prompt listlengths 2 2 | adversarial bool 1
class | source stringclasses 1
value | conv_id stringlengths 6 8 | unique_conv_id stringlengths 11 13 | turn_id int64 1 1 | data_source stringclasses 1
value | ability stringclasses 1
value | reward_model dict | extra_info dict |
|---|---|---|---|---|---|---|---|---|---|
[
{
"content": "\nThe assistant is designed to be helpful, proactive, and highly interactive.\n\nThe assistant strives to accurately interpret the user's intent throughout the conversation, acknowledging previous interactions to maintain context and continuity. If the user's message is unclear or lacks necessary ... | false | minerva | conv_0 | uniq_conv_0 | 1 | minerva | minerva | {
"ground_truth": "1.6",
"style": "Cute"
} | {
"adversarial": false,
"chat_history": [
{
"content": "Each of the two Magellan telescopes has a diameter of $6.5 \\mathrm{~m}$. In one configuration the effective focal length is $72 \\mathrm{~m}$. Find the diameter of the image of a planet (in $\\mathrm{cm}$ ) at this focus if the angular diameter of t... |
[
{
"content": "\nThe assistant is designed to be helpful, proactive, and highly interactive.\n\nThe assistant strives to accurately interpret the user's intent throughout the conversation, acknowledging previous interactions to maintain context and continuity. If the user's message is unclear or lacks necessary ... | false | minerva | conv_1 | uniq_conv_1 | 1 | minerva | minerva | {
"ground_truth": "4.5e33",
"style": "Cute"
} | {
"adversarial": false,
"chat_history": [
{
"content": "A white dwarf star has an effective temperature, $T_{e}=50,000$ degrees Kelvin, but its radius, $R_{\\mathrm{WD}}$, is comparable to that of the Earth. Take $R_{\\mathrm{WD}}=10^{4} \\mathrm{~km}\\left(10^{7} \\mathrm{~m}\\right.$ or $\\left.10^{9} \... |
[
{
"content": "\nThe assistant is designed to be helpful, proactive, and highly interactive.\n\nThe assistant strives to accurately interpret the user's intent throughout the conversation, acknowledging previous interactions to maintain context and continuity. If the user's message is unclear or lacks necessary ... | false | minerva | conv_2 | uniq_conv_2 | 1 | minerva | minerva | {
"ground_truth": "41.8",
"style": "Cute"
} | {
"adversarial": false,
"chat_history": [
{
"content": "Preamble: A prism is constructed from glass and has sides that form a right triangle with the other two angles equal to $45^{\\circ}$. The sides are $L, L$, and $H$, where $L$ is a leg and $H$ is the hypotenuse. A parallel light beam enters side $L$ ... |
[
{
"content": "\nThe assistant is designed to be helpful, proactive, and highly interactive.\n\nThe assistant strives to accurately interpret the user's intent throughout the conversation, acknowledging previous interactions to maintain context and continuity. If the user's message is unclear or lacks necessary ... | false | minerva | conv_3 | uniq_conv_3 | 1 | minerva | minerva | {
"ground_truth": "20.39",
"style": "Cute"
} | {
"adversarial": false,
"chat_history": [
{
"content": "A particular star has an absolute magnitude $M=-7$. If this star is observed in a galaxy that is at a distance of $3 \\mathrm{Mpc}$, what will its apparent magnitude be?",
"role": "user"
}
],
"index": 3,
"single_turn_completion": "20.... |
[
{
"content": "\nThe assistant is designed to be helpful, proactive, and highly interactive.\n\nThe assistant strives to accurately interpret the user's intent throughout the conversation, acknowledging previous interactions to maintain context and continuity. If the user's message is unclear or lacks necessary ... | false | minerva | conv_4 | uniq_conv_4 | 1 | minerva | minerva | {
"ground_truth": "0.006",
"style": "Cute"
} | {
"adversarial": false,
"chat_history": [
{
"content": "Find the gravitational acceleration due to the Sun at the location of the Earth's orbit (i.e., at a distance of $1 \\mathrm{AU}$ ). Give your answer in meters per second squared, and express it to one significant figure.",
"role": "user"
}... |
[
{
"content": "\nThe assistant is designed to be helpful, proactive, and highly interactive.\n\nThe assistant strives to accurately interpret the user's intent throughout the conversation, acknowledging previous interactions to maintain context and continuity. If the user's message is unclear or lacks necessary ... | false | minerva | conv_5 | uniq_conv_5 | 1 | minerva | minerva | {
"ground_truth": "np.arcsin(10/13)",
"style": "Cute"
} | {
"adversarial": false,
"chat_history": [
{
"content": "Preamble: A collimated light beam propagating in water is incident on the surface (air/water interface) at an angle $\\theta_w$ with respect to the surface normal.\n\nSubproblem 0: If the index of refraction of water is $n=1.3$, find an expression fo... |
[
{
"content": "\nThe assistant is designed to be helpful, proactive, and highly interactive.\n\nThe assistant strives to accurately interpret the user's intent throughout the conversation, acknowledging previous interactions to maintain context and continuity. If the user's message is unclear or lacks necessary ... | false | minerva | conv_6 | uniq_conv_6 | 1 | minerva | minerva | {
"ground_truth": "0.49",
"style": "Cute"
} | {
"adversarial": false,
"chat_history": [
{
"content": "Find the theoretical limiting angular resolution (in arcsec) of a commercial 8-inch (diameter) optical telescope being used in the visible spectrum (at $\\lambda=5000 \\AA=500 \\mathrm{~nm}=5 \\times 10^{-5} \\mathrm{~cm}=5 \\times 10^{-7} \\mathrm{~... |
[
{
"content": "\nThe assistant is designed to be helpful, proactive, and highly interactive.\n\nThe assistant strives to accurately interpret the user's intent throughout the conversation, acknowledging previous interactions to maintain context and continuity. If the user's message is unclear or lacks necessary ... | false | minerva | conv_7 | uniq_conv_7 | 1 | minerva | minerva | {
"ground_truth": "100",
"style": "Cute"
} | {
"adversarial": false,
"chat_history": [
{
"content": "A star has a measured parallax of $0.01^{\\prime \\prime}$, that is, $0.01$ arcseconds. How far away is it, in parsecs?",
"role": "user"
}
],
"index": 7,
"single_turn_completion": "100",
"single_turn_prompt": "A star has a measured ... |
[
{
"content": "\nThe assistant is designed to be helpful, proactive, and highly interactive.\n\nThe assistant strives to accurately interpret the user's intent throughout the conversation, acknowledging previous interactions to maintain context and continuity. If the user's message is unclear or lacks necessary ... | false | minerva | conv_8 | uniq_conv_8 | 1 | minerva | minerva | {
"ground_truth": "0.022",
"style": "Cute"
} | {
"adversarial": false,
"chat_history": [
{
"content": "An extrasolar planet has been observed which passes in front of (i.e., transits) its parent star. If the planet is dark (i.e., contributes essentially no light of its own) and has a surface area that is $2 \\%$ of that of its parent star, find the de... |
[
{
"content": "\nThe assistant is designed to be helpful, proactive, and highly interactive.\n\nThe assistant strives to accurately interpret the user's intent throughout the conversation, acknowledging previous interactions to maintain context and continuity. If the user's message is unclear or lacks necessary ... | false | minerva | conv_9 | uniq_conv_9 | 1 | minerva | minerva | {
"ground_truth": "9.6",
"style": "Cute"
} | {
"adversarial": false,
"chat_history": [
{
"content": "If the Bohr energy levels scale as $Z^{2}$, where $Z$ is the atomic number of the atom (i.e., the charge on the nucleus), estimate the wavelength of a photon that results from a transition from $n=3$ to $n=2$ in Fe, which has $Z=26$. Assume that the ... |
[
{
"content": "\nThe assistant is designed to be helpful, proactive, and highly interactive.\n\nThe assistant strives to accurately interpret the user's intent throughout the conversation, acknowledging previous interactions to maintain context and continuity. If the user's message is unclear or lacks necessary ... | false | minerva | conv_10 | uniq_conv_10 | 1 | minerva | minerva | {
"ground_truth": "3.83e35",
"style": "Cute"
} | {
"adversarial": false,
"chat_history": [
{
"content": "If the Sun's absolute magnitude is $+5$, find the luminosity of a star of magnitude $0$ in ergs/s. A useful constant: the luminosity of the sun is $3.83 \\times 10^{33}$ ergs/s.",
"role": "user"
}
],
"index": 10,
"single_turn_completi... |
[
{
"content": "\nThe assistant is designed to be helpful, proactive, and highly interactive.\n\nThe assistant strives to accurately interpret the user's intent throughout the conversation, acknowledging previous interactions to maintain context and continuity. If the user's message is unclear or lacks necessary ... | false | minerva | conv_11 | uniq_conv_11 | 1 | minerva | minerva | {
"ground_truth": "300",
"style": "Cute"
} | {
"adversarial": false,
"chat_history": [
{
"content": "Preamble: A spectrum is taken of a single star (i.e., one not in a binary). Among the observed spectral lines is one from oxygen whose rest wavelength is $5007 \\AA$. The Doppler shifted oxygen line from this star is observed to be at a wavelength of... |
[
{
"content": "\nThe assistant is designed to be helpful, proactive, and highly interactive.\n\nThe assistant strives to accurately interpret the user's intent throughout the conversation, acknowledging previous interactions to maintain context and continuity. If the user's message is unclear or lacks necessary ... | false | minerva | conv_12 | uniq_conv_12 | 1 | minerva | minerva | {
