instruction_seed stringlengths 5 2.9k | response_seed stringlengths 3 9.55k | input stringclasses 1
value | _source stringclasses 1
value |
|---|---|---|---|
Product of 3 and -0.089563.\n | -0.268689\n | ibivibiv/math_instruct | |
Expand (-2*k**4 - k**4 + 4*k**4)*(81*k - 120*k + 72*k).\n | 33*k**5\n | ibivibiv/math_instruct | |
Expand 5*x**2 + 5*x**2 - 125*x**2 + ((-2 + 6 + 0)*(x + 2*x - x) + 18*x - 24*x + 17*x + (-3 + 5 - 4)*(-2 - x + 2))*(-3*x + 4*x - 3*x).\n | -157*x**2\n | ibivibiv/math_instruct | |
Let n(m) = -718*m - 2246. What is n(-3)?\n | -92\n | ibivibiv/math_instruct | |
(-19)/(-152) - (-7)/(-168)*3\n | 0\n | ibivibiv/math_instruct | |
Let u(i) = 11. Let z = -5 + 10. Let p(a) = a - 6. Let m(j) = z*p(j) + 3*u(j). Let h = 0 + -6. Let o(d) = 4*d + 3. What is h*o(n) + 5*m(n)?\n | n - 3\n | ibivibiv/math_instruct | |
Let a(w) = 5 + 2*w - w**2 - 2 - 8*w. What is the remainder when a(-6) is divided by 3?\n | 0\n | ibivibiv/math_instruct | |
Suppose -2*y - 1 = -11. Let v = 23 + -6. Let k = v + -9. Calculate the remainder when k is divided by y.\n | 3\n | ibivibiv/math_instruct | |
Let j(p) = -9*p**2 - 135*p + 3. Let s be j(-15). Solve -4*o + 3*q = 23, 2*q + 0 + s = -o for o.\n | -5\n | ibivibiv/math_instruct | |
Let o = 158 - 146.9. Let c = 482 + -470. Let f = c - o. Sort -4/7, f, 3/4 in descending order.\n | f, 3/4, -4/7\n | ibivibiv/math_instruct | |
What is the tens digit of 43?\n | 4\n | ibivibiv/math_instruct | |
Write an educational piece suited for college students related to the following text snippet:
"# Axiomatization of the real numbers in first order logic
Let $$P:=\bigcup_{n\in \mathbb{N}} \mathcal{P}_n$$ and $$F:=\bigcup_{n\in \mathbb{N}} \mathcal{F}_n$$, where $$P\cap F=\varnothing$$. Let $$\mathcal{L}:=P\cup F$$.
T... | We begin by defining the components necessary to build a first order theory $T$ for the real numbers. At its foundation lies a lexicon $\mathcal{L}$, which consists of two sets: $\mathcal{P}_n$ containing $n$-ary relation symbols, and $\mathcal{F}_n$ containing $n$-ary function symbols. Together, these form the entire... | ibivibiv/math_instruct | |
Sort -3, -5, 5, -1065, 0, 24.\n | -1065, -5, -3, 0, 5, 24\n | ibivibiv/math_instruct | |
Let b(c) = c - 1. Let h(y) = -y**2 + 4*y - 6. Let n(u) = 3*u**2 - 7*u + 13. Let p(g) = 5*h(g) + 2*n(g). What is -6*b(r) + p(r)?\n | r**2 + 2\n | ibivibiv/math_instruct | |
Find q, given that 182/3*q + 2/3*q**3 - 94/3*q**2 - 30 = 0.\n | 1, 45\n | ibivibiv/math_instruct | |
What is the highest common divisor of 3172 and 156?\n | 52\n | ibivibiv/math_instruct | |
What is the third derivative of 4125*d**3 + 1843*d**2 wrt d?\n | 24750\n | ibivibiv/math_instruct | |
What is the nearest to -0.03 in 0, -21, -2/9?\n | 0\n | ibivibiv/math_instruct | |
Let j(f) = -f**2 + 1079*f. Let v(k) = 68 + 60 - 209 + 81 - k. What is j(v(q))?\n | -q**2 - 1079*q\n | ibivibiv/math_instruct | |
Calculate -4 divided by 6132.\n | -1/1533\n | ibivibiv/math_instruct | |
Let i(o) be the second derivative of o**6/72 - o**5/120 - o**3/6 - 2*o. Let s(a) be the second derivative of i(a). Let z be s(1). Solve -3 + 11 = -z*r for r.\n | -2\n | ibivibiv/math_instruct | |
