Response:
Reasoning:
1. Use the ideal gas law P V = n R T.
2. Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.
3. Compute P = 1.26 * 8.314 * 373 / 60.5.
Final: {"answer": 64.5854, "unit": "kPa"}

Answer: 64.5854

Prompt: An ideal gas sample has n=1.26 mol, T=373 K, and V=60.5 L. Using R=8.314 kPa*L/(mol*K), compute the pressure in kPa.

Use the ideal gas law P V = n R T.
Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.
Compute P = 1.26 * 8.314 * 373 / 60.5.


Response:
Reasoning:
1. Keep the boundary values fixed and update only the three interior grid points.
2. For each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.
3. Multiply each Laplacian by r=0.16 and add it to the current value.
Final: {"answer": [1.938, 0.676, 0.258], "unit": "temperature_units"}

Answer: 1.938

Answer: 0.676

Answer: 0.258

Prompt: For the 1D heat equation explicit finite-difference step, use u_i(next)=u_i+r*(u_{i-1}-2*u_i+u_{i+1}). Boundary values are left=2.05, right=1.75; current interior values are [2.25, 0.5, -0.15]. Use r=0.16. Return the next interior vector.

Keep the boundary values fixed and update only the three interior grid points.
For each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.
Multiply each Laplacian by r=0.16 and add it to the current value.


Response:
Reasoning:
1. Use Newton's second law F = m a.
2. Substitute m = 15.8 kg and a = 11.05 m/s^2.
3. The unit kg*m/s^2 is one newton.
Final: {"answer": 174.59, "unit": "N"}

Answer: 174.59

Prompt: A cart has mass 15.8 kg and measured acceleration 11.05 m/s^2. Compute the net force. Check the SI units and give only the final JSON after reasoning.

Use Newton's second law F = m a.
Substitute m = 15.8 kg and a = 11.05 m/s^2.
The unit kg*m/s^2 is one newton.


Response:
Reasoning:
1. Explicit Euler updates y_{n+1} = y_n + h f(y_n).
2. Here f(y) = -0.96 y, so each step multiplies y by 1 - h*0.96.
3. Apply that update for 3 steps and round the final state.
Final: {"answer": 11.0088, "unit": "state_units"}

Answer: 11.0088

Prompt: Use explicit Euler on dy/dt = -0.96 y with y(0)=30.5, step size h=0.3, for 3 steps. What is y after the final step?

Explicit Euler updates y_{n+1} = y_n + h f(y_n).
Here f(y) = -0.96 y, so each step multiplies y by 1 - h*0.96.
Apply that update for 3 steps and round the final state.


Response:
Reasoning:
1. Compare the dimensions on both sides of the equation.
2. density times acceleration times height gives kg/(m*s^2), or pascal
3. The equation is valid only if both sides have identical dimensions.
Final: {"answer": "consistent"}

Answer: consistent

Prompt: In field worksheet case 626983, check dimensional consistency for p = rho * g * h. The left side has dimensions Pa and the right side has dimensions Pa. Return consistent or inconsistent with a brief reason.

Compare the dimensions on both sides of the equation.
density times acceleration times height gives kg/(m*s^2), or pascal
The equation is valid only if both sides have identical dimensions.

Answer: consistent


Response:
Reasoning:
1. Explicit Euler updates y_{n+1} = y_n + h f(y_n).
2. Here f(y) = -0.15 y, so each step multiplies y by 1 - h*0.15.
3. Apply that update for 8 steps and round the final state.
Final: {"answer": 9.6109, "unit": "state_units"}

Answer: 9.6109

Prompt: Use explicit Euler on dy/dt = -0.15 y with y(0)=54.5, step size h=1.3, for 8 steps. What is y after the final step?

Explicit Euler updates y_{n+1} = y_n + h f(y_n).
Here f(y) = -0.15 y, so each step multiplies y by 1 - h*0.15.
Apply that update for 8 steps and round the final state.


Response:
Reasoning:
1. Keep the boundary values fixed and update only the three interior grid points.
2. For each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.
3. Multiply each Laplacian by r=0.02 and add it to the current value.
Final: {"answer": [-1.029, 2.112, -1.147], "unit": "temperature_units"}

Answer: -1.029

Answer: 2.112

Answer: -1.147

Prompt: For the 1D heat equation explicit finite-difference step, use u_i(next)=u_i+r*(u_{i-1}-2*u_i+u_{i+1}). Boundary values are left=-0.9, right=2.8; current interior values are [-1.1, 2.25, -1.3]. Use r=0.02. Return the next interior vector.

Keep the boundary values fixed and update only the three interior grid points.
For each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.
Multiply each Laplacian by r=0.02 and add it to the current value.


Response:
Reasoning:
1. The x component is magnitude times cos(theta).
2. The y component is magnitude times sin(theta).
3. Use theta=107 degrees and keep the unit as newtons.
Final: {"answer": [-18.2732, 59.769], "unit": "N"}

Answer: -18.2732

Answer: 59.769

Prompt: A vector has magnitude 62.5 N at 107 degrees counterclockwise from the +x axis. Return its [x, y] components in newtons.

The x component is magnitude times cos(theta).
The y component is magnitude times sin(theta).
Use theta=107 degrees and keep the unit as newtons.

[magnitude * math.cos(math.radians(angle_deg)), magnitude * math.sin(math.radians(angle_deg))]


Response:
Reasoning:
1. Mass equals amount in moles times molar mass.
2. Use m = 6.91 mol * 100.087 g/mol.
3. The mole unit cancels, leaving grams.
Final: {"answer": 691.6012, "unit": "g"}

Answer: 691.6012

Prompt: A sample contains 6.91 mol of calcium carbonate. Using molar mass 100.087 g/mol, compute the sample mass in grams.

Mass equals amount in moles times molar mass.
Use m = 6.91 mol * 100.087 g/mol.
The mole unit cancels, leaving grams.


Response:
Reasoning:
1. Molarity is moles of solute divided by solution volume in liters.
2. Convert 1715 mL to 1.715 L.
3. Compute M = 1.31 / 1.715.
Final: {"answer": 0.7638, "unit": "mol/L"}

Answer: 0.7638

Prompt: A solution contains 1.31 mol of solute in 1715 mL of solution. Compute the molarity in mol/L.

Molarity is moles of solute divided by solution volume in liters.
Convert 1715 mL to 1.715 L.
Compute M = 1.31 / 1.715.


Response:
Reasoning:
1. For level-ground projectile motion, R = v^2 sin(2 theta) / g.
2. Convert theta=54 degrees through the sine of 2 theta.
3. Substitute v=15.3 m/s and g=9.81 m/s^2.
Final: {"answer": 22.6945, "unit": "m"}

Answer: 22.6945

Prompt: A projectile is launched on level ground with no air resistance at speed 15.3 m/s and angle 54 degrees. Compute the horizontal range in meters using g=9.81 m/s^2.

For level-ground projectile motion, R = v^2 sin(2 theta) / g.
Convert theta=54 degrees through the sine of 2 theta.
Substitute v=15.3 m/s and g=9.81 m/s^2.

speed ** 2 * math.sin(math.radians(2 * angle_deg)) / gravity


Response:
Reasoning:
1. Use the ideal gas law P V = n R T.
2. Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.
3. Compute P = 2.86 * 8.314 * 268 / 48.5.
Final: {"answer": 131.3921, "unit": "kPa"}

Answer: 131.3921

Prompt: An ideal gas sample has n=2.86 mol, T=268 K, and V=48.5 L. Using R=8.314 kPa*L/(mol*K), compute the pressure in kPa.

Use the ideal gas law P V = n R T.
Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.
Compute P = 2.86 * 8.314 * 268 / 48.5.


Response:
Reasoning:
1. Use Q = m c DeltaT.
2. The mass is already in grams, matching the specific heat denominator.
3. Compute Q = 995 * 4.465 * 106.
Final: {"answer": 470923.55, "unit": "J"}

Answer: 470923.55

Prompt: A 995 g sample has specific heat 4.465 J/(g*K). How much heat is needed to raise its temperature by 106 K?

Use Q = m c DeltaT.
The mass is already in grams, matching the specific heat denominator.
Compute Q = 995 * 4.465 * 106.


Response:
Reasoning:
1. Ohm's law gives I = V / R.
2. Power can be written as P = V I = V^2 / R.
3. Substitute V=4.4 V and R=162.1 ohm.
Final: {"answer": 0.1194, "unit": "W"}

Answer: 0.1194

Prompt: A resistor has resistance 162.1 ohm and voltage 4.4 V across it. Compute the dissipated power in watts.

Ohm's law gives I = V / R.
Power can be written as P = V I = V^2 / R.
Substitute V=4.4 V and R=162.1 ohm.


Response:
Reasoning:
1. For level-ground projectile motion, R = v^2 sin(2 theta) / g.
2. Convert theta=71 degrees through the sine of 2 theta.
3. Substitute v=8.6 m/s and g=9.81 m/s^2.
Final: {"answer": 4.6416, "unit": "m"}

Answer: 4.6416

Prompt: A projectile is launched on level ground with no air resistance at speed 8.6 m/s and angle 71 degrees. Compute the horizontal range in meters using g=9.81 m/s^2.

For level-ground projectile motion, R = v^2 sin(2 theta) / g.
Convert theta=71 degrees through the sine of 2 theta.
Substitute v=8.6 m/s and g=9.81 m/s^2.