"ground_truth": "\\frac{2 \\pi c^{2} R^{2}}{\\lambda^{5}\\left[e^{h c /(\\lambda k T)}-1\\right] d^{2}}",
"style": "Cute"
} | {
"adversarial": false,
"chat_history": [
{
"content": "The differential luminosity from a star, $\\Delta L$, with an approximate blackbody spectrum, is given by:\n\\[\n\\Delta L=\\frac{8 \\pi^{2} c^{2} R^{2}}{\\lambda^{5}\\left[e^{h c /(\\lambda k T)}-1\\right]} \\Delta \\lambda\n\\]\nwhere $R$ is the ra... |
[
{
"content": "\nThe assistant is designed to be helpful, proactive, and highly interactive.\n\nThe assistant strives to accurately interpret the user's intent throughout the conversation, acknowledging previous interactions to maintain context and continuity. If the user's message is unclear or lacks necessary ... | false | minerva | conv_13 | uniq_conv_13 | 1 | minerva | minerva | {
"ground_truth": "8.7e8",
"style": "Cute"
} | {
"adversarial": false,
"chat_history": [
{
"content": "Preamble: A very hot star is detected in the galaxy M31 located at a distance of $800 \\mathrm{kpc}$. The star has a temperature $T = 6 \\times 10^{5} K$ and produces a flux of $10^{-12} \\mathrm{erg} \\cdot \\mathrm{s}^{-1} \\mathrm{cm}^{-2}$ at the... |
[
{
"content": "\nThe assistant is designed to be helpful, proactive, and highly interactive.\n\nThe assistant strives to accurately interpret the user's intent throughout the conversation, acknowledging previous interactions to maintain context and continuity. If the user's message is unclear or lacks necessary ... | false | minerva | conv_14 | uniq_conv_14 | 1 | minerva | minerva | {
"ground_truth": "0.003",
"style": "Cute"
} | {
"adversarial": false,
"chat_history": [
{
"content": "A star is at a distance from the Earth of $300 \\mathrm{pc}$. Find its parallax angle, $\\pi$, in arcseconds to one significant figure.",
"role": "user"
}
],
"index": 14,
"single_turn_completion": "0.003",
"single_turn_prompt": "A s... |
[
{
"content": "\nThe assistant is designed to be helpful, proactive, and highly interactive.\n\nThe assistant strives to accurately interpret the user's intent throughout the conversation, acknowledging previous interactions to maintain context and continuity. If the user's message is unclear or lacks necessary ... | false | minerva | conv_15 | uniq_conv_15 | 1 | minerva | minerva | {
"ground_truth": "4e33",
"style": "Cute"
} | {
"adversarial": false,
"chat_history": [
{
"content": "The Sun's effective temperature, $T_{e}$, is 5800 Kelvin, and its radius is $7 \\times 10^{10} \\mathrm{~cm}\\left(7 \\times 10^{8}\\right.$ m). Compute the luminosity (power output) of the Sun in erg/s. Treat the Sun as a blackbody radiator, and giv... |
[
{
"content": "\nThe assistant is designed to be helpful, proactive, and highly interactive.\n\nThe assistant strives to accurately interpret the user's intent throughout the conversation, acknowledging previous interactions to maintain context and continuity. If the user's message is unclear or lacks necessary ... | false | minerva | conv_16 | uniq_conv_16 | 1 | minerva | minerva | {
"ground_truth": "4.49",
"style": "Cute"
} | {
"adversarial": false,
"chat_history": [
{
"content": "Use the Bohr model of the atom to compute the wavelength of the transition from the $n=100$ to $n=99$ levels, in centimeters. [Uscful relation: the wavelength of $L \\alpha$ ( $\\mathrm{n}=2$ to $\\mathrm{n}=1$ transition) is $1216 \\AA$.]",
"r... |
[
{
"content": "\nThe assistant is designed to be helpful, proactive, and highly interactive.\n\nThe assistant strives to accurately interpret the user's intent throughout the conversation, acknowledging previous interactions to maintain context and continuity. If the user's message is unclear or lacks necessary ... | false | minerva | conv_17 | uniq_conv_17 | 1 | minerva | minerva | {
"ground_truth": "0.01",
"style": "Cute"
} | {
"adversarial": false,
"chat_history": [
{
"content": "Preamble: A radio interferometer, operating at a wavelength of $1 \\mathrm{~cm}$, consists of 100 small dishes, each $1 \\mathrm{~m}$ in diameter, distributed randomly within a $1 \\mathrm{~km}$ diameter circle. \n\nWhat is the angular resolution of ... |
[
{
"content": "\nThe assistant is designed to be helpful, proactive, and highly interactive.\n\nThe assistant strives to accurately interpret the user's intent throughout the conversation, acknowledging previous interactions to maintain context and continuity. If the user's message is unclear or lacks necessary ... | false | minerva | conv_18 | uniq_conv_18 | 1 | minerva | minerva | {
"ground_truth": "3.3e12",
"style": "Cute"
} | {
"adversarial": false,
"chat_history": [
{
"content": "Preamble: Orbital Dynamics: A binary system consists of two stars in circular orbit about a common center of mass, with an orbital period, $P_{\\text {orb }}=10$ days. Star 1 is observed in the visible band, and Doppler measurements show that its orb... |
[
{
"content": "\nThe assistant is designed to be helpful, proactive, and highly interactive.\n\nThe assistant strives to accurately interpret the user's intent throughout the conversation, acknowledging previous interactions to maintain context and continuity. If the user's message is unclear or lacks necessary ... | false | minerva | conv_19 | uniq_conv_19 | 1 | minerva | minerva | {
"ground_truth": "10",
"style": "Cute"
} | {
"adversarial": false,
"chat_history": [
{
"content": "If a star cluster is made up of $10^{4}$ stars, each of whose absolute magnitude is $-5$, compute the combined apparent magnitude of the cluster if it is located at a distance of $1 \\mathrm{Mpc}$.",
"role": "user"
}
],
"index": 19,
"... |
[
{
"content": "\nThe assistant is designed to be helpful, proactive, and highly interactive.\n\nThe assistant strives to accurately interpret the user's intent throughout the conversation, acknowledging previous interactions to maintain context and continuity. If the user's message is unclear or lacks necessary ... | false | minerva | conv_20 | uniq_conv_20 | 1 | minerva | minerva | {
"ground_truth": "6630",
"style": "Cute"
} | {
"adversarial": false,
"chat_history": [
{
"content": "A galaxy moves directly away from us with a speed of $3000 \\mathrm{~km} \\mathrm{~s}^{-1}$. Find the wavelength of the $\\mathrm{H} \\alpha$ line observed at the Earth, in Angstroms. The rest wavelength of $\\mathrm{H} \\alpha$ is $6565 \\AA$. Take... |
[
{
"content": "\nThe assistant is designed to be helpful, proactive, and highly interactive.\n\nThe assistant strives to accurately interpret the user's intent throughout the conversation, acknowledging previous interactions to maintain context and continuity. If the user's message is unclear or lacks necessary ... | false | minerva | conv_21 | uniq_conv_21 | 1 | minerva | minerva | {
"ground_truth": "1.2",
"style": "Cute"
} | {
"adversarial": false,
"chat_history": [
{
"content": "The Spitzer Space Telescope has an effective diameter of $85 \\mathrm{cm}$, and a typical wavelength used for observation of $5 \\mu \\mathrm{m}$, or 5 microns. Based on this information, compute an estimate for the angular resolution of the Spitzer ... |
[
{
"content": "\nThe assistant is designed to be helpful, proactive, and highly interactive.\n\nThe assistant strives to accurately interpret the user's intent throughout the conversation, acknowledging previous interactions to maintain context and continuity. If the user's message is unclear or lacks necessary ... | false | minerva | conv_22 | uniq_conv_22 | 1 | minerva | minerva | {
"ground_truth": "3e6",
"style": "Cute"
} | {
"adversarial": false,
"chat_history": [
{
"content": "It has long been suspected that there is a massive black hole near the center of our Galaxy. Recently, a group of astronmers determined the parameters of a star that is orbiting the suspected black hole. The orbital period is 15 years, and the orbita... |
[
{
"content": "\nThe assistant is designed to be helpful, proactive, and highly interactive.\n\nThe assistant strives to accurately interpret the user's intent throughout the conversation, acknowledging previous interactions to maintain context and continuity. If the user's message is unclear or lacks necessary ... | false | minerva | conv_23 | uniq_conv_23 | 1 | minerva | minerva | {
"ground_truth": "7e37",
"style": "Cute"
} | {
"adversarial": false,
"chat_history": [
{
"content": "Preamble: A very hot star is detected in the galaxy M31 located at a distance of $800 \\mathrm{kpc}$. The star has a temperature $T = 6 \\times 10^{5} K$ and produces a flux of $10^{-12} \\mathrm{erg} \\cdot \\mathrm{s}^{-1} \\mathrm{cm}^{-2}$ at the... |
[
{
"content": "\nThe assistant is designed to be helpful, proactive, and highly interactive.\n\nThe assistant strives to accurately interpret the user's intent throughout the conversation, acknowledging previous interactions to maintain context and continuity. If the user's message is unclear or lacks necessary ... | false | minerva | conv_24 | uniq_conv_24 | 1 | minerva | minerva | {
"ground_truth": "50",
"style": "Cute"
} | {
"adversarial": false,
"chat_history": [
{
"content": "A large ground-based telescope has an effective focal length of 10 meters. Two astronomical objects are separated by 1 arc second in the sky. How far apart will the two corresponding images be in the focal plane, in microns?",