Suppose 0 = 3*f - 4*i + 4, -2*i + 4 = 2. Find the third derivative of f*h**2 + 2*h**4 - 3*h**2 + 0*h**2 wrt h.\n | 48*h\n | ibivibiv/math_instruct | |
What is -1.308 rounded to 1 decimal place?\n | -1.3\n | ibivibiv/math_instruct | |
Calculate the greatest common divisor of 14706230 and 2485.\n | 2485\n | ibivibiv/math_instruct | |
What is the greatest common divisor of 287126 and 10206?\n | 14\n | ibivibiv/math_instruct | |
Let c = 9.939 + -0.239. Let b = -10.4 + c. Which is greater: b or 0?\n | 0\n | ibivibiv/math_instruct | |
Suppose 5*t + 2*j + 241 = 288, -3*j = 5*t - 58. Let x(b) = -4*b - 6. Let k be x(-4). Solve t = -2*u - q + 17, -5*q + k = 0 for u.\n | 5\n | ibivibiv/math_instruct | |
Suppose -18*v + 22*v + 1600428 = 0. Is v/(-63) + 6/63 + -4 composite?\n | True\n | ibivibiv/math_instruct | |
Let h be 170/(-8) - 4/(-16). Let v = h + 65. Is 12 a factor of v?\n | False\n | ibivibiv/math_instruct | |
Let t(p) = -p**2 - 5*p - 1. Let o(l) = -4*l**3 + l**2 - 1. Let y be o(1). Let m be t(y). Suppose -3*g = -0 - m. What is the units digit of g?\n | 1\n | ibivibiv/math_instruct | |
Let d(h) = 38*h + 536. Let z be d(-14). Solve -4*f - 2*t = -z + 8, 0 = 3*t - 12 for f.\n | -3\n | ibivibiv/math_instruct | |
4 - (-2 + 4 - 1)\n | 3\n | ibivibiv/math_instruct | |
Calculate (-2043)/227*2/2.\n | -9\n | ibivibiv/math_instruct | |
Expand -3 + q + 3 + (-2*q - 2 + 2)*(-3 + 2 + 0) - q - q + q - 448*q + 6232*q - 2412*q - 923*q.\n | 2451*q\n | ibivibiv/math_instruct | |
Let o be 0 - 8/(-2) - 3. Let k = -1 + 0.9. Let t be ((-3)/12)/((-14)/16). Put t, o, k in descending order.\n | o, t, k\n | ibivibiv/math_instruct | |
List the prime factors of 765021439.\n | 7, 13, 8406829\n | ibivibiv/math_instruct | |
Simplify ((w*w*w/w**2*w**(-30))**(-1/9))**16 assuming w is positive.\n | w**(464/9)\n | ibivibiv/math_instruct | |
What is the ten millions digit of 3813063714?\n | 1\n | ibivibiv/math_instruct | |
Suppose -5*f - 6*j + 100 = -5*j, 2*f + 4*j - 22 = 0. What is the highest common divisor of f and 3?\n | 3\n | ibivibiv/math_instruct | |
Suppose -5*h + z - 139 = -377, -152 = -3*h - 4*z. Which is smaller: h or 46?\n | 46\n | ibivibiv/math_instruct | |
Calculate the remainder when 438608 is divided by 7974.\n | 38\n | ibivibiv/math_instruct | |
Solve -228 = -9*t + 25*t - 28*t for t.\n | 19\n | ibivibiv/math_instruct | |
What is the derivative of -104 - 2*d**3 - 4103*d**2 + 1734*d**2 + 2111*d**2 + 22 + 1098 wrt d?\n | -6*d**2 - 516*d\n | ibivibiv/math_instruct | |
Solve 533 = -x - 3*j + 546, 6 = 2*x + j for x.\n | 1\n | ibivibiv/math_instruct | |
List the prime factors of 60052328.\n | 2, 7, 1072363\n | ibivibiv/math_instruct | |
Let t be 5*1*(3 + -2). Let u = 1231 - 1231. Let y be (-6)/1*4/(-6). Solve -o + 5 = 2*m - y*o, u = t*m - 3*o + 10 for m.\n | -5\n | ibivibiv/math_instruct | |
Let g(p) = p**2 - 6*p - 6. Let a be g(7). Let l(s) = -s**3 - 5*s**2 - 2*s - 11. Let v be l(-5). Let h = 9 + v. What is the highest common factor of a and h?\n | 1\n | ibivibiv/math_instruct | |