Response:
Reasoning:
1. Mass equals amount in moles times molar mass.
2. Use m = 1.81 mol * 100.087 g/mol.
3. The mole unit cancels, leaving grams.
Final: {"answer": 181.1575, "unit": "g"}

Answer: 181.1575

Prompt: A sample contains 1.81 mol of calcium carbonate. Using molar mass 100.087 g/mol, compute the sample mass in grams.

Mass equals amount in moles times molar mass.
Use m = 1.81 mol * 100.087 g/mol.
The mole unit cancels, leaving grams.


Response:
Reasoning:
1. The x component is magnitude times cos(theta).
2. The y component is magnitude times sin(theta).
3. Use theta=221 degrees and keep the unit as newtons.
Final: {"answer": [-151.3193, -131.5398], "unit": "N"}

Answer: -151.3193

Answer: -131.5398

Prompt: A vector has magnitude 200.5 N at 221 degrees counterclockwise from the +x axis. Return its [x, y] components in newtons.

The x component is magnitude times cos(theta).
The y component is magnitude times sin(theta).
Use theta=221 degrees and keep the unit as newtons.


Response:
Reasoning:
1. Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).
2. Use N0=427.5 mg, t=295.5 h, and T_half=119 h.
3. The remaining amount has the same mass unit as the initial amount.
Final: {"answer": 76.4576, "unit": "mg"}

Answer: 76.4576

Prompt: A radioactive sample starts with 427.5 mg. Its half-life is 119 hours. How many mg remain after 295.5 hours?

Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).
Use N0=427.5 mg, t=295.5 h, and T_half=119 h.
The remaining amount has the same mass unit as the initial amount.

initial_amount * 0.5 ** (elapsed_time / half_life)


Response:
Reasoning:
1. Mass equals amount in moles times molar mass.
2. Use m = 3.12 mol * 100.087 g/mol.
3. The mole unit cancels, leaving grams.
Final: {"answer": 312.2714, "unit": "g"}

Answer: 312.2714

Prompt: A sample contains 3.12 mol of calcium carbonate. Using molar mass 100.087 g/mol, compute the sample mass in grams.

Mass equals amount in moles times molar mass.
Use m = 3.12 mol * 100.087 g/mol.
The mole unit cancels, leaving grams.


Response:
Reasoning:
1. The x component is magnitude times cos(theta).
2. The y component is magnitude times sin(theta).
3. Use theta=108 degrees and keep the unit as newtons.
Final: {"answer": [-97.8039, 301.0094], "unit": "N"}

Answer: -97.8039

Answer: 301.0094

Prompt: A vector has magnitude 316.5 N at 108 degrees counterclockwise from the +x axis. Return its [x, y] components in newtons.

The x component is magnitude times cos(theta).
The y component is magnitude times sin(theta).
Use theta=108 degrees and keep the unit as newtons.


Response:
Reasoning:
1. Compare the dimensions on both sides of the equation.
2. m*v is momentum, not energy
3. The equation is valid only if both sides have identical dimensions.
Final: {"answer": "inconsistent"}

Answer: inconsistent

Prompt: In instrument manual case 211509, check dimensional consistency for E = m * v. The left side has dimensions kg*m^2/s^2 and the right side has dimensions kg*m/s. Return consistent or inconsistent with a brief reason.

Compare the dimensions on both sides of the equation.
m*v is momentum, not energy
The equation is valid only if both sides have identical dimensions.

Answer: inconsistent


Response:
Reasoning:
1. For level-ground projectile motion, R = v^2 sin(2 theta) / g.
2. Convert theta=82 degrees through the sine of 2 theta.
3. Substitute v=41.6 m/s and g=9.81 m/s^2.
Final: {"answer": 48.6246, "unit": "m"}

Answer: 48.6246

Prompt: A projectile is launched on level ground with no air resistance at speed 41.6 m/s and angle 82 degrees. Compute the horizontal range in meters using g=9.81 m/s^2.

For level-ground projectile motion, R = v^2 sin(2 theta) / g.
Convert theta=82 degrees through the sine of 2 theta.
Substitute v=41.6 m/s and g=9.81 m/s^2.


Response:
Reasoning:
1. Mass equals amount in moles times molar mass.
2. Use m = 4.64 mol * 58.44 g/mol.
3. The mole unit cancels, leaving grams.
Final: {"answer": 271.1616, "unit": "g"}

Answer: 271.1616

Prompt: A sample contains 4.64 mol of sodium chloride. Using molar mass 58.44 g/mol, compute the sample mass in grams.

Mass equals amount in moles times molar mass.
Use m = 4.64 mol * 58.44 g/mol.
The mole unit cancels, leaving grams.


Response:
Reasoning:
1. Molarity is moles of solute divided by solution volume in liters.
2. Convert 3485 mL to 3.485 L.
3. Compute M = 3.665 / 3.485.
Final: {"answer": 1.0516, "unit": "mol/L"}

Answer: 1.0516

Prompt: A solution contains 3.665 mol of solute in 3485 mL of solution. Compute the molarity in mol/L.

Molarity is moles of solute divided by solution volume in liters.
Convert 3485 mL to 3.485 L.
Compute M = 3.665 / 3.485.


Response:
Reasoning:
1. Keep the boundary values fixed and update only the three interior grid points.
2. For each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.
3. Multiply each Laplacian by r=0.32 and add it to the current value.
Final: {"answer": [0.602, 0.15, 0.074], "unit": "temperature_units"}

Answer: 0.602

Answer: 0.15

Answer: 0.074

Prompt: For the 1D heat equation explicit finite-difference step, use u_i(next)=u_i+r*(u_{i-1}-2*u_i+u_{i+1}). Boundary values are left=0.75, right=-0.45; current interior values are [-0.55, 1.75, -0.95]. Use r=0.32. Return the next interior vector.

Keep the boundary values fixed and update only the three interior grid points.
For each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.
Multiply each Laplacian by r=0.32 and add it to the current value.


Response:
Reasoning:
1. The x component is magnitude times cos(theta).
2. The y component is magnitude times sin(theta).
3. Use theta=280 degrees and keep the unit as newtons.
Final: {"answer": [35.9452, -203.8552], "unit": "N"}

Answer: 35.9452

Answer: -203.8552

Prompt: A vector has magnitude 207 N at 280 degrees counterclockwise from the +x axis. Return its [x, y] components in newtons.

The x component is magnitude times cos(theta).
The y component is magnitude times sin(theta).
Use theta=280 degrees and keep the unit as newtons.


Response:
Reasoning:
1. The slope is (y2-y1)/(x2-x1).
2. The intercept is y1 - slope*x1.
3. Return the pair in [slope, intercept] order.
Final: {"answer": [1.2, -13.25], "unit": "dimensionless"}

Answer: 1.2

Answer: -13.25

Prompt: A line passes through points (13.25, 2.65) and (14.75, 4.45). Return [slope, intercept] for y = slope*x + intercept.

The slope is (y2-y1)/(x2-x1).
The intercept is y1 - slope*x1.
Return the pair in [slope, intercept] order.


Response:
Reasoning:
1. Mass equals amount in moles times molar mass.
2. Use m = 7.98 mol * 44.01 g/mol.
3. The mole unit cancels, leaving grams.
Final: {"answer": 351.1998, "unit": "g"}

Answer: 351.1998

Prompt: A sample contains 7.98 mol of carbon dioxide. Using molar mass 44.01 g/mol, compute the sample mass in grams.

Mass equals amount in moles times molar mass.
Use m = 7.98 mol * 44.01 g/mol.
The mole unit cancels, leaving grams.


Response:
Reasoning:
1. The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.
2. Evaluate f(9.2)=3.86 and f(14.5)=13.4.
3. The interval width is 5.3.
Final: {"answer": 45.739, "unit": "area_units"}

Answer: 45.739

Prompt: Use the trapezoid rule with one interval to approximate the integral of f(x)=1.8x+-12.7 from x=9.2 to x=14.5. Return the numeric integral estimate.

The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.
Evaluate f(9.2)=3.86 and f(14.5)=13.4.
The interval width is 5.3.

(x1 - x0) * ((slope * x0 + intercept) + (slope * x1 + intercept)) / 2


Response:
Reasoning:
1. The function contract has a normal path and at least one edge case.
2. The implementation checks the edge case before returning the normal result.

```python
def pairwise_ratios_003634(numerators, denominators):
    if len(numerators) != len(denominators):
        raise ValueError('length mismatch')
    out = []
    for numerator, denominator in zip(numerators, denominators):
        if denominator == 0:
            raise ValueError('zero denominator')
        out.append(numerator / denominator)
    return out
```
Final: {"answer": "python_code", "function": "pairwise_ratios_003634"}

Answer: python_code

Prompt: Write a Python function pairwise_ratios_003634(numerators, denominators) that returns a list of n/d values. Raise ValueError if lengths differ or any denominator is zero. Return a single fenced Python code block.