"role": "user"
... |
[
{
"content": "\nThe assistant is designed to be helpful, proactive, and highly interactive.\n\nThe assistant strives to accurately interpret the user's intent throughout the conversation, acknowledging previous interactions to maintain context and continuity. If the user's message is unclear or lacks necessary ... | false | minerva | conv_25 | uniq_conv_25 | 1 | minerva | minerva | {
"ground_truth": "\\frac{a M^{1 / 3}}{G M^{2 / 3}+b}",
"style": "Cute"
} | {
"adversarial": false,
"chat_history": [
{
"content": "The equation of state for cold (non-relativistic) matter may be approximated as:\n\\[\nP=a \\rho^{5 / 3}-b \\rho^{4 / 3}\n\\]\nwhere $P$ is the pressure, $\\rho$ the density, and $a$ and $b$ are fixed constants. Use a dimensional analysis of the equa... |
[
{
"content": "\nThe assistant is designed to be helpful, proactive, and highly interactive.\n\nThe assistant strives to accurately interpret the user's intent throughout the conversation, acknowledging previous interactions to maintain context and continuity. If the user's message is unclear or lacks necessary ... | false | minerva | conv_26 | uniq_conv_26 | 1 | minerva | minerva | {
"ground_truth": "7.5e7",
"style": "Cute"
} | {
"adversarial": false,
"chat_history": [
{
"content": "Take the total energy (potential plus thermal) of the Sun to be given by the simple expression:\n\\[\nE \\simeq-\\frac{G M^{2}}{R}\n\\]\nwhere $M$ and $R$ are the mass and radius, respectively. Suppose that the energy generation in the Sun were sudde... |
[
{
"content": "\nThe assistant is designed to be helpful, proactive, and highly interactive.\n\nThe assistant strives to accurately interpret the user's intent throughout the conversation, acknowledging previous interactions to maintain context and continuity. If the user's message is unclear or lacks necessary ... | false | minerva | conv_27 | uniq_conv_27 | 1 | minerva | minerva | {
"ground_truth": "\\frac{dM}{dt}=\\frac{10^{5} L_{\\odot}}{0.007 c^{2} M_{\\odot}^{6}} M^{6}",
"style": "Cute"
} | {
"adversarial": false,
"chat_history": [
{
"content": "Preamble: Once a star like the Sun starts to ascend the giant branch its luminosity, to a good approximation, is given by:\n\\[\nL=\\frac{10^{5} L_{\\odot}}{M_{\\odot}^{6}} M_{\\text {core }}^{6}\n\\]\nwhere the symbol $\\odot$ stands for the solar v... |
[
{
"content": "\nThe assistant is designed to be helpful, proactive, and highly interactive.\n\nThe assistant strives to accurately interpret the user's intent throughout the conversation, acknowledging previous interactions to maintain context and continuity. If the user's message is unclear or lacks necessary ... | false | minerva | conv_28 | uniq_conv_28 | 1 | minerva | minerva | {
"ground_truth": "\\left[P_{0}^{2 / 5}-\\frac{2}{5} g K^{-3 / 5} z\\right]^{5 / 2}",
"style": "Cute"
} | {
"adversarial": false,
"chat_history": [
{
"content": "A star of radius, $R$, and mass, $M$, has an atmosphere that obeys a polytropic equation of state:\n\\[\nP=K \\rho^{5 / 3} \\text {, }\n\\]\nwhere $P$ is the gas pressure, $\\rho$ is the gas density (mass per unit volume), and $K$ is a constant throu... |
[
{
"content": "\nThe assistant is designed to be helpful, proactive, and highly interactive.\n\nThe assistant strives to accurately interpret the user's intent throughout the conversation, acknowledging previous interactions to maintain context and continuity. If the user's message is unclear or lacks necessary ... | false | minerva | conv_29 | uniq_conv_29 | 1 | minerva | minerva | {
"ground_truth": "1.75",
"style": "Cute"
} | {
"adversarial": false,
"chat_history": [
{
"content": "An eclipsing binary consists of two stars of different radii and effective temperatures. Star 1 has radius $R_{1}$ and $T_{1}$, and Star 2 has $R_{2}=0.5 R_{1}$ and $T_{2}=2 T_{1}$. Find the change in bolometric magnitude of the binary, $\\Delta m_{\... |
[
{
"content": "\nThe assistant is designed to be helpful, proactive, and highly interactive.\n\nThe assistant strives to accurately interpret the user's intent throughout the conversation, acknowledging previous interactions to maintain context and continuity. If the user's message is unclear or lacks necessary ... | false | minerva | conv_30 | uniq_conv_30 | 1 | minerva | minerva | {
"ground_truth": "\\sqrt{4 \\pi G \\rho_{0} r_{0}^{2}}",
"style": "Cute"
} | {
"adversarial": false,
"chat_history": [
{
"content": "Preamble: It has been suggested that our Galaxy has a spherically symmetric dark-matter halo with a density distribution, $\\rho_{\\text {dark }}(r)$, given by:\n\\[\n\\rho_{\\text {dark }}(r)=\\rho_{0}\\left(\\frac{r_{0}}{r}\\right)^{2},\n\\]\nwhere... |
[
{
"content": "\nThe assistant is designed to be helpful, proactive, and highly interactive.\n\nThe assistant strives to accurately interpret the user's intent throughout the conversation, acknowledging previous interactions to maintain context and continuity. If the user's message is unclear or lacks necessary ... | false | minerva | conv_31 | uniq_conv_31 | 1 | minerva | minerva | {
"ground_truth": "0.33",
"style": "Cute"
} | {
"adversarial": false,
"chat_history": [
{
"content": "The Very Large Array (VLA) telescope has an effective diameter of $36 \\mathrm{~km}$, and a typical wavelength used for observation at this facility might be $6 \\mathrm{~cm}$. Based on this information, compute an estimate for the angular resolutio... |
[
{
"content": "\nThe assistant is designed to be helpful, proactive, and highly interactive.\n\nThe assistant strives to accurately interpret the user's intent throughout the conversation, acknowledging previous interactions to maintain context and continuity. If the user's message is unclear or lacks necessary ... | false | minerva | conv_32 | uniq_conv_32 | 1 | minerva | minerva | {
"ground_truth": "27.39",
"style": "Cute"
} | {
"adversarial": false,
"chat_history": [
{
"content": "Subproblem 0: A particular star has an absolute magnitude $M=-7$. If this star is observed in a galaxy that is at a distance of $3 \\mathrm{Mpc}$, what will its apparent magnitude be? \n\n\nSolution: \\[\n\\text { Given: } M=-7 \\text { and } d=3 \\m... |
[
{
"content": "\nThe assistant is designed to be helpful, proactive, and highly interactive.\n\nThe assistant strives to accurately interpret the user's intent throughout the conversation, acknowledging previous interactions to maintain context and continuity. If the user's message is unclear or lacks necessary ... | false | minerva | conv_33 | uniq_conv_33 | 1 | minerva | minerva | {
"ground_truth": "24.4",
"style": "Cute"
} | {
"adversarial": false,
"chat_history": [
{
"content": "Find the distance modulus to the Andromeda galaxy (M31). Take the distance to Andromeda to be $750 \\mathrm{kpc}$, and answer to three significant figures.",
"role": "user"
}
],
"index": 33,
"single_turn_completion": "24.4",
"single... |
[
{
"content": "\nThe assistant is designed to be helpful, proactive, and highly interactive.\n\nThe assistant strives to accurately interpret the user's intent throughout the conversation, acknowledging previous interactions to maintain context and continuity. If the user's message is unclear or lacks necessary ... | false | minerva | conv_34 | uniq_conv_34 | 1 | minerva | minerva | {
"ground_truth": "0.05",
"style": "Cute"
} | {
"adversarial": false,
"chat_history": [
{
"content": "The Hubble Space telescope has an effective diameter of $2.5 \\mathrm{~m}$, and a typical wavelength used for observation by the Hubble might be $0.6 \\mu \\mathrm{m}$, or 600 nanometers (typical optical wavelength). Based on this information, comput... |
[
{
"content": "\nThe assistant is designed to be helpful, proactive, and highly interactive.\n\nThe assistant strives to accurately interpret the user's intent throughout the conversation, acknowledging previous interactions to maintain context and continuity. If the user's message is unclear or lacks necessary ... | false | minerva | conv_35 | uniq_conv_35 | 1 | minerva | minerva | {
"ground_truth": "\\arcsin{1.3 \\sin{\\theta_w}}",
"style": "Cute"
} | {
"adversarial": false,
"chat_history": [
{
"content": "Preamble: A collimated light beam propagating in water is incident on the surface (air/water interface) at an angle $\\theta_w$ with respect to the surface normal.\n\nIf the index of refraction of water is $n=1.3$, find an expression for the angle of... |
[
{
"content": "\nThe assistant is designed to be helpful, proactive, and highly interactive.\n\nThe assistant strives to accurately interpret the user's intent throughout the conversation, acknowledging previous interactions to maintain context and continuity. If the user's message is unclear or lacks necessary ... | false | minerva | conv_36 | uniq_conv_36 | 1 | minerva | minerva | {
"ground_truth": "0.15",
"style": "Cute"
} | {
"adversarial": false,
"chat_history": [
{
"content": "What fraction of the rest mass energy is released (in the form of radiation) when a mass $\\Delta M$ is dropped from infinity onto the surface of a neutron star with $M=1 M_{\\odot}$ and $R=10$ $\\mathrm{km}$ ?",
"role": "user"
}
],
"in... |
[
{
"content": "\nThe assistant is designed to be helpful, proactive, and highly interactive.\n\nThe assistant strives to accurately interpret the user's intent throughout the conversation, acknowledging previous interactions to maintain context and continuity. If the user's message is unclear or lacks necessary ... | false | minerva | conv_37 | uniq_conv_37 | 1 | minerva | minerva | {