Let k(c) = -2*c**2 - 6. Let b(p) = -p**2 - 7. What is 4*b(t) - 5*k(t)?\n | 6*t**2 + 2\n | ibivibiv/math_instruct | |
Let n(y) = -4*y**2 - 495*y + 17868. Calculate n(-153).\n | -33\n | ibivibiv/math_instruct | |
What is 56017 divided by 1?\n | 56017\n | ibivibiv/math_instruct | |
What is the common denominator of -19/9 and -85/10236?\n | 30708\n | ibivibiv/math_instruct | |
What is next in -454, -460, -478, -514, -574?\n | -664\n | ibivibiv/math_instruct | |
Express (-19*i + 97*i - 38*i + (-3 + 1 + 3)*(0*i + 2*i - 3*i))*(-2*i + 3*i + 5*i) in the form t*i + d*i**2 + m and give d.\n | 234\n | ibivibiv/math_instruct | |
Solve -w = 2*v - 11, -3*v + w + 33 = 29 for v.\n | 3\n | ibivibiv/math_instruct | |
Let b be 32973/27 + 4/(-18). Let m = b - 4801/4. Calculate the common denominator of m and -1/4.\n | 4\n | ibivibiv/math_instruct | |
Calculate 25 divided by 27051.\n | 25/27051\n | ibivibiv/math_instruct | |
b"What is the qth term of -4774, -4722, -4670?\n" | 52*q - 4826\n | ibivibiv/math_instruct | |
What is the fifth biggest value in -1/6, -2/7, 3/7, -5, 0, -2507?\n | -5\n | ibivibiv/math_instruct | |
Suppose 0 = a + 2*a - 18. Let d be ((-4)/a)/((-10)/45). Suppose 0 = d*u + 1 - 7. List the prime factors of u.\n | 2\n | ibivibiv/math_instruct | |
Let f be (2 - ((-152)/18 + 5)) + -5. Let p = 11 - 9. Factor -2/3 + 2/9*t**p - f*t.\n | 2*(t - 3)*(t + 1)/9\n | ibivibiv/math_instruct | |
b"What is the pth term of 6399, 6400, 6401?\n" | p + 6398\n | ibivibiv/math_instruct | |
Four letters picked without replacement from vvvvv. Give prob of picking 4 v.\n | 1\n | ibivibiv/math_instruct | |
What is the hundred thousands digit of 970448?\n | 9\n | ibivibiv/math_instruct | |
Let l(g) = -8926*g. Let h(j) = 4*j. Determine l(h(y)).\n | -35704*y\n | ibivibiv/math_instruct | |
Let q be 25/(-6) - 5/(-30). Let n be ((-12)/q)/((-6)/76). Let t be (-2)/(-6) - n/(-78). Which is the second biggest value? (a) t (b) 3/7 (c) -4\n | a\n | ibivibiv/math_instruct | |
What is the greatest common factor of 4 and 6608308?\n | 4\n | ibivibiv/math_instruct | |
Calculate the least common multiple of 26 and 10.\n | 130\n | ibivibiv/math_instruct | |
Find i, given that 423/4 - 1/4*i**2 + 69/2*i = 0.\n | -3, 141\n | ibivibiv/math_instruct | |
What are the prime factors of 10467258?\n | 2, 3, 1744543\n | ibivibiv/math_instruct | |
Is 64634147 a composite number?\n | True\n | ibivibiv/math_instruct | |
Let y(f) = f**3 + 6*f**2 - 7*f + 6. Suppose 4*z - 2*c = -0*c - 24, 3*z - 2*c = -17. Calculate y(z).\n | 6\n | ibivibiv/math_instruct | |
What is 4.313930138 rounded to one decimal place?\n | 4.3\n | ibivibiv/math_instruct | |
What is prob of picking 1 w and 2 k when three letters picked without replacement from {f: 1, k: 3, b: 1, w: 5}?\n | 1/8\n | ibivibiv/math_instruct | |
Rearrange 10*v**2 + 0*v - 11*v - 8*v**3 + 11*v**2 + v**4 + 5*v**3 + 4*v**3 to z*v**2 + k*v**3 + n + d*v**4 + y*v and give k.\n | 1\n | ibivibiv/math_instruct | |
Suppose -4*z - 5*r = -26, 3*z + 5*r - 21 - 1 = 0. Let n be -10*5/z*2880. Round n to the nearest ten thousand.\n | -40000\n | ibivibiv/math_instruct | |
