 11*a = f*a - 4. Suppose 2*t - 2*l - 11 = -5, l - 12 = -a*t. Solve 3*w = 1 + t for w.\n | 2\n | ibivibiv/math_instruct | |
Put 41, -0.07, -20533 in ascending order.\n | -20533, -0.07, 41\n | ibivibiv/math_instruct |
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