"ground_truth": "2e27",
"style": "Cute"
} | {
"adversarial": false,
"chat_history": [
{
"content": "Preamble: The density of stars in a particular globular star cluster is $10^{6} \\mathrm{pc}^{-3}$. Take the stars to have the same radius as the Sun, and to have an average speed of $10 \\mathrm{~km} \\mathrm{sec}^{-1}$.\n\nFind the mean free path f... |
[
{
"content": "\nThe assistant is designed to be helpful, proactive, and highly interactive.\n\nThe assistant strives to accurately interpret the user's intent throughout the conversation, acknowledging previous interactions to maintain context and continuity. If the user's message is unclear or lacks necessary ... | false | minerva | conv_38 | uniq_conv_38 | 1 | minerva | minerva | {
"ground_truth": "-1./3",
"style": "Cute"
} | {
"adversarial": false,
"chat_history": [
{
"content": "For a gas supported by degenerate electron pressure, the pressure is given by:\n\\[\nP=K \\rho^{5 / 3}\n\\]\nwhere $K$ is a constant and $\\rho$ is the mass density. If a star is totally supported by degenerate electron pressure, use a dimensional an... |
[
{
"content": "\nThe assistant is designed to be helpful, proactive, and highly interactive.\n\nThe assistant strives to accurately interpret the user's intent throughout the conversation, acknowledging previous interactions to maintain context and continuity. If the user's message is unclear or lacks necessary ... | false | minerva | conv_39 | uniq_conv_39 | 1 | minerva | minerva | {
"ground_truth": "0.033",
"style": "Cute"
} | {
"adversarial": false,
"chat_history": [
{
"content": "A galaxy moves directly away from us with speed $v$, and the wavelength of its $\\mathrm{H} \\alpha$ line is observed to be $6784 \\AA$. The rest wavelength of $\\mathrm{H} \\alpha$ is $6565 \\AA$. Find $v/c$.",
"role": "user"
}
],
"ind... |
[
{
"content": "\nThe assistant is designed to be helpful, proactive, and highly interactive.\n\nThe assistant strives to accurately interpret the user's intent throughout the conversation, acknowledging previous interactions to maintain context and continuity. If the user's message is unclear or lacks necessary ... | false | minerva | conv_40 | uniq_conv_40 | 1 | minerva | minerva | {
"ground_truth": "0.5613",
"style": "Cute"
} | {
"adversarial": false,
"chat_history": [
{
"content": "A candle has a power in the visual band of roughly $3$ Watts. When this candle is placed at a distance of $3 \\mathrm{~km}$ it has the same apparent brightness as a certain star. Assume that this star has the same luminosity as the Sun in the visual ... |
[
{
"content": "\nThe assistant is designed to be helpful, proactive, and highly interactive.\n\nThe assistant strives to accurately interpret the user's intent throughout the conversation, acknowledging previous interactions to maintain context and continuity. If the user's message is unclear or lacks necessary ... | false | minerva | conv_41 | uniq_conv_41 | 1 | minerva | minerva | {
"ground_truth": "\\frac{v_{0}}{r_{0}} \\frac{1}{\\left(1+r / r_{0}\\right)^{3 / 2}}",
"style": "Cute"
} | {
"adversarial": false,
"chat_history": [
{
"content": "Preamble: A galaxy is found to have a rotation curve, $v(r)$, given by\n\\[\nv(r)=\\frac{\\left(\\frac{r}{r_{0}}\\right)}{\\left(1+\\frac{r}{r_{0}}\\right)^{3 / 2}} v_{0}\n\\]\nwhere $r$ is the radial distance from the center of the galaxy, $r_{0}$ i... |
[
{
"content": "\nThe assistant is designed to be helpful, proactive, and highly interactive.\n\nThe assistant strives to accurately interpret the user's intent throughout the conversation, acknowledging previous interactions to maintain context and continuity. If the user's message is unclear or lacks necessary ... | false | minerva | conv_42 | uniq_conv_42 | 1 | minerva | minerva | {
"ground_truth": "2.75e11",
"style": "Cute"
} | {
"adversarial": false,
"chat_history": [
{
"content": "Preamble: Orbital Dynamics: A binary system consists of two stars in circular orbit about a common center of mass, with an orbital period, $P_{\\text {orb }}=10$ days. Star 1 is observed in the visible band, and Doppler measurements show that its orb... |
[
{
"content": "\nThe assistant is designed to be helpful, proactive, and highly interactive.\n\nThe assistant strives to accurately interpret the user's intent throughout the conversation, acknowledging previous interactions to maintain context and continuity. If the user's message is unclear or lacks necessary ... | false | minerva | conv_43 | uniq_conv_43 | 1 | minerva | minerva | {
"ground_truth": "6e13",
"style": "Cute"
} | {
"adversarial": false,
"chat_history": [
{
"content": "Preamble: The density of stars in a particular globular star cluster is $10^{6} \\mathrm{pc}^{-3}$. Take the stars to have the same radius as the Sun, and to have an average speed of $10 \\mathrm{~km} \\mathrm{sec}^{-1}$.\n\nSubproblem 0: Find the me... |
[
{
"content": "\nThe assistant is designed to be helpful, proactive, and highly interactive.\n\nThe assistant strives to accurately interpret the user's intent throughout the conversation, acknowledging previous interactions to maintain context and continuity. If the user's message is unclear or lacks necessary ... | false | minerva | conv_44 | uniq_conv_44 | 1 | minerva | minerva | {
"ground_truth": "1e-5",
"style": "Cute"
} | {
"adversarial": false,
"chat_history": [
{
"content": "Preamble: A radio interferometer, operating at a wavelength of $1 \\mathrm{~cm}$, consists of 100 small dishes, each $1 \\mathrm{~m}$ in diameter, distributed randomly within a $1 \\mathrm{~km}$ diameter circle. \n\nSubproblem 0: What is the angular ... |
[
{
"content": "\nThe assistant is designed to be helpful, proactive, and highly interactive.\n\nThe assistant strives to accurately interpret the user's intent throughout the conversation, acknowledging previous interactions to maintain context and continuity. If the user's message is unclear or lacks necessary ... | false | minerva | conv_45 | uniq_conv_45 | 1 | minerva | minerva | {
"ground_truth": "-10",
"style": "Cute"
} | {
"adversarial": false,
"chat_history": [
{
"content": "If a star cluster is made up of $10^{6}$ stars whose absolute magnitude is the same as that of the Sun (+5), compute the combined magnitude of the cluster if it is located at a distance of $10 \\mathrm{pc}$.",
"role": "user"
}
],
"index... |
[
{
"content": "\nThe assistant is designed to be helpful, proactive, and highly interactive.\n\nThe assistant strives to accurately interpret the user's intent throughout the conversation, acknowledging previous interactions to maintain context and continuity. If the user's message is unclear or lacks necessary ... | false | minerva | conv_46 | uniq_conv_46 | 1 | minerva | minerva | {
"ground_truth": "15625",
"style": "Cute"
} | {
"adversarial": false,
"chat_history": [
{
"content": "A certain red giant has a radius that is 500 times that of the Sun, and a temperature that is $1 / 2$ that of the Sun's temperature. Find its bolometric (total) luminosity in units of the bolometric luminosity of the Sun.",
"role": "user"
}... |
[
{
"content": "\nThe assistant is designed to be helpful, proactive, and highly interactive.\n\nThe assistant strives to accurately interpret the user's intent throughout the conversation, acknowledging previous interactions to maintain context and continuity. If the user's message is unclear or lacks necessary ... | false | minerva | conv_47 | uniq_conv_47 | 1 | minerva | minerva | {
"ground_truth": "1e-3",
"style": "Cute"
} | {
"adversarial": false,
"chat_history": [
{
"content": "Suppose air molecules have a collision cross section of $10^{-16} \\mathrm{~cm}^{2}$. If the (number) density of air molecules is $10^{19} \\mathrm{~cm}^{-3}$, what is the collision mean free path in cm? Answer to one significant figure.",
"rol... |
[
{
"content": "\nThe assistant is designed to be helpful, proactive, and highly interactive.\n\nThe assistant strives to accurately interpret the user's intent throughout the conversation, acknowledging previous interactions to maintain context and continuity. If the user's message is unclear or lacks necessary ... | false | minerva | conv_48 | uniq_conv_48 | 1 | minerva | minerva | {
"ground_truth": "3",
"style": "Cute"
} | {
"adversarial": false,
"chat_history": [
{
"content": "Two stars have the same surface temperature. Star 1 has a radius that is $2.5$ times larger than the radius of star 2. Star 1 is ten times farther away than star 2. What is the absolute value of the difference in apparent magnitude between the two st... |
[
{
"content": "\nThe assistant is designed to be helpful, proactive, and highly interactive.\n\nThe assistant strives to accurately interpret the user's intent throughout the conversation, acknowledging previous interactions to maintain context and continuity. If the user's message is unclear or lacks necessary ... | false | minerva | conv_49 | uniq_conv_49 | 1 | minerva | minerva | {
"ground_truth": "-3./2",
"style": "Cute"
} | {
"adversarial": false,
"chat_history": [
{
"content": "What is the slope of a $\\log N(>F)$ vs. $\\log F$ curve for a homogeneous distribution of objects, each of luminosity, $L$, where $F$ is the flux at the observer, and $N$ is the number of objects observed per square degree on the sky?",
"role"... |
[
{