Calculate -54 divided by -5.\n | 54/5\n | ibivibiv/math_instruct | |
What is -3235.4 plus 103?\n | -3132.4\n | ibivibiv/math_instruct | |
Let m be (-16)/(-28)*((-126)/24 - -5). Which is the closest to -2/5? (a) 0.3 (b) -2 (c) -1/5 (d) m\n | c\n | ibivibiv/math_instruct | |
Solve 2*t - 3*w - 4 = -1, 0 = w + 1 for t.\n | 0\n | ibivibiv/math_instruct | |
Let r(z) = -z**3 + 10*z**2 - 6*z - 2. Let p be r(9). Let i be 3/3*0/1. Solve 3*s + 15 = -w, -5*s - w + i*w - p = 0 for s.\n | -5\n | ibivibiv/math_instruct | |
Let r(p) = -p**3 - 8*p**2 - 16*p + 5. Let g = -51 + 47. What is the remainder when (18/10)/((-7)/(-35)) is divided by r(g)?\n | 4\n | ibivibiv/math_instruct | |
Solve -13*f = 664 - 651 for f.\n | -1\n | ibivibiv/math_instruct | |
Calculate the highest common factor of 38 and 209.\n | 19\n | ibivibiv/math_instruct | |
Expand (-18 - 1 - 12)*(3*h**3 - 3*h**3 + h**5) - h**5 + 2*h**5 + 0*h**5.\n | -30*h**5\n | ibivibiv/math_instruct | |
Let s(b) = 9*b**4 - 31. Let p(m) = 4*m**4 - 15. Let r(g) = -14*p(g) + 6*s(g). Differentiate r(n) wrt n.\n | -8*n**3\n | ibivibiv/math_instruct | |
Solve 8*n = 2*r - 38, r + 650*n - 647*n = -16 for r.\n | -1\n | ibivibiv/math_instruct | |
Collect the terms in -68*g + 14*g + 26*g + 19*g + 26*g - 16*g.\n | g\n | ibivibiv/math_instruct | |
-0.251*-1.29\n | 0.32379\n | ibivibiv/math_instruct | |
Simplify (((sqrt(275) + -1*sqrt(275))*1 - sqrt(275))/(sqrt(704) + sqrt(704)*-2))/((1*sqrt(225))/(sqrt(80)*2)).\n | sqrt(5)/3\n | ibivibiv/math_instruct | |
Calculate prob of sequence bf when two letters picked without replacement from {w: 3, b: 2, v: 1, f: 1, n: 1, o: 5}.\n | 1/78\n | ibivibiv/math_instruct | |
What is the second derivative of -113845130*k**2 + 5*k + 3370985?\n | -227690260\n | ibivibiv/math_instruct | |
Let n(x) = -21*x. Let c(v) be the second derivative of 10*v**4/3 - 2*v + 5149. Determine c(n(w)).\n | 17640*w**2\n | ibivibiv/math_instruct | |
Suppose -4*h + 8 = -4. Suppose 0 = -3*c - h*j + 12, -c - 3*j = -2*c. Suppose 0 = -n + c*q + 19, -15 - 50 = -4*n + q. Is n a multiple of 16?\n | True\n | ibivibiv/math_instruct | |
Suppose 224 = -0*s - 8*s. Let l be s/98 - 59/14. Let n(p) = 2*p + 6. Let z be n(-5). Is l != z?\n | True\n | ibivibiv/math_instruct | |
Suppose 2*s + 85 = 5*h - 193, 0 = 5*s + 20. Let j be (2 + -1 + 51)/2. Suppose 0 = 4*v - j - h. What is the remainder when 59 is divided by v?\n | 19\n | ibivibiv/math_instruct | |
Suppose 0 = -4*p - 4. Let a(i) = -2*i + 1. Calculate a(p).\n | 3\n | ibivibiv/math_instruct | |
In base 14, what is -3 + 230?\n | 22b\n | ibivibiv/math_instruct | |
Calculate prob of sequence dhdh when four letters picked without replacement from {j: 5, d: 2, h: 2}.\n | 1/756\n | ibivibiv/math_instruct | |
Express (3 - 3 - 2*r)*(-20 - 214 - 322) - 6*r + 4*r + 0*r - 4 - 10*r + 4 + 0*r in the form g + n*r and give g.\n | 0\n | ibivibiv/math_instruct | |
(-2 - -2) + -42 - (-16 - (29 + -29 - 24))\n | -50\n | ibivibiv/math_instruct |
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