Identify required edge cases before writing the function.
Implement the shortest total function that satisfies the stated contract.
Avoid global state and return deterministic outputs.

try:
    pairwise_ratios_003634([1], [0])
    raise AssertionError('expected ValueError')
except ValueError:
    pass

try:
    pairwise_ratios_003634([1, 2], [1])
    raise AssertionError('expected ValueError')
except ValueError:
    pass


Response:
Reasoning:
1. Use Newton's second law F = m a.
2. Substitute m = 16.3 kg and a = 14.85 m/s^2.
3. The unit kg*m/s^2 is one newton.
Final: {"answer": 242.055, "unit": "N"}

Answer: 242.055

Prompt: A cart has mass 16.3 kg and measured acceleration 14.85 m/s^2. Compute the net force. Check the SI units and give only the final JSON after reasoning.

Use Newton's second law F = m a.
Substitute m = 16.3 kg and a = 14.85 m/s^2.
The unit kg*m/s^2 is one newton.


Response:
Reasoning:
1. Mass equals amount in moles times molar mass.
2. Use m = 0.1 mol * 58.44 g/mol.
3. The mole unit cancels, leaving grams.
Final: {"answer": 5.844, "unit": "g"}

Answer: 5.844

Prompt: A sample contains 0.1 mol of sodium chloride. Using molar mass 58.44 g/mol, compute the sample mass in grams.

Mass equals amount in moles times molar mass.
Use m = 0.1 mol * 58.44 g/mol.
The mole unit cancels, leaving grams.


Response:
Reasoning:
1. Kinetic energy is KE = 1/2 m v^2.
2. Compute v^2 = 43.45^2 and multiply by 0.5 * 25.15.
3. The unit kg*m^2/s^2 is one joule.
Final: {"answer": 23740.3739, "unit": "J"}

Answer: 23740.3739

Prompt: A body of mass 25.15 kg moves at 43.45 m/s. Find its kinetic energy in joules with unit reasoning.

Kinetic energy is KE = 1/2 m v^2.
Compute v^2 = 43.45^2 and multiply by 0.5 * 25.15.
The unit kg*m^2/s^2 is one joule.


Response:
Reasoning:
1. Mass equals amount in moles times molar mass.
2. Use m = 2.06 mol * 58.44 g/mol.
3. The mole unit cancels, leaving grams.
Final: {"answer": 120.3864, "unit": "g"}

Answer: 120.3864

Prompt: A sample contains 2.06 mol of sodium chloride. Using molar mass 58.44 g/mol, compute the sample mass in grams.

Mass equals amount in moles times molar mass.
Use m = 2.06 mol * 58.44 g/mol.
The mole unit cancels, leaving grams.


Response:
Reasoning:
1. Use Newton's second law F = m a.
2. Substitute m = 9.4 kg and a = 13.55 m/s^2.
3. The unit kg*m/s^2 is one newton.
Final: {"answer": 127.37, "unit": "N"}

Answer: 127.37

Prompt: A cart has mass 9.4 kg and measured acceleration 13.55 m/s^2. Compute the net force. Check the SI units and give only the final JSON after reasoning.

Use Newton's second law F = m a.
Substitute m = 9.4 kg and a = 13.55 m/s^2.
The unit kg*m/s^2 is one newton.


Response:
Reasoning:
1. Mass equals amount in moles times molar mass.
2. Use m = 7.09 mol * 58.44 g/mol.
3. The mole unit cancels, leaving grams.
Final: {"answer": 414.3396, "unit": "g"}

Answer: 414.3396

Prompt: A sample contains 7.09 mol of sodium chloride. Using molar mass 58.44 g/mol, compute the sample mass in grams.

Mass equals amount in moles times molar mass.
Use m = 7.09 mol * 58.44 g/mol.
The mole unit cancels, leaving grams.


Response:
Reasoning:
1. Molarity is moles of solute divided by solution volume in liters.
2. Convert 2930 mL to 2.93 L.
3. Compute M = 2.47 / 2.93.
Final: {"answer": 0.843, "unit": "mol/L"}

Answer: 0.843

Prompt: A solution contains 2.47 mol of solute in 2930 mL of solution. Compute the molarity in mol/L.

Molarity is moles of solute divided by solution volume in liters.
Convert 2930 mL to 2.93 L.
Compute M = 2.47 / 2.93.


Response:
Reasoning:
1. Use the ideal gas law P V = n R T.
2. Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.
3. Compute P = 3.31 * 8.314 * 348 / 56.2.
Final: {"answer": 170.4045, "unit": "kPa"}

Answer: 170.4045

Prompt: An ideal gas sample has n=3.31 mol, T=348 K, and V=56.2 L. Using R=8.314 kPa*L/(mol*K), compute the pressure in kPa.

Use the ideal gas law P V = n R T.
Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.
Compute P = 3.31 * 8.314 * 348 / 56.2.


Response:
Reasoning:
1. There are 100 centimeters in one meter.
2. Apply the conversion factor directly to the given value.
3. Compute 4888.0 / 100.
Final: {"answer": 48.88, "unit": "m"}

Answer: 48.88

Prompt: Convert 4888 cm to m. Return the converted value with unit.

There are 100 centimeters in one meter.
Apply the conversion factor directly to the given value.
Compute 4888.0 / 100.


Response:
Reasoning:
1. Check whether all variables required by the governing equation or specification are present.
2. The missing required information is: required_fields, allowed_transformations.
3. A numeric or code answer would require inventing unstated assumptions, so abstain.
Final: {"answer": "INSUFFICIENT_INFO", "missing": ["required_fields", "allowed_transformations"]}

Answer: INSUFFICIENT_INFO

Prompt: Write a sanitizer for valid mobile experiment records in release 429910, but the prompt does not state which fields are required or which transformations are allowed. If there is insufficient information, say so explicitly.

Check whether all variables required by the governing equation or specification are present.
The missing required information is: required_fields, allowed_transformations.
A numeric or code answer would require inventing unstated assumptions, so abstain.


Response:
Reasoning:
1. Use the ideal gas law P V = n R T.
2. Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.
3. Compute P = 0.29 * 8.314 * 353 / 84.3.
Final: {"answer": 10.0961, "unit": "kPa"}

Answer: 10.0961

Prompt: An ideal gas sample has n=0.29 mol, T=353 K, and V=84.3 L. Using R=8.314 kPa*L/(mol*K), compute the pressure in kPa.

Use the ideal gas law P V = n R T.
Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.
Compute P = 0.29 * 8.314 * 353 / 84.3.


Response:
Reasoning:
1. The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.
2. Evaluate f(-0.5)=6.55 and f(8.4)=-31.72.
3. The interval width is 8.9.
Final: {"answer": -112.0065, "unit": "area_units"}

Answer: -112.0065

Prompt: Use the trapezoid rule with one interval to approximate the integral of f(x)=-4.3x+4.4 from x=-0.5 to x=8.4. Return the numeric integral estimate.

The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.
Evaluate f(-0.5)=6.55 and f(8.4)=-31.72.
The interval width is 8.9.


Response:
Reasoning:
1. There are 1000 grams in one kilogram.
2. Apply the conversion factor directly to the given value.
3. Compute 73.0 / 1000.
Final: {"answer": 0.073, "unit": "kg"}

Answer: 0.073

Prompt: Convert 73 g to kg. Return the converted value with unit.

There are 1000 grams in one kilogram.
Apply the conversion factor directly to the given value.
Compute 73.0 / 1000.


Response:
Reasoning:
1. There are 1000 grams in one kilogram.
2. Apply the conversion factor directly to the given value.
3. Compute 13938.0 / 1000.
Final: {"answer": 13.938, "unit": "kg"}

Answer: 13.938

Prompt: Convert 13938 g to kg. Return the converted value with unit.

There are 1000 grams in one kilogram.
Apply the conversion factor directly to the given value.
Compute 13938.0 / 1000.


Response:
Reasoning:
1. The slope is (y2-y1)/(x2-x1).
2. The intercept is y1 - slope*x1.
3. Return the pair in [slope, intercept] order.
Final: {"answer": [-9.35, -4.0], "unit": "dimensionless"}

Answer: -9.35

Answer: -4.0

Prompt: A line passes through points (5.25, -53.0875) and (14.25, -137.237). Return [slope, intercept] for y = slope*x + intercept.

The slope is (y2-y1)/(x2-x1).
The intercept is y1 - slope*x1.
Return the pair in [slope, intercept] order.


Response:
Reasoning:
1. The slope is (y2-y1)/(x2-x1).
2. The intercept is y1 - slope*x1.
3. Return the pair in [slope, intercept] order.
Final: {"answer": [4.6, 22.25], "unit": "dimensionless"}

Answer: 4.6

Answer: 22.25

Prompt: A line passes through points (16.75, 99.3) and (30.25, 161.4). Return [slope, intercept] for y = slope*x + intercept.

The slope is (y2-y1)/(x2-x1).
The intercept is y1 - slope*x1.
Return the pair in [slope, intercept] order.


Response:
Reasoning:
1. The x component is magnitude times cos(theta).
2. The y component is magnitude times sin(theta).
3. Use theta=115 degrees and keep the unit as newtons.
Final: {"answer": [-154.467, 331.2555], "unit": "N"}

Answer: -154.467

Answer: 331.2555

Prompt: A vector has magnitude 365.5 N at 115 degrees counterclockwise from the +x axis. Return its [x, y] components in newtons.

The x component is magnitude times cos(theta).
The y component is magnitude times sin(theta).
Use theta=115 degrees and keep the unit as newtons.