"content": "\nThe assistant is designed to be helpful, proactive, and highly interactive.\n\nThe assistant strives to accurately interpret the user's intent throughout the conversation, acknowledging previous interactions to maintain context and continuity. If the user's message is unclear or lacks necessary ... | false | minerva | conv_50 | uniq_conv_50 | 1 | minerva | minerva | {
"ground_truth": "2.7778e-6",
"style": "Cute"
} | {
"adversarial": false,
"chat_history": [
{
"content": "Preamble: Comparison of Radio and Optical Telescopes.\n\nThe Very Large Array (VLA) is used to make an interferometric map of the Orion Nebula at a wavelength of $10 \\mathrm{~cm}$. What is the best angular resolution of the radio image that can be p... |
[
{
"content": "\nThe assistant is designed to be helpful, proactive, and highly interactive.\n\nThe assistant strives to accurately interpret the user's intent throughout the conversation, acknowledging previous interactions to maintain context and continuity. If the user's message is unclear or lacks necessary ... | false | minerva | conv_51 | uniq_conv_51 | 1 | minerva | minerva | {
"ground_truth": "-7",
"style": "Cute"
} | {
"adversarial": false,
"chat_history": [
{
"content": "A globular cluster has $10^{6}$ stars each of apparent magnitude $+8$. What is the combined apparent magnitude of the entire cluster?",
"role": "user"
}
],
"index": 51,
"single_turn_completion": "-7",
"single_turn_prompt": "A globul... |
[
{
"content": "\nThe assistant is designed to be helpful, proactive, and highly interactive.\n\nThe assistant strives to accurately interpret the user's intent throughout the conversation, acknowledging previous interactions to maintain context and continuity. If the user's message is unclear or lacks necessary ... | false | minerva | conv_52 | uniq_conv_52 | 1 | minerva | minerva | {
"ground_truth": "48",
"style": "Cute"
} | {
"adversarial": false,
"chat_history": [
{
"content": "Preamble: A very hot star is detected in the galaxy M31 located at a distance of $800 \\mathrm{kpc}$. The star has a temperature $T = 6 \\times 10^{5} K$ and produces a flux of $10^{-12} \\mathrm{erg} \\cdot \\mathrm{s}^{-1} \\mathrm{cm}^{-2}$ at the... |
[
{
"content": "\nThe assistant is designed to be helpful, proactive, and highly interactive.\n\nThe assistant strives to accurately interpret the user's intent throughout the conversation, acknowledging previous interactions to maintain context and continuity. If the user's message is unclear or lacks necessary ... | false | minerva | conv_53 | uniq_conv_53 | 1 | minerva | minerva | {
"ground_truth": "16",
"style": "Cute"
} | {
"adversarial": false,
"chat_history": [
{
"content": "A Boolean function $F(A, B)$ is said to be universal if any arbitrary boolean function can be constructed by using nested $F(A, B)$ functions. A universal function is useful, since using it we can build any function we wish out of a single part. For ... |
[
{
"content": "\nThe assistant is designed to be helpful, proactive, and highly interactive.\n\nThe assistant strives to accurately interpret the user's intent throughout the conversation, acknowledging previous interactions to maintain context and continuity. If the user's message is unclear or lacks necessary ... | false | minerva | conv_54 | uniq_conv_54 | 1 | minerva | minerva | {
"ground_truth": "0.192",
"style": "Cute"
} | {
"adversarial": false,
"chat_history": [
{
"content": "Unfortunately, a mutant gene can turn box people into triangles late in life. A laboratory test has been developed which can spot the gene early so that the dreaded triangle transformation can be prevented by medications. This test is 95 percent accu... |
[
{
"content": "\nThe assistant is designed to be helpful, proactive, and highly interactive.\n\nThe assistant strives to accurately interpret the user's intent throughout the conversation, acknowledging previous interactions to maintain context and continuity. If the user's message is unclear or lacks necessary ... | false | minerva | conv_55 | uniq_conv_55 | 1 | minerva | minerva | {
"ground_truth": "0.5978",
"style": "Cute"
} | {
"adversarial": false,
"chat_history": [
{
"content": "Buzz, the hot new dining spot on campus, emphasizes simplicity. It only has two items on the menu, burgers and zucchini. Customers make a choice as they enter (they are not allowed to order both), and inform the cooks in the back room by shouting out... |
[
{
"content": "\nThe assistant is designed to be helpful, proactive, and highly interactive.\n\nThe assistant strives to accurately interpret the user's intent throughout the conversation, acknowledging previous interactions to maintain context and continuity. If the user's message is unclear or lacks necessary ... | false | minerva | conv_56 | uniq_conv_56 | 1 | minerva | minerva | {
"ground_truth": "11000",
"style": "Cute"
} | {
"adversarial": false,
"chat_history": [
{
"content": "Preamble: Given the following data from an Experimental Forest, answer the following questions. Show your work and units.\n$\\begin{array}{ll}\\text { Total vegetative biomass } & 80,000 \\mathrm{kcal} \\mathrm{m}^{-2} \\\\ \\text { Detritus and orga... |
[
{
"content": "\nThe assistant is designed to be helpful, proactive, and highly interactive.\n\nThe assistant strives to accurately interpret the user's intent throughout the conversation, acknowledging previous interactions to maintain context and continuity. If the user's message is unclear or lacks necessary ... | false | minerva | conv_57 | uniq_conv_57 | 1 | minerva | minerva | {
"ground_truth": "0.53",
"style": "Cute"
} | {
"adversarial": false,
"chat_history": [
{
"content": "Preamble: A population of 100 ferrets is introduced to a large island in the beginning of 1990 . Ferrets have an intrinsic growth rate, $r_{\\max }$ of $1.3 \\mathrm{yr}^{-1}$.\n\nSubproblem 0: Assuming unlimited resources-i.e., there are enough reso... |
[
{
"content": "\nThe assistant is designed to be helpful, proactive, and highly interactive.\n\nThe assistant strives to accurately interpret the user's intent throughout the conversation, acknowledging previous interactions to maintain context and continuity. If the user's message is unclear or lacks necessary ... | false | minerva | conv_58 | uniq_conv_58 | 1 | minerva | minerva | {
"ground_truth": "15000",
"style": "Cute"
} | {
"adversarial": false,
"chat_history": [
{
"content": "Preamble: Given the following data from an Experimental Forest, answer the following questions. Show your work and units.\n$\\begin{array}{ll}\\text { Total vegetative biomass } & 80,000 \\mathrm{kcal} \\mathrm{m}^{-2} \\\\ \\text { Detritus and orga... |
[
{
"content": "\nThe assistant is designed to be helpful, proactive, and highly interactive.\n\nThe assistant strives to accurately interpret the user's intent throughout the conversation, acknowledging previous interactions to maintain context and continuity. If the user's message is unclear or lacks necessary ... | false | minerva | conv_59 | uniq_conv_59 | 1 | minerva | minerva | {
"ground_truth": "1538",
"style": "Cute"
} | {
"adversarial": false,
"chat_history": [
{
"content": "Preamble: The Peak District Moorlands in the United Kingdom store 20 million tonnes of carbon, almost half of the carbon stored in the soils of the entire United Kingdom (the Moorlands are only $8 \\%$ of the land area). In pristine condition, these ... |
[
{
"content": "\nThe assistant is designed to be helpful, proactive, and highly interactive.\n\nThe assistant strives to accurately interpret the user's intent throughout the conversation, acknowledging previous interactions to maintain context and continuity. If the user's message is unclear or lacks necessary ... | false | minerva | conv_60 | uniq_conv_60 | 1 | minerva | minerva | {
"ground_truth": "4.4e7",
"style": "Cute"
} | {
"adversarial": false,
"chat_history": [
{
"content": "Preamble: A population of 100 ferrets is introduced to a large island in the beginning of 1990 . Ferrets have an intrinsic growth rate, $r_{\\max }$ of $1.3 \\mathrm{yr}^{-1}$.\n\nAssuming unlimited resources-i.e., there are enough resources on this ... |
[
{
"content": "\nThe assistant is designed to be helpful, proactive, and highly interactive.\n\nThe assistant strives to accurately interpret the user's intent throughout the conversation, acknowledging previous interactions to maintain context and continuity. If the user's message is unclear or lacks necessary ... | false | minerva | conv_61 | uniq_conv_61 | 1 | minerva | minerva | {
"ground_truth": "I(0)",
"style": "Cute"
} | {
"adversarial": false,
"chat_history": [
{
"content": "Preamble: The following subproblems refer to a circuit with the following parameters. Denote by $I(t)$ the current (where the positive direction is, say, clockwise) in the circuit and by $V(t)$ the voltage increase across the voltage source, at time ... |
[
{
"content": "\nThe assistant is designed to be helpful, proactive, and highly interactive.\n\nThe assistant strives to accurately interpret the user's intent throughout the conversation, acknowledging previous interactions to maintain context and continuity. If the user's message is unclear or lacks necessary ... | false | minerva | conv_62 | uniq_conv_62 | 1 | minerva | minerva | {
"ground_truth": "y^{\\prime}+r y-r x(t)=0",
"style": "Cute"
} | {
"adversarial": false,
"chat_history": [
{
