jeggers/fermi huggingface dataset:
Question: If the Sun were to collapse into a neutron star, how far is the Earth from the Sun assuming no other changes except reduction in size?
CONTEXT:
F1: The approximate reduction in radius of the sun is 600000 km
F2: The distance from earth to sun is 151e+6 km
PROGRAM:
Q1: What would the approximate reduction in radius of the sun be when it turns into a neutron star?
Q2: What is the distance from earth to sun?
A1: 6e+5 km
A2: 1510e+5 km=Q2 -> A2 | F2=Q1 -> A1 | F1
P: Add (Q1, Q2)
Answer: 1516e+5 km
Question: How many Americans are polled in political polls every year?
CONTEXT:
F1: Around 10 major agencies conduct the annual political polls in the country.
F2: Each agency surveys the poll on a total population of around 10000 people.
PROGRAM:
Q1: How many agencies conduct the annual political polls with Americans?
Q2: What is the average number of people surveyed by a single agency?
A1: 10
A2: 10000=Q2 -> A2 | F2=Q1 -> A1 | F1
P: Mul (Q1, Q2)
Answer: 100000
Question: How long would it take to count to a million?
CONTEXT:
F1: There are 24 hours in a day.
F2: There are 60 minutes in an hour.
F3: There are 60 seconds in a minute.
F4: There are 1000000 numbers in a million
F5: It takes around 1 second to count a number
PROGRAM:
Q1: How many hours does it take to count to a million?
Q2: How many hours are there in a day?
Q3: How many minutes are there in an hour?
Q4: How many minutes does it take to count to a million?
Q5: How many seconds does it take to count to a million?
Q6: How many numbers are there in a million
Q7: What is the average time taken to count a number?
Q8: How many seconds are there in a minute?
A1: 24 hour/day
A2: 60 minute/hour
A3: 60 second/minute
A4: 1000000
A5: 1 second=Q7 -> A5 | F5=Q6 -> A4 | F4=Q5 -> Mul (Q6, Q7)=Q8 -> A3 | F3=Q4 -> Div (Q5, Q8)=Q3 -> A2 | F2=Q1 -> Div(Q4,Q3)=Q2 -> A1 | F1
P: Div(Q1, Q2)
Answer: 11.5 days
Question: Assuming that it has the same density as a gold nucleus, what is the diameter, cm, of an electron?
CONTEXT:
F1: The relation between 4 times the diameter cube and diameter is a cube root.
F2: The mass of electron is 9e-31 kg
F3: The density of gold nucleus is 0.02 kg per cc
PROGRAM:
Q1: What is the 4*diameter cube of the neutron star?
Q2: What is the relation between 4*diameter cube and the diameter of the electron?
Q3: What is the mass of the electron?
Q4: What is the density of the gold nucleus?
A1: 9e-31 kg
A2: 0.02 kg*cm**-3
A3: 1/3=Q4 -> A2 | F2=Q3 -> A1 | F1=Q1 -> Div (Q3, Q4)=Q2 -> A3 | F3
P: Pow (Q1, Q2)
Answer: 3.5e-10 cm
Question: The actual diameter of an atom is about 1 Angstrom. In order to develop some intuition for the molecular scale of a gas, assume that you are considering a liter of air (mostly nitrogen and oxygen ) at room temperature and a pressure of 105 Pa. Calculate the number of molecules in the sample of gas.
CONTEXT:
F1: The volume of air in the setting is 0.001 m**3
F2: The number of atoms in a single molecule of air is 2
F3: The diameter of an atom is 1e-10 m
F4: The volume of an atom is approximately a cube of its diameter.
PROGRAM:
Q1: What is the volume of air in the setting?
Q2: What is the total volume of a molecule of air?
Q3: What is the volume of a single atom of N/O?
Q4: What is the number of atoms in a single molecule of air?
Q5: What is the diameter of the atom?
Q6: What is the relationship between diameter and volume of an atom?
A1: 0.001 m**3
A2: 2
A3: 1e-10 m
A4: 3=Q6 -> A4 | F4=Q5 -> A3 | F3=Q4 -> Pow (Q5, Q6)=Q3 -> A2 | F2=Q2 -> Mul (Q3, Q4)=Q1 -> A1 | F1
P: Div (Q1, Q2)
Answer: 5.00E+26
Question: How much closer was the Moon to Earth when the last dinosaurs roamed?
CONTEXT:
F1: The distance that Earth moves away from the moon each year is 4e-5 km.
F2: It has been 65e+6 years since the dinosaurs last existed.
PROGRAM:
Q1: What is the distance that Earth moves away from the moon each year?
Q2: How many years has it been when the dinosaurs were last existing?
A1: 4e-5 km*year**-1
A2: 65e+6 years=Q2 -> A2| F2=Q1 -> A1 | F1
P: Mul (Q1, Q2)
Answer: 2600 km
Question: How much would it cost to fill this room with popcorn?
CONTEXT:
F1: The cost of one tub of popcorn is 5 USD
F2: Roughly, 400 tubs of popcorn can be filled in one room.
PROGRAM:
Q1: What is the cost of one tub of popcorn?
Q2: How many tubs of popcorn fit in one room?
A1: $5
A2: 400=Q2 -> A2 | F2=Q1 -> A1 | F1
P: Mul (Q1, Q2)
Answer: $2000