Response:
Reasoning:
1. The slope is (y2-y1)/(x2-x1).
2. The intercept is y1 - slope*x1.
3. Return the pair in [slope, intercept] order.
Final: {"answer": [-0.65, -3.25], "unit": "dimensionless"}

Answer: -0.65

Answer: -3.25

Prompt: A line passes through points (-18.75, 8.9375) and (-5, 0). Return [slope, intercept] for y = slope*x + intercept.

The slope is (y2-y1)/(x2-x1).
The intercept is y1 - slope*x1.
Return the pair in [slope, intercept] order.


Response:
Reasoning:
1. Use the ideal gas law P V = n R T.
2. Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.
3. Compute P = 2.97 * 8.314 * 525 / 97.0.
Final: {"answer": 133.6454, "unit": "kPa"}

Answer: 133.6454

Prompt: An ideal gas sample has n=2.97 mol, T=525 K, and V=97.0 L. Using R=8.314 kPa*L/(mol*K), compute the pressure in kPa.

Use the ideal gas law P V = n R T.
Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.
Compute P = 2.97 * 8.314 * 525 / 97.0.


Response:
Reasoning:
1. The x component is magnitude times cos(theta).
2. The y component is magnitude times sin(theta).
3. Use theta=6 degrees and keep the unit as newtons.
Final: {"answer": [171.0578, 17.9789], "unit": "N"}

Answer: 171.0578

Answer: 17.9789

Prompt: A vector has magnitude 172 N at 6 degrees counterclockwise from the +x axis. Return its [x, y] components in newtons.

The x component is magnitude times cos(theta).
The y component is magnitude times sin(theta).
Use theta=6 degrees and keep the unit as newtons.


Response:
Reasoning:
1. The slope is (y2-y1)/(x2-x1).
2. The intercept is y1 - slope*x1.
3. Return the pair in [slope, intercept] order.
Final: {"answer": [-1.55, -24.75], "unit": "dimensionless"}

Answer: -1.55

Answer: -24.75

Prompt: A line passes through points (-0.5, -23.975) and (5.75, -33.6625). Return [slope, intercept] for y = slope*x + intercept.

The slope is (y2-y1)/(x2-x1).
The intercept is y1 - slope*x1.
Return the pair in [slope, intercept] order.


Response:
Reasoning:
1. Check whether all variables required by the governing equation or specification are present.
2. The missing required information is: rate_constant, number_of_steps.
3. A numeric or code answer would require inventing unstated assumptions, so abstain.
Final: {"answer": "INSUFFICIENT_INFO", "missing": ["rate_constant", "number_of_steps"]}

Answer: INSUFFICIENT_INFO

Prompt: Use explicit Euler for dy/dt = -k y. The prompt gives y(0)=67.5 and h=1.9, but omits both k and the number of steps. If there is insufficient information, say so explicitly.

Check whether all variables required by the governing equation or specification are present.
The missing required information is: rate_constant, number_of_steps.
A numeric or code answer would require inventing unstated assumptions, so abstain.


Response:
Reasoning:
1. The slope is (y2-y1)/(x2-x1).
2. The intercept is y1 - slope*x1.
3. Return the pair in [slope, intercept] order.
Final: {"answer": [-1.3, -9.25], "unit": "dimensionless"}

Answer: -1.3

Answer: -9.25

Prompt: A line passes through points (-4.75, -3.075) and (3, -13.15). Return [slope, intercept] for y = slope*x + intercept.

The slope is (y2-y1)/(x2-x1).
The intercept is y1 - slope*x1.
Return the pair in [slope, intercept] order.


Response:
Reasoning:
1. Explicit Euler updates y_{n+1} = y_n + h f(y_n).
2. Here f(y) = -0.86 y, so each step multiplies y by 1 - h*0.86.
3. Apply that update for 2 steps and round the final state.
Final: {"answer": 8.4085, "unit": "state_units"}

Answer: 8.4085

Prompt: Use explicit Euler on dy/dt = -0.86 y with y(0)=28, step size h=1.8, for 2 steps. What is y after the final step?

Explicit Euler updates y_{n+1} = y_n + h f(y_n).
Here f(y) = -0.86 y, so each step multiplies y by 1 - h*0.86.
Apply that update for 2 steps and round the final state.


Response:
Reasoning:
1. Ohm's law gives I = V / R.
2. Power can be written as P = V I = V^2 / R.
3. Substitute V=197.5 V and R=199.2 ohm.
Final: {"answer": 195.8145, "unit": "W"}

Answer: 195.8145

Prompt: A resistor has resistance 199.2 ohm and voltage 197.5 V across it. Compute the dissipated power in watts.

Ohm's law gives I = V / R.
Power can be written as P = V I = V^2 / R.
Substitute V=197.5 V and R=199.2 ohm.


Response:
Reasoning:
1. For level-ground projectile motion, R = v^2 sin(2 theta) / g.
2. Convert theta=37 degrees through the sine of 2 theta.
3. Substitute v=16.9 m/s and g=9.81 m/s^2.
Final: {"answer": 27.9863, "unit": "m"}

Answer: 27.9863

Prompt: A projectile is launched on level ground with no air resistance at speed 16.9 m/s and angle 37 degrees. Compute the horizontal range in meters using g=9.81 m/s^2.

For level-ground projectile motion, R = v^2 sin(2 theta) / g.
Convert theta=37 degrees through the sine of 2 theta.
Substitute v=16.9 m/s and g=9.81 m/s^2.


Response:
Reasoning:
1. Check whether all variables required by the governing equation or specification are present.
2. The missing required information is: launch_angle_or_vertical_velocity.
3. A numeric or code answer would require inventing unstated assumptions, so abstain.
Final: {"answer": "INSUFFICIENT_INFO", "missing": ["launch_angle_or_vertical_velocity"]}

Answer: INSUFFICIENT_INFO

Prompt: Compute projectile range on level ground. The prompt gives initial speed 58.9 m/s but does not give launch angle or vertical velocity. If there is insufficient information, say so explicitly.

Check whether all variables required by the governing equation or specification are present.
The missing required information is: launch_angle_or_vertical_velocity.
A numeric or code answer would require inventing unstated assumptions, so abstain.


Response:
Reasoning:
1. Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).
2. Use N0=630 mg, t=84.5 h, and T_half=9.5 h.
3. The remaining amount has the same mass unit as the initial amount.
Final: {"answer": 1.3236, "unit": "mg"}

Answer: 1.3236

Prompt: A radioactive sample starts with 630 mg. Its half-life is 9.5 hours. How many mg remain after 84.5 hours?

Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).
Use N0=630 mg, t=84.5 h, and T_half=9.5 h.
The remaining amount has the same mass unit as the initial amount.


Response:
Reasoning:
1. The function contract has a normal path and at least one edge case.
2. The implementation checks the edge case before returning the normal result.

```python
def clamp_003958(x, lo, hi):
    if lo > hi:
        raise ValueError('lo must be <= hi')
    return min(max(x, lo), hi)
```
Final: {"answer": "python_code", "function": "clamp_003958"}

Answer: python_code

Prompt: Write a Python function clamp_003958(x, lo, hi) that clips x into the inclusive interval [lo, hi]. It must raise ValueError if lo > hi. Return a single fenced Python code block.

Identify required edge cases before writing the function.
Implement the shortest total function that satisfies the stated contract.
Avoid global state and return deterministic outputs.

try:
    clamp_003958(1, 3, 2)
    raise AssertionError('expected ValueError')
except ValueError:
    pass


Response:
Reasoning:
1. Use Newton's second law F = m a.
2. Substitute m = 17.5 kg and a = 9.2 m/s^2.
3. The unit kg*m/s^2 is one newton.
Final: {"answer": 161.0, "unit": "N"}

Answer: 161.0

Prompt: A cart has mass 17.5 kg and measured acceleration 9.2 m/s^2. Compute the net force. Check the SI units and give only the final JSON after reasoning.

Use Newton's second law F = m a.
Substitute m = 17.5 kg and a = 9.2 m/s^2.
The unit kg*m/s^2 is one newton.


Response:
Reasoning:
1. Kinetic energy is KE = 1/2 m v^2.
2. Compute v^2 = 33.45^2 and multiply by 0.5 * 20.8.
3. The unit kg*m^2/s^2 is one joule.
Final: {"answer": 11636.586, "unit": "J"}

Answer: 11636.586

Prompt: A body of mass 20.8 kg moves at 33.45 m/s. Find its kinetic energy in joules with unit reasoning.

Kinetic energy is KE = 1/2 m v^2.
Compute v^2 = 33.45^2 and multiply by 0.5 * 20.8.
The unit kg*m^2/s^2 is one joule.


Response:
Reasoning:
1. Use Newton's second law F = m a.
2. Substitute m = 11.5 kg and a = 13.5 m/s^2.
3. The unit kg*m/s^2 is one newton.
Final: {"answer": 155.25, "unit": "N"}

Answer: 155.25

Prompt: A cart has mass 11.5 kg and measured acceleration 13.5 m/s^2. Compute the net force. Check the SI units and give only the final JSON after reasoning.

Use Newton's second law F = m a.
Substitute m = 11.5 kg and a = 13.5 m/s^2.
The unit kg*m/s^2 is one newton.