"content": "Consider the following \"mixing problem.\" A tank holds $V$ liters of salt water. Suppose that a saline solution with concentration of $c \\mathrm{gm} /$ liter is added at the rate of $r$ liters/minute. A mixer keeps the salt essentially uniformly di... |
[
{
"content": "\nThe assistant is designed to be helpful, proactive, and highly interactive.\n\nThe assistant strives to accurately interpret the user's intent throughout the conversation, acknowledging previous interactions to maintain context and continuity. If the user's message is unclear or lacks necessary ... | false | minerva | conv_63 | uniq_conv_63 | 1 | minerva | minerva | {
"ground_truth": "c x^{-2}-\\frac{\\cos (2 x)}{2 x^{2}}",
"style": "Cute"
} | {
"adversarial": false,
"chat_history": [
{
"content": "Find the general solution of $x^{2} y^{\\prime}+2 x y=\\sin (2 x)$, solving for $y$. Note that a general solution to a differential equation has the form $x=x_{p}+c x_{h}$ where $x_{h}$ is a nonzero solution of the homogeneous equation $\\dot{x}+p x=... |
[
{
"content": "\nThe assistant is designed to be helpful, proactive, and highly interactive.\n\nThe assistant strives to accurately interpret the user's intent throughout the conversation, acknowledging previous interactions to maintain context and continuity. If the user's message is unclear or lacks necessary ... | false | minerva | conv_64 | uniq_conv_64 | 1 | minerva | minerva | {
"ground_truth": "\\frac{d x}{d t}=k x-a",
"style": "Cute"
} | {
"adversarial": false,
"chat_history": [
{
"content": "An African government is trying to come up with good policy regarding the hunting of oryx. They are using the following model: the oryx population has a natural growth rate of $k$, and we suppose a constant harvesting rate of $a$ oryxes per year.\nWr... |
[
{
"content": "\nThe assistant is designed to be helpful, proactive, and highly interactive.\n\nThe assistant strives to accurately interpret the user's intent throughout the conversation, acknowledging previous interactions to maintain context and continuity. If the user's message is unclear or lacks necessary ... | false | minerva | conv_65 | uniq_conv_65 | 1 | minerva | minerva | {
"ground_truth": "4",
"style": "Cute"
} | {
"adversarial": false,
"chat_history": [
{
"content": "If the complex number $z$ is given by $z = 1+\\sqrt{3} i$, what is the magnitude of $z^2$?",
"role": "user"
}
],
"index": 65,
"single_turn_completion": "4",
"single_turn_prompt": "If the complex number $z$ is given by $z = 1+\\sqrt{... |
[
{
"content": "\nThe assistant is designed to be helpful, proactive, and highly interactive.\n\nThe assistant strives to accurately interpret the user's intent throughout the conversation, acknowledging previous interactions to maintain context and continuity. If the user's message is unclear or lacks necessary ... | false | minerva | conv_66 | uniq_conv_66 | 1 | minerva | minerva | {
"ground_truth": "2",
"style": "Cute"
} | {
"adversarial": false,
"chat_history": [
{
"content": "In the polar representation $(r, \\theta)$ of the complex number $z=1+\\sqrt{3} i$, what is $r$?",
"role": "user"
}
],
"index": 66,
"single_turn_completion": "2",
"single_turn_prompt": "In the polar representation $(r, \\theta)$ of ... |
[
{
"content": "\nThe assistant is designed to be helpful, proactive, and highly interactive.\n\nThe assistant strives to accurately interpret the user's intent throughout the conversation, acknowledging previous interactions to maintain context and continuity. If the user's message is unclear or lacks necessary ... | false | minerva | conv_67 | uniq_conv_67 | 1 | minerva | minerva | {
"ground_truth": "1+\\sqrt{3} i",
"style": "Cute"
} | {
"adversarial": false,
"chat_history": [
{
"content": "Preamble: In the following problems, take $a = \\ln 2$ and $b = \\pi / 3$. \n\nGiven $a = \\ln 2$ and $b = \\pi / 3$, rewrite $e^{a+b i}$ in the form $x + yi$, where $x, y$ are real numbers.",
"role": "user"
}
],
"index": 67,
"single_... |
[
{
"content": "\nThe assistant is designed to be helpful, proactive, and highly interactive.\n\nThe assistant strives to accurately interpret the user's intent throughout the conversation, acknowledging previous interactions to maintain context and continuity. If the user's message is unclear or lacks necessary ... | false | minerva | conv_68 | uniq_conv_68 | 1 | minerva | minerva | {
"ground_truth": "0",
"style": "Cute"
} | {
"adversarial": false,
"chat_history": [
{
"content": "Subproblem 0: Find the general solution of the differential equation $y^{\\prime}=x-2 y$ analytically using integrating factors, solving for $y$. Note that a function $u(t)$ such that $u \\dot{x}+u p x=\\frac{d}{d t}(u x)$ is an integrating factor. A... |
[
{
"content": "\nThe assistant is designed to be helpful, proactive, and highly interactive.\n\nThe assistant strives to accurately interpret the user's intent throughout the conversation, acknowledging previous interactions to maintain context and continuity. If the user's message is unclear or lacks necessary ... | false | minerva | conv_69 | uniq_conv_69 | 1 | minerva | minerva | {
"ground_truth": "-0.875",
"style": "Cute"
} | {
"adversarial": false,
"chat_history": [
{
"content": "Preamble: The following subproblems relate to applying Euler's Method (a first-order numerical procedure for solving ordinary differential equations with a given initial value) onto $y^{\\prime}=y^{2}-x^{2}=F(x, y)$ at $y(0)=-1$, with $h=0.5$. Recall... |
[
{
"content": "\nThe assistant is designed to be helpful, proactive, and highly interactive.\n\nThe assistant strives to accurately interpret the user's intent throughout the conversation, acknowledging previous interactions to maintain context and continuity. If the user's message is unclear or lacks necessary ... | false | minerva | conv_70 | uniq_conv_70 | 1 | minerva | minerva | {
"ground_truth": "\\sqrt{2} \\cos (2 t-\\pi / 4)",
"style": "Cute"
} | {
"adversarial": false,
"chat_history": [
{
"content": "Rewrite the function $f(t) = \\cos (2 t)+\\sin (2 t)$ in the form $A \\cos (\\omega t-\\phi)$. It may help to begin by drawing a right triangle with sides $a$ and $b$.",
"role": "user"
}
],
"index": 70,
"single_turn_completion": "\\sq... |
[
{
"content": "\nThe assistant is designed to be helpful, proactive, and highly interactive.\n\nThe assistant strives to accurately interpret the user's intent throughout the conversation, acknowledging previous interactions to maintain context and continuity. If the user's message is unclear or lacks necessary ... | false | minerva | conv_71 | uniq_conv_71 | 1 | minerva | minerva | {
"ground_truth": "\\frac{1}{2a}(\\exp{a*t} - \\exp{-a*t})",
"style": "Cute"
} | {
"adversarial": false,
"chat_history": [
{
"content": "Given the ordinary differential equation $\\ddot{x}-a^{2} x=0$, where $a$ is a nonzero real-valued constant, find a solution $x(t)$ to this equation such that $x(0) = 0$ and $\\dot{x}(0)=1$.",
"role": "user"
}
],
"index": 71,
"single_... |
[
{
"content": "\nThe assistant is designed to be helpful, proactive, and highly interactive.\n\nThe assistant strives to accurately interpret the user's intent throughout the conversation, acknowledging previous interactions to maintain context and continuity. If the user's message is unclear or lacks necessary ... | false | minerva | conv_72 | uniq_conv_72 | 1 | minerva | minerva | {
"ground_truth": "x_{0} \\cos (\\omega t)+$ $\\dot{x}_{0} \\sin (\\omega t) / \\omega",
"style": "Cute"
} | {
"adversarial": false,
"chat_history": [
{
"content": "Find a solution to the differential equation $\\ddot{x}+\\omega^{2} x=0$ satisfying the initial conditions $x(0)=x_{0}$ and $\\dot{x}(0)=\\dot{x}_{0}$.",
"role": "user"
}
],
"index": 72,
"single_turn_completion": "x_{0} \\cos (\\omega... |
[
{
"content": "\nThe assistant is designed to be helpful, proactive, and highly interactive.\n\nThe assistant strives to accurately interpret the user's intent throughout the conversation, acknowledging previous interactions to maintain context and continuity. If the user's message is unclear or lacks necessary ... | false | minerva | conv_73 | uniq_conv_73 | 1 | minerva | minerva | {
"ground_truth": "\\ln 2 + i\\pi / 3",
"style": "Cute"
} | {
"adversarial": false,
"chat_history": [
{
"content": "Find the complex number $a+b i$ with the smallest possible positive $b$ such that $e^{a+b i}=1+\\sqrt{3} i$.",
"role": "user"
}
],
"index": 73,
"single_turn_completion": "\\ln 2 + i\\pi / 3",
"single_turn_prompt": "Find the complex ... |
[
{
"content": "\nThe assistant is designed to be helpful, proactive, and highly interactive.\n\nThe assistant strives to accurately interpret the user's intent throughout the conversation, acknowledging previous interactions to maintain context and continuity. If the user's message is unclear or lacks necessary ... | false | minerva | conv_74 | uniq_conv_74 | 1 | minerva | minerva | {
"ground_truth": "e^{t} / 3",
"style": "Cute"
} | {
"adversarial": false,
"chat_history": [
{
"content": "Subproblem 0: Find the general solution of the differential equation $\\dot{x}+2 x=e^{t}$, using $c$ for the arbitrary constant of integration which will occur.\n\n\nSolution: We can use integrating factors to get $(u x)^{\\prime}=u e^{t}$ for $u=e^{... |
[
{