Response:
Reasoning:
1. The slope is (y2-y1)/(x2-x1).
2. The intercept is y1 - slope*x1.
3. Return the pair in [slope, intercept] order.
Final: {"answer": [-5.65, -21.5], "unit": "dimensionless"}

Answer: -5.65

Answer: -21.5

Prompt: A line passes through points (-0.25, -20.0875) and (13.5, -97.775). Return [slope, intercept] for y = slope*x + intercept.

The slope is (y2-y1)/(x2-x1).
The intercept is y1 - slope*x1.
Return the pair in [slope, intercept] order.


Response:
Reasoning:
1. For level-ground projectile motion, R = v^2 sin(2 theta) / g.
2. Convert theta=73 degrees through the sine of 2 theta.
3. Substitute v=19.1 m/s and g=9.81 m/s^2.
Final: {"answer": 20.795, "unit": "m"}

Answer: 20.795

Prompt: A projectile is launched on level ground with no air resistance at speed 19.1 m/s and angle 73 degrees. Compute the horizontal range in meters using g=9.81 m/s^2.

For level-ground projectile motion, R = v^2 sin(2 theta) / g.
Convert theta=73 degrees through the sine of 2 theta.
Substitute v=19.1 m/s and g=9.81 m/s^2.


Response:
Reasoning:
1. Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).
2. Use N0=10 mg, t=345.5 h, and T_half=67.5 h.
3. The remaining amount has the same mass unit as the initial amount.
Final: {"answer": 0.2879, "unit": "mg"}

Answer: 0.2879

Prompt: A radioactive sample starts with 10 mg. Its half-life is 67.5 hours. How many mg remain after 345.5 hours?

Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).
Use N0=10 mg, t=345.5 h, and T_half=67.5 h.
The remaining amount has the same mass unit as the initial amount.


Response:
Reasoning:
1. The slope is (y2-y1)/(x2-x1).
2. The intercept is y1 - slope*x1.
3. Return the pair in [slope, intercept] order.
Final: {"answer": [-4.5, -15.25], "unit": "dimensionless"}

Answer: -4.5

Answer: -15.25

Prompt: A line passes through points (9.5, -58) and (19.75, -104.125). Return [slope, intercept] for y = slope*x + intercept.

The slope is (y2-y1)/(x2-x1).
The intercept is y1 - slope*x1.
Return the pair in [slope, intercept] order.


Response:
Reasoning:
1. Explicit Euler updates y_{n+1} = y_n + h f(y_n).
2. Here f(y) = -0.97 y, so each step multiplies y by 1 - h*0.97.
3. Apply that update for 5 steps and round the final state.
Final: {"answer": -5.7474, "unit": "state_units"}

Answer: -5.7474

Prompt: Use explicit Euler on dy/dt = -0.97 y with y(0)=13.5, step size h=1.9, for 5 steps. What is y after the final step?

Explicit Euler updates y_{n+1} = y_n + h f(y_n).
Here f(y) = -0.97 y, so each step multiplies y by 1 - h*0.97.
Apply that update for 5 steps and round the final state.


Response:
Reasoning:
1. The x component is magnitude times cos(theta).
2. The y component is magnitude times sin(theta).
3. Use theta=120 degrees and keep the unit as newtons.
Final: {"answer": [-48.25, 83.5715], "unit": "N"}

Answer: -48.25

Answer: 83.5715

Prompt: A vector has magnitude 96.5 N at 120 degrees counterclockwise from the +x axis. Return its [x, y] components in newtons.

The x component is magnitude times cos(theta).
The y component is magnitude times sin(theta).
Use theta=120 degrees and keep the unit as newtons.


Response:
Reasoning:
1. Use Newton's second law F = m a.
2. Substitute m = 14.35 kg and a = 5.35 m/s^2.
3. The unit kg*m/s^2 is one newton.
Final: {"answer": 76.7725, "unit": "N"}

Answer: 76.7725

Prompt: A cart has mass 14.35 kg and measured acceleration 5.35 m/s^2. Compute the net force. Check the SI units and give only the final JSON after reasoning.

Use Newton's second law F = m a.
Substitute m = 14.35 kg and a = 5.35 m/s^2.
The unit kg*m/s^2 is one newton.


Response:
Reasoning:
1. Use Q = m c DeltaT.
2. The mass is already in grams, matching the specific heat denominator.
3. Compute Q = 1625 * 1.12 * 66.
Final: {"answer": 120120.0, "unit": "J"}

Answer: 120120.0

Prompt: A 1625 g sample has specific heat 1.12 J/(g*K). How much heat is needed to raise its temperature by 66 K?

Use Q = m c DeltaT.
The mass is already in grams, matching the specific heat denominator.
Compute Q = 1625 * 1.12 * 66.


Response:
Reasoning:
1. Keep the boundary values fixed and update only the three interior grid points.
2. For each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.
3. Multiply each Laplacian by r=0.02 and add it to the current value.
Final: {"answer": [-0.869, -1.196, 1.086], "unit": "temperature_units"}

Answer: -0.869

Answer: -1.196

Answer: 1.086

Prompt: For the 1D heat equation explicit finite-difference step, use u_i(next)=u_i+r*(u_{i-1}-2*u_i+u_{i+1}). Boundary values are left=1, right=2.75; current interior values are [-0.9, -1.25, 1.1]. Use r=0.02. Return the next interior vector.

Keep the boundary values fixed and update only the three interior grid points.
For each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.
Multiply each Laplacian by r=0.02 and add it to the current value.


Response:
Reasoning:
1. For level-ground projectile motion, R = v^2 sin(2 theta) / g.
2. Convert theta=55 degrees through the sine of 2 theta.
3. Substitute v=46.3 m/s and g=9.81 m/s^2.
Final: {"answer": 205.3425, "unit": "m"}

Answer: 205.3425

Prompt: A projectile is launched on level ground with no air resistance at speed 46.3 m/s and angle 55 degrees. Compute the horizontal range in meters using g=9.81 m/s^2.

For level-ground projectile motion, R = v^2 sin(2 theta) / g.
Convert theta=55 degrees through the sine of 2 theta.
Substitute v=46.3 m/s and g=9.81 m/s^2.


Response:
Reasoning:
1. Compare the dimensions on both sides of the equation.
2. m*v is momentum, not energy
3. The equation is valid only if both sides have identical dimensions.
Final: {"answer": "inconsistent"}

Answer: inconsistent

Prompt: In field worksheet case 383356, check dimensional consistency for E = m * v. The left side has dimensions kg*m^2/s^2 and the right side has dimensions kg*m/s. Return consistent or inconsistent with a brief reason.

Compare the dimensions on both sides of the equation.
m*v is momentum, not energy
The equation is valid only if both sides have identical dimensions.

Answer: inconsistent


Response:
Reasoning:
1. Molarity is moles of solute divided by solution volume in liters.
2. Convert 4295 mL to 4.295 L.
3. Compute M = 3.355 / 4.295.
Final: {"answer": 0.7811, "unit": "mol/L"}

Answer: 0.7811

Prompt: A solution contains 3.355 mol of solute in 4295 mL of solution. Compute the molarity in mol/L.

Molarity is moles of solute divided by solution volume in liters.
Convert 4295 mL to 4.295 L.
Compute M = 3.355 / 4.295.


Response:
Reasoning:
1. Explicit Euler updates y_{n+1} = y_n + h f(y_n).
2. Here f(y) = -0.81 y, so each step multiplies y by 1 - h*0.81.
3. Apply that update for 9 steps and round the final state.
Final: {"answer": 0.0, "unit": "state_units"}

Answer: 0.0

Prompt: Use explicit Euler on dy/dt = -0.81 y with y(0)=59, step size h=1.3, for 9 steps. What is y after the final step?

Explicit Euler updates y_{n+1} = y_n + h f(y_n).
Here f(y) = -0.81 y, so each step multiplies y by 1 - h*0.81.
Apply that update for 9 steps and round the final state.


Response:
Reasoning:
1. The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.
2. Evaluate f(3)=6.8 and f(9.2)=-10.56.
3. The interval width is 6.2.
Final: {"answer": -11.656, "unit": "area_units"}

Answer: -11.656

Prompt: Use the trapezoid rule with one interval to approximate the integral of f(x)=-2.8x+15.2 from x=3 to x=9.2. Return the numeric integral estimate.

The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.
Evaluate f(3)=6.8 and f(9.2)=-10.56.
The interval width is 6.2.


Response:
Reasoning:
1. The x component is magnitude times cos(theta).
2. The y component is magnitude times sin(theta).
3. Use theta=118 degrees and keep the unit as newtons.
Final: {"answer": [-71.8291, 135.091], "unit": "N"}

Answer: -71.8291

Answer: 135.091

Prompt: A vector has magnitude 153 N at 118 degrees counterclockwise from the +x axis. Return its [x, y] components in newtons.

The x component is magnitude times cos(theta).
The y component is magnitude times sin(theta).
Use theta=118 degrees and keep the unit as newtons.


Response:
Reasoning:
1. There are 100 centimeters in one meter.
2. Apply the conversion factor directly to the given value.
3. Compute 3861.0 / 100.
Final: {"answer": 38.61, "unit": "m"}

Answer: 38.61

Prompt: Convert 3861 cm to m. Return the converted value with unit.

There are 100 centimeters in one meter.
Apply the conversion factor directly to the given value.
Compute 3861.0 / 100.


Response:
Reasoning:
1. The x component is magnitude times cos(theta).
2. The y component is magnitude times sin(theta).
3. Use theta=25 degrees and keep the unit as newtons.
Final: {"answer": [224.3112, 104.598], "unit": "N"}

Answer: 224.3112

Answer: 104.598

Prompt: A vector has magnitude 247.5 N at 25 degrees counterclockwise from the +x axis. Return its [x, y] components in newtons.

The x component is magnitude times cos(theta).
The y component is magnitude times sin(theta).
Use theta=25 degrees and keep the unit as newtons.


Response:
Reasoning:
1. The slope is (y2-y1)/(x2-x1).
2. The intercept is y1 - slope*x1.
3. Return the pair in [slope, intercept] order.
Final: {"answer": [-6.8, 22.75], "unit": "dimensionless"}

Answer: -6.8

Answer: 22.75

Prompt: A line passes through points (-9, 83.95) and (-3.5, 46.55). Return [slope, intercept] for y = slope*x + intercept.

The slope is (y2-y1)/(x2-x1).
The intercept is y1 - slope*x1.
Return the pair in [slope, intercept] order.


Response:
Reasoning:
1. Molarity is moles of solute divided by solution volume in liters.
2. Convert 4100 mL to 4.1 L.
3. Compute M = 4.18 / 4.1.
Final: {"answer": 1.0195, "unit": "mol/L"}

Answer: 1.0195

Prompt: A solution contains 4.18 mol of solute in 4100 mL of solution. Compute the molarity in mol/L.

Molarity is moles of solute divided by solution volume in liters.
Convert 4100 mL to 4.1 L.
Compute M = 4.18 / 4.1.


Response:
Reasoning:
1. Mass equals amount in moles times molar mass.
2. Use m = 6.56 mol * 100.087 g/mol.
3. The mole unit cancels, leaving grams.
Final: {"answer": 656.5707, "unit": "g"}

Answer: 656.5707

Prompt: A sample contains 6.56 mol of calcium carbonate. Using molar mass 100.087 g/mol, compute the sample mass in grams.

Mass equals amount in moles times molar mass.
Use m = 6.56 mol * 100.087 g/mol.
The mole unit cancels, leaving grams.


Response:
Reasoning:
1. Kinetic energy is KE = 1/2 m v^2.
2. Compute v^2 = 5.7^2 and multiply by 0.5 * 13.45.
3. The unit kg*m^2/s^2 is one joule.
Final: {"answer": 218.4952, "unit": "J"}

Answer: 218.4952

Prompt: A body of mass 13.45 kg moves at 5.7 m/s. Find its kinetic energy in joules with unit reasoning.

Kinetic energy is KE = 1/2 m v^2.
Compute v^2 = 5.7^2 and multiply by 0.5 * 13.45.
The unit kg*m^2/s^2 is one joule.


Response:
Reasoning:
1. Explicit Euler updates y_{n+1} = y_n + h f(y_n).
2. Here f(y) = -0.8 y, so each step multiplies y by 1 - h*0.8.
3. Apply that update for 6 steps and round the final state.
Final: {"answer": 0.015, "unit": "state_units"}

Answer: 0.015

Prompt: Use explicit Euler on dy/dt = -0.8 y with y(0)=14, step size h=1.65, for 6 steps. What is y after the final step?

Explicit Euler updates y_{n+1} = y_n + h f(y_n).
Here f(y) = -0.8 y, so each step multiplies y by 1 - h*0.8.
Apply that update for 6 steps and round the final state.


Response:
Reasoning:
1. The x component is magnitude times cos(theta).
2. The y component is magnitude times sin(theta).
3. Use theta=231 degrees and keep the unit as newtons.
Final: {"answer": [-140.3384, -173.3035], "unit": "N"}

Answer: -140.3384

Answer: -173.3035

Prompt: A vector has magnitude 223 N at 231 degrees counterclockwise from the +x axis. Return its [x, y] components in newtons.

The x component is magnitude times cos(theta).
The y component is magnitude times sin(theta).
Use theta=231 degrees and keep the unit as newtons.


Response:
Reasoning:
1. Compare the dimensions on both sides of the equation.
2. mass times acceleration has newton dimensions
3. The equation is valid only if both sides have identical dimensions.
Final: {"answer": "consistent"}

Answer: consistent

Prompt: In sensor calibration case 498299, check dimensional consistency for F = m * a. The left side has dimensions kg*m/s^2 and the right side has dimensions kg*m/s^2. Return consistent or inconsistent with a brief reason.

Compare the dimensions on both sides of the equation.
mass times acceleration has newton dimensions
The equation is valid only if both sides have identical dimensions.

Answer: consistent


Response:
Reasoning:
1. Explicit Euler updates y_{n+1} = y_n + h f(y_n).
2. Here f(y) = -0.31 y, so each step multiplies y by 1 - h*0.31.
3. Apply that update for 12 steps and round the final state.
Final: {"answer": 0.0003, "unit": "state_units"}

Answer: 0.0003

Prompt: Use explicit Euler on dy/dt = -0.31 y with y(0)=38.5, step size h=2, for 12 steps. What is y after the final step?

Explicit Euler updates y_{n+1} = y_n + h f(y_n).
Here f(y) = -0.31 y, so each step multiplies y by 1 - h*0.31.
Apply that update for 12 steps and round the final state.


Response:
Reasoning:
1. Compare the dimensions on both sides of the equation.
2. m*v is momentum, not energy
3. The equation is valid only if both sides have identical dimensions.
Final: {"answer": "inconsistent"}

Answer: inconsistent

Prompt: In student derivation case 869793, check dimensional consistency for E = m * v. The left side has dimensions kg*m^2/s^2 and the right side has dimensions kg*m/s. Return consistent or inconsistent with a brief reason.

Compare the dimensions on both sides of the equation.
m*v is momentum, not energy
The equation is valid only if both sides have identical dimensions.

Answer: inconsistent


Response:
Reasoning:
1. Use Newton's second law F = m a.
2. Substitute m = 6.05 kg and a = 11.65 m/s^2.
3. The unit kg*m/s^2 is one newton.
Final: {"answer": 70.4825, "unit": "N"}

Answer: 70.4825

Prompt: A cart has mass 6.05 kg and measured acceleration 11.65 m/s^2. Compute the net force. Check the SI units and give only the final JSON after reasoning.

Use Newton's second law F = m a.
Substitute m = 6.05 kg and a = 11.65 m/s^2.
The unit kg*m/s^2 is one newton.


Response:
Reasoning:
1. Mass equals amount in moles times molar mass.
2. Use m = 0.44 mol * 18.015 g/mol.
3. The mole unit cancels, leaving grams.
Final: {"answer": 7.9266, "unit": "g"}

Answer: 7.9266

Prompt: A sample contains 0.44 mol of water. Using molar mass 18.015 g/mol, compute the sample mass in grams.

Mass equals amount in moles times molar mass.
Use m = 0.44 mol * 18.015 g/mol.
The mole unit cancels, leaving grams.


Response:
Reasoning:
1. Molarity is moles of solute divided by solution volume in liters.
2. Convert 1010 mL to 1.01 L.
3. Compute M = 1.45 / 1.01.
Final: {"answer": 1.4356, "unit": "mol/L"}

Answer: 1.4356

Prompt: A solution contains 1.45 mol of solute in 1010 mL of solution. Compute the molarity in mol/L.

Molarity is moles of solute divided by solution volume in liters.
Convert 1010 mL to 1.01 L.
Compute M = 1.45 / 1.01.


Response:
Reasoning:
1. Use Newton's second law F = m a.
2. Substitute m = 18.2 kg and a = 7.3 m/s^2.
3. The unit kg*m/s^2 is one newton.
Final: {"answer": 132.86, "unit": "N"}

Answer: 132.86

Prompt: A cart has mass 18.2 kg and measured acceleration 7.3 m/s^2. Compute the net force. Check the SI units and give only the final JSON after reasoning.

Use Newton's second law F = m a.
Substitute m = 18.2 kg and a = 7.3 m/s^2.
The unit kg*m/s^2 is one newton.


Response:
Reasoning:
1. Kinetic energy is KE = 1/2 m v^2.
2. Compute v^2 = 43.8^2 and multiply by 0.5 * 15.75.
3. The unit kg*m^2/s^2 is one joule.
Final: {"answer": 15107.715, "unit": "J"}

Answer: 15107.715

Prompt: A body of mass 15.75 kg moves at 43.8 m/s. Find its kinetic energy in joules with unit reasoning.

Kinetic energy is KE = 1/2 m v^2.
Compute v^2 = 43.8^2 and multiply by 0.5 * 15.75.
The unit kg*m^2/s^2 is one joule.


Response:
Reasoning:
1. Ohm's law gives I = V / R.
2. Power can be written as P = V I = V^2 / R.
3. Substitute V=100 V and R=78.5 ohm.
Final: {"answer": 127.3885, "unit": "W"}

Answer: 127.3885

Prompt: A resistor has resistance 78.5 ohm and voltage 100 V across it. Compute the dissipated power in watts.

Ohm's law gives I = V / R.
Power can be written as P = V I = V^2 / R.
Substitute V=100 V and R=78.5 ohm.