"content": "\nThe assistant is designed to be helpful, proactive, and highly interactive.\n\nThe assistant strives to accurately interpret the user's intent throughout the conversation, acknowledging previous interactions to maintain context and continuity. If the user's message is unclear or lacks necessary ... | false | minerva | conv_75 | uniq_conv_75 | 1 | minerva | minerva | {
"ground_truth": "2",
"style": "Cute"
} | {
"adversarial": false,
"chat_history": [
{
"content": "Subproblem 0: For $\\omega \\geq 0$, find $A$ such that $A \\cos (\\omega t)$ is a solution of $\\ddot{x}+4 x=\\cos (\\omega t)$.\n\n\nSolution: If $x=A \\cos (\\omega t)$, then taking derivatives gives us $\\ddot{x}=-\\omega^{2} A \\cos (\\omega t)$... |
[
{
"content": "\nThe assistant is designed to be helpful, proactive, and highly interactive.\n\nThe assistant strives to accurately interpret the user's intent throughout the conversation, acknowledging previous interactions to maintain context and continuity. If the user's message is unclear or lacks necessary ... | false | minerva | conv_76 | uniq_conv_76 | 1 | minerva | minerva | {
"ground_truth": "\\frac{\\cos (2 t)}{15}+C_{1} e^{t}+C_{2} e^{-t}+C_{3} \\cos (t)+C_{4} \\sin (t)",
"style": "Cute"
} | {
"adversarial": false,
"chat_history": [
{
"content": "Subproblem 0: Find a purely sinusoidal solution of $\\frac{d^{4} x}{d t^{4}}-x=\\cos (2 t)$.\n\n\nSolution: We choose an exponential input function whose real part is $\\cos (2 t)$, namely $e^{2 i t}$. Since $p(s)=s^{4}-1$ and $p(2 i)=15 \\neq 0$, th... |
[
{
"content": "\nThe assistant is designed to be helpful, proactive, and highly interactive.\n\nThe assistant strives to accurately interpret the user's intent throughout the conversation, acknowledging previous interactions to maintain context and continuity. If the user's message is unclear or lacks necessary ... | false | minerva | conv_77 | uniq_conv_77 | 1 | minerva | minerva | {
"ground_truth": "\\frac{1}{4-\\omega^{2}}",
"style": "Cute"
} | {
"adversarial": false,
"chat_history": [
{
"content": "For $\\omega \\geq 0$, find $A$ such that $A \\cos (\\omega t)$ is a solution of $\\ddot{x}+4 x=\\cos (\\omega t)$.",
"role": "user"
}
],
"index": 77,
"single_turn_completion": "\\frac{1}{4-\\omega^{2}}",
"single_turn_prompt": "For ... |
[
{
"content": "\nThe assistant is designed to be helpful, proactive, and highly interactive.\n\nThe assistant strives to accurately interpret the user's intent throughout the conversation, acknowledging previous interactions to maintain context and continuity. If the user's message is unclear or lacks necessary ... | false | minerva | conv_78 | uniq_conv_78 | 1 | minerva | minerva | {
"ground_truth": "\\frac{\\cos (2 t)+\\sin (2 t)}{4}",
"style": "Cute"
} | {
"adversarial": false,
"chat_history": [
{
"content": "Find a solution to $\\dot{x}+2 x=\\cos (2 t)$ in the form $k_0\\left[f(k_1t) + g(k_2t)\\right]$, where $f, g$ are trigonometric functions. Do not include homogeneous solutions to this ODE in your solution.",
"role": "user"
}
],
"index"... |
[
{
"content": "\nThe assistant is designed to be helpful, proactive, and highly interactive.\n\nThe assistant strives to accurately interpret the user's intent throughout the conversation, acknowledging previous interactions to maintain context and continuity. If the user's message is unclear or lacks necessary ... | false | minerva | conv_79 | uniq_conv_79 | 1 | minerva | minerva | {
"ground_truth": "-0.2",
"style": "Cute"
} | {
"adversarial": false,
"chat_history": [
{
"content": "Preamble: The following subproblems refer to the differential equation. $\\ddot{x}+4 x=\\sin (3 t)$\n\nFind $A$ so that $A \\sin (3 t)$ is a solution of $\\ddot{x}+4 x=\\sin (3 t)$.",
"role": "user"
}
],
"index": 79,
"single_turn_comp... |
[
{
"content": "\nThe assistant is designed to be helpful, proactive, and highly interactive.\n\nThe assistant strives to accurately interpret the user's intent throughout the conversation, acknowledging previous interactions to maintain context and continuity. If the user's message is unclear or lacks necessary ... | false | minerva | conv_80 | uniq_conv_80 | 1 | minerva | minerva | {
"ground_truth": "x / 2-1 / 4+c e^{-2 x}",
"style": "Cute"
} | {
"adversarial": false,
"chat_history": [
{
"content": "Find the general solution of the differential equation $y^{\\prime}=x-2 y$ analytically using integrating factors, solving for $y$. Note that a function $u(t)$ such that $u \\dot{x}+u p x=\\frac{d}{d t}(u x)$ is an integrating factor. Additionally, n... |
[
{
"content": "\nThe assistant is designed to be helpful, proactive, and highly interactive.\n\nThe assistant strives to accurately interpret the user's intent throughout the conversation, acknowledging previous interactions to maintain context and continuity. If the user's message is unclear or lacks necessary ... | false | minerva | conv_81 | uniq_conv_81 | 1 | minerva | minerva | {
"ground_truth": "\\frac{e^{-2 t}}{15}+C_{1} e^{t}+C_{2} e^{-t}+ C_{3} \\cos (t)+C_{4} \\sin (t)",
"style": "Cute"
} | {
"adversarial": false,
"chat_history": [
{
"content": "Subproblem 0: Find a purely exponential solution of $\\frac{d^{4} x}{d t^{4}}-x=e^{-2 t}$.\n\n\nSolution: The characteristic polynomial of the homogeneous equation is given by $p(s)=$ $s^{4}-1$. Since $p(-2)=15 \\neq 0$, the exponential response form... |
[
{
"content": "\nThe assistant is designed to be helpful, proactive, and highly interactive.\n\nThe assistant strives to accurately interpret the user's intent throughout the conversation, acknowledging previous interactions to maintain context and continuity. If the user's message is unclear or lacks necessary ... | false | minerva | conv_82 | uniq_conv_82 | 1 | minerva | minerva | {
"ground_truth": "s^{2}+\\omega^{2}",
"style": "Cute"
} | {
"adversarial": false,
"chat_history": [
{
"content": "Preamble: Consider the differential equation $\\ddot{x}+\\omega^{2} x=0$. \\\\\n\nA differential equation $m \\ddot{x}+b \\dot{x}+k x=0$ (where $m, b$, and $k$ are real constants, and $m \\neq 0$ ) has corresponding characteristic polynomial $p(s)=m ... |
[
{
"content": "\nThe assistant is designed to be helpful, proactive, and highly interactive.\n\nThe assistant strives to accurately interpret the user's intent throughout the conversation, acknowledging previous interactions to maintain context and continuity. If the user's message is unclear or lacks necessary ... | false | minerva | conv_83 | uniq_conv_83 | 1 | minerva | minerva | {
"ground_truth": "2 \\cos (\\pi t+\\pi / 3)",
"style": "Cute"
} | {
"adversarial": false,
"chat_history": [
{
"content": "Rewrite the function $\\cos (\\pi t)-\\sqrt{3} \\sin (\\pi t)$ in the form $A \\cos (\\omega t-\\phi)$. It may help to begin by drawing a right triangle with sides $a$ and $b$.",
"role": "user"
}
],
"index": 83,
"single_turn_completio... |
[
{
"content": "\nThe assistant is designed to be helpful, proactive, and highly interactive.\n\nThe assistant strives to accurately interpret the user's intent throughout the conversation, acknowledging previous interactions to maintain context and continuity. If the user's message is unclear or lacks necessary ... | false | minerva | conv_84 | uniq_conv_84 | 1 | minerva | minerva | {
"ground_truth": "2 \\pi / \\omega",
"style": "Cute"
} | {
"adversarial": false,
"chat_history": [
{
"content": "Preamble: The following subproblems refer to the damped sinusoid $x(t)=A e^{-a t} \\cos (\\omega t)$.\n\nWhat is the spacing between successive maxima of $x(t)$? Assume that $\\omega \\neq 0$.",
"role": "user"
}
],
"index": 84,
"singl... |
[
{
"content": "\nThe assistant is designed to be helpful, proactive, and highly interactive.\n\nThe assistant strives to accurately interpret the user's intent throughout the conversation, acknowledging previous interactions to maintain context and continuity. If the user's message is unclear or lacks necessary ... | false | minerva | conv_85 | uniq_conv_85 | 1 | minerva | minerva | {
"ground_truth": "\\frac{4 A}{3+3 i} e^{i t}",
"style": "Cute"
} | {
"adversarial": false,
"chat_history": [
{
"content": "Preamble: The following subproblems refer to a spring/mass/dashpot system driven through the spring modeled by the equation $m \\ddot{x}+b \\dot{x}+k x=k y$. Here $x$ measures the position of the mass, $y$ measures the position of the other end of th... |
[
{
"content": "\nThe assistant is designed to be helpful, proactive, and highly interactive.\n\nThe assistant strives to accurately interpret the user's intent throughout the conversation, acknowledging previous interactions to maintain context and continuity. If the user's message is unclear or lacks necessary ... | false | minerva | conv_86 | uniq_conv_86 | 1 | minerva | minerva | {
"ground_truth": "I(0) e^{-\\frac{t}{R C}}",
"style": "Cute"
} | {
"adversarial": false,
"chat_history": [
{
"content": "Preamble: The following subproblems refer to a circuit with the following parameters. Denote by $I(t)$ the current (where the positive direction is, say, clockwise) in the circuit and by $V(t)$ the voltage increase across the voltage source, at time ... |
[
{
"content": "\nThe assistant is designed to be helpful, proactive, and highly interactive.\n\nThe assistant strives to accurately interpret the user's intent throughout the conversation, acknowledging previous interactions to maintain context and continuity. If the user's message is unclear or lacks necessary ... | false | minerva | conv_87 | uniq_conv_87 | 1 | minerva | minerva | {
"ground_truth": "\\frac{e^{2 i t}}{(2+2 i)}",
"style": "Cute"
} | {