Response:
Reasoning:
1. Kelvin equals Celsius plus 273.15.
2. Apply the conversion factor directly to the given value.
3. Compute 249.5 + 273.15.
Final: {"answer": 522.65, "unit": "K"}

Answer: 522.65

Prompt: Convert 249.5 degC to K. Return the converted value with unit.

Kelvin equals Celsius plus 273.15.
Apply the conversion factor directly to the given value.
Compute 249.5 + 273.15.


Response:
Reasoning:
1. Compare the dimensions on both sides of the equation.
2. grams cancel with J/(g*K), and kelvin cancels, leaving joules
3. The equation is valid only if both sides have identical dimensions.
Final: {"answer": "consistent"}

Answer: consistent

Prompt: In quality-control check case 60851, check dimensional consistency for Q = m * c * DeltaT. The left side has dimensions J and the right side has dimensions J. Return consistent or inconsistent with a brief reason.

Compare the dimensions on both sides of the equation.
grams cancel with J/(g*K), and kelvin cancels, leaving joules
The equation is valid only if both sides have identical dimensions.

Answer: consistent


Response:
Reasoning:
1. Use Q = m c DeltaT.
2. The mass is already in grams, matching the specific heat denominator.
3. Compute Q = 285 * 3.845 * 79.
Final: {"answer": 86570.175, "unit": "J"}

Answer: 86570.175

Prompt: A 285 g sample has specific heat 3.845 J/(g*K). How much heat is needed to raise its temperature by 79 K?

Use Q = m c DeltaT.
The mass is already in grams, matching the specific heat denominator.
Compute Q = 285 * 3.845 * 79.


Response:
Reasoning:
1. Check whether all variables required by the governing equation or specification are present.
2. The missing required information is: launch_angle_or_vertical_velocity.
3. A numeric or code answer would require inventing unstated assumptions, so abstain.
Final: {"answer": "INSUFFICIENT_INFO", "missing": ["launch_angle_or_vertical_velocity"]}

Answer: INSUFFICIENT_INFO

Prompt: Compute projectile range on level ground. The prompt gives initial speed 27.3 m/s but does not give launch angle or vertical velocity. If there is insufficient information, say so explicitly.

Check whether all variables required by the governing equation or specification are present.
The missing required information is: launch_angle_or_vertical_velocity.
A numeric or code answer would require inventing unstated assumptions, so abstain.


Response:
Reasoning:
1. Use Newton's second law F = m a.
2. Substitute m = 18.55 kg and a = 11.25 m/s^2.
3. The unit kg*m/s^2 is one newton.
Final: {"answer": 208.6875, "unit": "N"}

Answer: 208.6875

Prompt: A cart has mass 18.55 kg and measured acceleration 11.25 m/s^2. Compute the net force. Check the SI units and give only the final JSON after reasoning.

Use Newton's second law F = m a.
Substitute m = 18.55 kg and a = 11.25 m/s^2.
The unit kg*m/s^2 is one newton.


Response:
Reasoning:
1. There are 100 centimeters in one meter.
2. Apply the conversion factor directly to the given value.
3. Compute 3788.0 / 100.
Final: {"answer": 37.88, "unit": "m"}

Answer: 37.88

Prompt: Convert 3788 cm to m. Return the converted value with unit.

There are 100 centimeters in one meter.
Apply the conversion factor directly to the given value.
Compute 3788.0 / 100.


Response:
Reasoning:
1. Ohm's law gives I = V / R.
2. Power can be written as P = V I = V^2 / R.
3. Substitute V=0.6 V and R=59.1 ohm.
Final: {"answer": 0.0061, "unit": "W"}

Answer: 0.0061

Prompt: A resistor has resistance 59.1 ohm and voltage 0.6 V across it. Compute the dissipated power in watts.

Ohm's law gives I = V / R.
Power can be written as P = V I = V^2 / R.
Substitute V=0.6 V and R=59.1 ohm.


Response:
Reasoning:
1. Explicit Euler updates y_{n+1} = y_n + h f(y_n).
2. Here f(y) = -0.03 y, so each step multiplies y by 1 - h*0.03.
3. Apply that update for 4 steps and round the final state.
Final: {"answer": 6.3967, "unit": "state_units"}

Answer: 6.3967

Prompt: Use explicit Euler on dy/dt = -0.03 y with y(0)=7.5, step size h=1.3, for 4 steps. What is y after the final step?

Explicit Euler updates y_{n+1} = y_n + h f(y_n).
Here f(y) = -0.03 y, so each step multiplies y by 1 - h*0.03.
Apply that update for 4 steps and round the final state.


Response:
Reasoning:
1. There are 100 centimeters in one meter.
2. Apply the conversion factor directly to the given value.
3. Compute 4003.5 / 100.
Final: {"answer": 40.035, "unit": "m"}

Answer: 40.035

Prompt: Convert 4003.5 cm to m. Return the converted value with unit.

There are 100 centimeters in one meter.
Apply the conversion factor directly to the given value.
Compute 4003.5 / 100.


Response:
Reasoning:
1. The x component is magnitude times cos(theta).
2. The y component is magnitude times sin(theta).
3. Use theta=213 degrees and keep the unit as newtons.
Final: {"answer": [-257.4719, -167.2042], "unit": "N"}

Answer: -257.4719

Answer: -167.2042

Prompt: A vector has magnitude 307 N at 213 degrees counterclockwise from the +x axis. Return its [x, y] components in newtons.

The x component is magnitude times cos(theta).
The y component is magnitude times sin(theta).
Use theta=213 degrees and keep the unit as newtons.


Response:
Reasoning:
1. Kinetic energy is KE = 1/2 m v^2.
2. Compute v^2 = 44.65^2 and multiply by 0.5 * 22.85.
3. The unit kg*m^2/s^2 is one joule.
Final: {"answer": 22777.1371, "unit": "J"}

Answer: 22777.1371

Prompt: A body of mass 22.85 kg moves at 44.65 m/s. Find its kinetic energy in joules with unit reasoning.

Kinetic energy is KE = 1/2 m v^2.
Compute v^2 = 44.65^2 and multiply by 0.5 * 22.85.
The unit kg*m^2/s^2 is one joule.


Response:
Reasoning:
1. Use the ideal gas law P V = n R T.
2. Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.
3. Compute P = 3.01 * 8.314 * 469 / 75.8.
Final: {"answer": 154.8389, "unit": "kPa"}

Answer: 154.8389

Prompt: An ideal gas sample has n=3.01 mol, T=469 K, and V=75.8 L. Using R=8.314 kPa*L/(mol*K), compute the pressure in kPa.

Use the ideal gas law P V = n R T.
Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.
Compute P = 3.01 * 8.314 * 469 / 75.8.


Response:
Reasoning:
1. Compare the dimensions on both sides of the equation.
2. mass times acceleration has newton dimensions
3. The equation is valid only if both sides have identical dimensions.
Final: {"answer": "consistent"}

Answer: consistent

Prompt: In lab notebook case 40051, check dimensional consistency for F = m * a. The left side has dimensions kg*m/s^2 and the right side has dimensions kg*m/s^2. Return consistent or inconsistent with a brief reason.

Compare the dimensions on both sides of the equation.
mass times acceleration has newton dimensions
The equation is valid only if both sides have identical dimensions.

Answer: consistent


Response:
Reasoning:
1. Kinetic energy is KE = 1/2 m v^2.
2. Compute v^2 = 32.25^2 and multiply by 0.5 * 15.15.
3. The unit kg*m^2/s^2 is one joule.
Final: {"answer": 7878.4734, "unit": "J"}

Answer: 7878.4734

Prompt: A body of mass 15.15 kg moves at 32.25 m/s. Find its kinetic energy in joules with unit reasoning.

Kinetic energy is KE = 1/2 m v^2.
Compute v^2 = 32.25^2 and multiply by 0.5 * 15.15.
The unit kg*m^2/s^2 is one joule.


Response:
Reasoning:
1. Molarity is moles of solute divided by solution volume in liters.
2. Convert 2885 mL to 2.885 L.
3. Compute M = 1.7 / 2.885.
Final: {"answer": 0.5893, "unit": "mol/L"}

Answer: 0.5893

Prompt: A solution contains 1.7 mol of solute in 2885 mL of solution. Compute the molarity in mol/L.

Molarity is moles of solute divided by solution volume in liters.
Convert 2885 mL to 2.885 L.
Compute M = 1.7 / 2.885.


Response:
Reasoning:
1. The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.
2. Evaluate f(-1.2)=-0.8 and f(-1.1)=-0.5.
3. The interval width is 0.1.
Final: {"answer": -0.065, "unit": "area_units"}

Answer: -0.065

Prompt: Use the trapezoid rule with one interval to approximate the integral of f(x)=3x+2.8 from x=-1.2 to x=-1.1. Return the numeric integral estimate.

The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.
Evaluate f(-1.2)=-0.8 and f(-1.1)=-0.5.
The interval width is 0.1.


Response:
Reasoning:
1. The slope is (y2-y1)/(x2-x1).
2. The intercept is y1 - slope*x1.
3. Return the pair in [slope, intercept] order.
Final: {"answer": [-6.9, 7.75], "unit": "dimensionless"}

Answer: -6.9

Answer: 7.75

Prompt: A line passes through points (11.75, -73.325) and (26, -171.65). Return [slope, intercept] for y = slope*x + intercept.

The slope is (y2-y1)/(x2-x1).
The intercept is y1 - slope*x1.
Return the pair in [slope, intercept] order.