"adversarial": false,
"chat_history": [
{
"content": "Subproblem 0: Find the general (complex-valued) solution of the differential equation $\\dot{z}+2 z=e^{2 i t}$, using $C$ to stand for any complex-valued integration constants which may arise.\n\n\nSolution: Using integrating factors, we get $e^{2 t}... |
[
{
"content": "\nThe assistant is designed to be helpful, proactive, and highly interactive.\n\nThe assistant strives to accurately interpret the user's intent throughout the conversation, acknowledging previous interactions to maintain context and continuity. If the user's message is unclear or lacks necessary ... | false | minerva | conv_88 | uniq_conv_88 | 1 | minerva | minerva | {
"ground_truth": "\\frac{2-\\omega^{2}-\\omega i / 4}{\\omega^{4}-\\frac{63}{16} \\omega^{2}+4}",
"style": "Cute"
} | {
"adversarial": false,
"chat_history": [
{
"content": "Preamble: The following subproblems consider a second order mass/spring/dashpot system driven by a force $F_{\\text {ext }}$ acting directly on the mass: $m \\ddot{x}+b \\dot{x}+k x=F_{\\text {ext }}$. So the input signal is $F_{\\text {ext }}$ and t... |
[
{
"content": "\nThe assistant is designed to be helpful, proactive, and highly interactive.\n\nThe assistant strives to accurately interpret the user's intent throughout the conversation, acknowledging previous interactions to maintain context and continuity. If the user's message is unclear or lacks necessary ... | false | minerva | conv_89 | uniq_conv_89 | 1 | minerva | minerva | {
"ground_truth": "x^{\\prime}+\\frac{r}{V} x-r c=0",
"style": "Cute"
} | {
"adversarial": false,
"chat_history": [
{
"content": "Preamble: The following subproblems refer to the following \"mixing problem\": A tank holds $V$ liters of salt water. Suppose that a saline solution with concentration of $c \\mathrm{gm} /$ liter is added at the rate of $r$ liters/minute. A mixer kee... |
[
{
"content": "\nThe assistant is designed to be helpful, proactive, and highly interactive.\n\nThe assistant strives to accurately interpret the user's intent throughout the conversation, acknowledging previous interactions to maintain context and continuity. If the user's message is unclear or lacks necessary ... | false | minerva | conv_90 | uniq_conv_90 | 1 | minerva | minerva | {
"ground_truth": "-t^2 - t - 3",
"style": "Cute"
} | {
"adversarial": false,
"chat_history": [
{
"content": "Find the polynomial solution of $\\ddot{x}-x=t^{2}+t+1$, solving for $x(t)$.",
"role": "user"
}
],
"index": 90,
"single_turn_completion": "-t^2 - t - 3",
"single_turn_prompt": "Find the polynomial solution of $\\ddot{x}-x=t^{2}+t+1$... |
[
{
"content": "\nThe assistant is designed to be helpful, proactive, and highly interactive.\n\nThe assistant strives to accurately interpret the user's intent throughout the conversation, acknowledging previous interactions to maintain context and continuity. If the user's message is unclear or lacks necessary ... | false | minerva | conv_91 | uniq_conv_91 | 1 | minerva | minerva | {
"ground_truth": "-8",
"style": "Cute"
} | {
"adversarial": false,
"chat_history": [
{
"content": "Preamble: In the following problems, take $a = \\ln 2$ and $b = \\pi / 3$. \n\nSubproblem 0: Given $a = \\ln 2$ and $b = \\pi / 3$, rewrite $e^{a+b i}$ in the form $x + yi$, where $x, y$ are real numbers. \n\n\nSolution: Using Euler's formula, we fin... |
[
{
"content": "\nThe assistant is designed to be helpful, proactive, and highly interactive.\n\nThe assistant strives to accurately interpret the user's intent throughout the conversation, acknowledging previous interactions to maintain context and continuity. If the user's message is unclear or lacks necessary ... | false | minerva | conv_92 | uniq_conv_92 | 1 | minerva | minerva | {
"ground_truth": "\\frac{\\cos (2 t)}{15}",
"style": "Cute"
} | {
"adversarial": false,
"chat_history": [
{
"content": "Find a purely sinusoidal solution of $\\frac{d^{4} x}{d t^{4}}-x=\\cos (2 t)$.",
"role": "user"
}
],
"index": 92,
"single_turn_completion": "\\frac{\\cos (2 t)}{15}",
"single_turn_prompt": "Find a purely sinusoidal solution of $\\fr... |
[
{
"content": "\nThe assistant is designed to be helpful, proactive, and highly interactive.\n\nThe assistant strives to accurately interpret the user's intent throughout the conversation, acknowledging previous interactions to maintain context and continuity. If the user's message is unclear or lacks necessary ... | false | minerva | conv_93 | uniq_conv_93 | 1 | minerva | minerva | {
"ground_truth": "-2+2 \\sqrt{3} i",
"style": "Cute"
} | {
"adversarial": false,
"chat_history": [
{
"content": "Preamble: In the following problems, take $a = \\ln 2$ and $b = \\pi / 3$. \n\nSubproblem 0: Given $a = \\ln 2$ and $b = \\pi / 3$, rewrite $e^{a+b i}$ in the form $x + yi$, where $x, y$ are real numbers. \n\n\nSolution: Using Euler's formula, we fin... |
[
{
"content": "\nThe assistant is designed to be helpful, proactive, and highly interactive.\n\nThe assistant strives to accurately interpret the user's intent throughout the conversation, acknowledging previous interactions to maintain context and continuity. If the user's message is unclear or lacks necessary ... | false | minerva | conv_94 | uniq_conv_94 | 1 | minerva | minerva | {
"ground_truth": "\\frac{t}{4} \\sin (2 t)",
"style": "Cute"
} | {
"adversarial": false,
"chat_history": [
{
"content": "Find a solution of $\\ddot{x}+4 x=\\cos (2 t)$, solving for $x(t)$, by using the ERF on a complex replacement. The ERF (Exponential Response Formula) states that a solution to $p(D) x=A e^{r t}$ is given by $x_{p}=A \\frac{e^{r t}}{p(r)}$, as long as... |
[
{
"content": "\nThe assistant is designed to be helpful, proactive, and highly interactive.\n\nThe assistant strives to accurately interpret the user's intent throughout the conversation, acknowledging previous interactions to maintain context and continuity. If the user's message is unclear or lacks necessary ... | false | minerva | conv_95 | uniq_conv_95 | 1 | minerva | minerva | {
"ground_truth": "\\frac{1}{2}(\\exp{a*t} + \\exp{-a*t})",
"style": "Cute"
} | {
"adversarial": false,
"chat_history": [
{
"content": "Given the ordinary differential equation $\\ddot{x}-a^{2} x=0$, where $a$ is a nonzero real-valued constant, find a solution $x(t)$ to this equation such that $x(0) = 1$ and $\\dot{x}(0)=0$.",
"role": "user"
}
],
"index": 95,
"single_... |
[
{
"content": "\nThe assistant is designed to be helpful, proactive, and highly interactive.\n\nThe assistant strives to accurately interpret the user's intent throughout the conversation, acknowledging previous interactions to maintain context and continuity. If the user's message is unclear or lacks necessary ... | false | minerva | conv_96 | uniq_conv_96 | 1 | minerva | minerva | {
"ground_truth": "\\frac{e^{t}} {3}+c e^{-2 t}",
"style": "Cute"
} | {
"adversarial": false,
"chat_history": [
{
"content": "Find the general solution of the differential equation $\\dot{x}+2 x=e^{t}$, using $c$ for the arbitrary constant of integration which will occur.",
"role": "user"
}
],
"index": 96,
"single_turn_completion": "\\frac{e^{t}} {3}+c e^{-2... |
[
{
"content": "\nThe assistant is designed to be helpful, proactive, and highly interactive.\n\nThe assistant strives to accurately interpret the user's intent throughout the conversation, acknowledging previous interactions to maintain context and continuity. If the user's message is unclear or lacks necessary ... | false | minerva | conv_97 | uniq_conv_97 | 1 | minerva | minerva | {
"ground_truth": "\\left(\\frac{t^{2}}{2}-t+C\\right) e^{-t}",
"style": "Cute"
} | {
"adversarial": false,
"chat_history": [
{
"content": "Find a solution of $\\ddot{x}+3 \\dot{x}+2 x=t e^{-t}$ in the form $x(t)=u(t) e^{-t}$ for some function $u(t)$. Use $C$ for an arbitrary constant, should it arise.",
"role": "user"
}
],
"index": 97,
"single_turn_completion": "\\left(... |
[
{
"content": "\nThe assistant is designed to be helpful, proactive, and highly interactive.\n\nThe assistant strives to accurately interpret the user's intent throughout the conversation, acknowledging previous interactions to maintain context and continuity. If the user's message is unclear or lacks necessary ... | false | minerva | conv_98 | uniq_conv_98 | 1 | minerva | minerva | {
"ground_truth": "-2",
"style": "Cute"
} | {
"adversarial": false,
"chat_history": [
{
"content": "If the complex number $z$ is given by $z = 1+\\sqrt{3} i$, what is the real part of $z^2$?",
"role": "user"
}
],
"index": 98,
"single_turn_completion": "-2",
"single_turn_prompt": "If the complex number $z$ is given by $z = 1+\\sqrt... |
[
{
"content": "\nThe assistant is designed to be helpful, proactive, and highly interactive.\n\nThe assistant strives to accurately interpret the user's intent throughout the conversation, acknowledging previous interactions to maintain context and continuity. If the user's message is unclear or lacks necessary ... | false | minerva | conv_99 | uniq_conv_99 | 1 | minerva | minerva | {
"ground_truth": "\\frac{e^{-2 t}}{15}",
"style": "Cute"
} | {
"adversarial": false,
"chat_history": [
{
"content": "Find a purely exponential solution of $\\frac{d^{4} x}{d t^{4}}-x=e^{-2 t}$.",
"role": "user"
}
],
"index": 99,
"single_turn_completion": "\\frac{e^{-2 t}}{15}",
"single_turn_prompt": "Find a purely exponential solution of $\\frac{d... |
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