Response:
Reasoning:
1. For level-ground projectile motion, R = v^2 sin(2 theta) / g.
2. Convert theta=78 degrees through the sine of 2 theta.
3. Substitute v=25.6 m/s and g=9.81 m/s^2.
Final: {"answer": 27.1722, "unit": "m"}

Answer: 27.1722

Prompt: A projectile is launched on level ground with no air resistance at speed 25.6 m/s and angle 78 degrees. Compute the horizontal range in meters using g=9.81 m/s^2.

For level-ground projectile motion, R = v^2 sin(2 theta) / g.
Convert theta=78 degrees through the sine of 2 theta.
Substitute v=25.6 m/s and g=9.81 m/s^2.


Response:
Reasoning:
1. Use the ideal gas law P V = n R T.
2. Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.
3. Compute P = 1.68 * 8.314 * 277 / 117.1.
Final: {"answer": 33.0402, "unit": "kPa"}

Answer: 33.0402

Prompt: An ideal gas sample has n=1.68 mol, T=277 K, and V=117.1 L. Using R=8.314 kPa*L/(mol*K), compute the pressure in kPa.

Use the ideal gas law P V = n R T.
Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.
Compute P = 1.68 * 8.314 * 277 / 117.1.


Response:
Reasoning:
1. Kelvin equals Celsius plus 273.15.
2. Apply the conversion factor directly to the given value.
3. Compute -76.5 + 273.15.
Final: {"answer": 196.65, "unit": "K"}

Answer: 196.65

Prompt: Convert -76.5 degC to K. Return the converted value with unit.

Kelvin equals Celsius plus 273.15.
Apply the conversion factor directly to the given value.
Compute -76.5 + 273.15.


Response:
Reasoning:
1. Use Newton's second law F = m a.
2. Substitute m = 16.05 kg and a = 12.7 m/s^2.
3. The unit kg*m/s^2 is one newton.
Final: {"answer": 203.835, "unit": "N"}

Answer: 203.835

Prompt: A cart has mass 16.05 kg and measured acceleration 12.7 m/s^2. Compute the net force. Check the SI units and give only the final JSON after reasoning.

Use Newton's second law F = m a.
Substitute m = 16.05 kg and a = 12.7 m/s^2.
The unit kg*m/s^2 is one newton.


Response:
Reasoning:
1. Use the ideal gas law P V = n R T.
2. Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.
3. Compute P = 3.72 * 8.314 * 412 / 64.0.
Final: {"answer": 199.0995, "unit": "kPa"}

Answer: 199.0995

Prompt: An ideal gas sample has n=3.72 mol, T=412 K, and V=64.0 L. Using R=8.314 kPa*L/(mol*K), compute the pressure in kPa.

Use the ideal gas law P V = n R T.
Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.
Compute P = 3.72 * 8.314 * 412 / 64.0.


Response:
Reasoning:
1. Compare the dimensions on both sides of the equation.
2. mass times acceleration has newton dimensions
3. The equation is valid only if both sides have identical dimensions.
Final: {"answer": "consistent"}

Answer: consistent

Prompt: In field worksheet case 503118, check dimensional consistency for F = m * a. The left side has dimensions kg*m/s^2 and the right side has dimensions kg*m/s^2. Return consistent or inconsistent with a brief reason.

Compare the dimensions on both sides of the equation.
mass times acceleration has newton dimensions
The equation is valid only if both sides have identical dimensions.

Answer: consistent


Response:
Reasoning:
1. Check whether all variables required by the governing equation or specification are present.
2. The missing required information is: target_schema, valid_examples.
3. A numeric or code answer would require inventing unstated assumptions, so abstain.
Final: {"answer": "INSUFFICIENT_INFO", "missing": ["target_schema", "valid_examples"]}

Answer: INSUFFICIENT_INFO

Prompt: Write a parser that converts each laboratory survey record from batch 53825 into the correct schema, but the prompt does not include the target schema or examples. If there is insufficient information, say so explicitly.

Check whether all variables required by the governing equation or specification are present.
The missing required information is: target_schema, valid_examples.
A numeric or code answer would require inventing unstated assumptions, so abstain.


Response:
Reasoning:
1. For level-ground projectile motion, R = v^2 sin(2 theta) / g.
2. Convert theta=48 degrees through the sine of 2 theta.
3. Substitute v=40.9 m/s and g=9.81 m/s^2.
Final: {"answer": 169.5868, "unit": "m"}

Answer: 169.5868

Prompt: A projectile is launched on level ground with no air resistance at speed 40.9 m/s and angle 48 degrees. Compute the horizontal range in meters using g=9.81 m/s^2.

For level-ground projectile motion, R = v^2 sin(2 theta) / g.
Convert theta=48 degrees through the sine of 2 theta.
Substitute v=40.9 m/s and g=9.81 m/s^2.


Response:
Reasoning:
1. Ohm's law gives I = V / R.
2. Power can be written as P = V I = V^2 / R.
3. Substitute V=226.3 V and R=146.8 ohm.
Final: {"answer": 348.8535, "unit": "W"}

Answer: 348.8535

Prompt: A resistor has resistance 146.8 ohm and voltage 226.3 V across it. Compute the dissipated power in watts.

Ohm's law gives I = V / R.
Power can be written as P = V I = V^2 / R.
Substitute V=226.3 V and R=146.8 ohm.


Response:
Reasoning:
1. The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.
2. Evaluate f(9.2)=-18.14 and f(14.7)=-32.99.
3. The interval width is 5.5.
Final: {"answer": -140.6075, "unit": "area_units"}

Answer: -140.6075

Prompt: Use the trapezoid rule with one interval to approximate the integral of f(x)=-2.7x+6.7 from x=9.2 to x=14.7. Return the numeric integral estimate.

The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.
Evaluate f(9.2)=-18.14 and f(14.7)=-32.99.
The interval width is 5.5.


Response:
Reasoning:
1. The x component is magnitude times cos(theta).
2. The y component is magnitude times sin(theta).
3. Use theta=217 degrees and keep the unit as newtons.
Final: {"answer": [-132.1742, -99.6004], "unit": "N"}

Answer: -132.1742

Answer: -99.6004

Prompt: A vector has magnitude 165.5 N at 217 degrees counterclockwise from the +x axis. Return its [x, y] components in newtons.

The x component is magnitude times cos(theta).
The y component is magnitude times sin(theta).
Use theta=217 degrees and keep the unit as newtons.


Response:
Reasoning:
1. Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).
2. Use N0=607.5 mg, t=358 h, and T_half=35 h.
3. The remaining amount has the same mass unit as the initial amount.
Final: {"answer": 0.5063, "unit": "mg"}

Answer: 0.5063

Prompt: A radioactive sample starts with 607.5 mg. Its half-life is 35 hours. How many mg remain after 358 hours?

Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).
Use N0=607.5 mg, t=358 h, and T_half=35 h.
The remaining amount has the same mass unit as the initial amount.


Response:
Reasoning:
1. Compare the dimensions on both sides of the equation.
2. amount times volume is not concentration
3. The equation is valid only if both sides have identical dimensions.
Final: {"answer": "inconsistent"}

Answer: inconsistent

Prompt: In sensor calibration case 445467, check dimensional consistency for C = n * V. The left side has dimensions mol/L and the right side has dimensions mol*L. Return consistent or inconsistent with a brief reason.

Compare the dimensions on both sides of the equation.
amount times volume is not concentration
The equation is valid only if both sides have identical dimensions.

Answer: inconsistent


Response:
Reasoning:
1. For level-ground projectile motion, R = v^2 sin(2 theta) / g.
2. Convert theta=36 degrees through the sine of 2 theta.
3. Substitute v=41.9 m/s and g=9.81 m/s^2.
Final: {"answer": 170.2023, "unit": "m"}

Answer: 170.2023

Prompt: A projectile is launched on level ground with no air resistance at speed 41.9 m/s and angle 36 degrees. Compute the horizontal range in meters using g=9.81 m/s^2.

For level-ground projectile motion, R = v^2 sin(2 theta) / g.
Convert theta=36 degrees through the sine of 2 theta.
Substitute v=41.9 m/s and g=9.81 m/s^2.


Response:
Reasoning:
1. The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.
2. Evaluate f(-3.1)=18.85 and f(3)=9.7.
3. The interval width is 6.1.
Final: {"answer": 87.0775, "unit": "area_units"}

Answer: 87.0775

Prompt: Use the trapezoid rule with one interval to approximate the integral of f(x)=-1.5x+14.2 from x=-3.1 to x=3. Return the numeric integral estimate.

The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.
Evaluate f(-3.1)=18.85 and f(3)=9.7.
The interval width is 6.1.


Response:
Reasoning:
1. There are 1000 grams in one kilogram.
2. Apply the conversion factor directly to the given value.
3. Compute 22348.0 / 1000.
Final: {"answer": 22.348, "unit": "kg"}

Answer: 22.348

Prompt: Convert 22348 g to kg. Return the converted value with unit.

There are 1000 grams in one kilogram.
Apply the conversion factor directly to the given value.
Compute 22348.0 / 1000.


Response:
Reasoning:
1. Molarity is moles of solute divided by solution volume in liters.
2. Convert 3885 mL to 3.885 L.
3. Compute M = 2.045 / 3.885.
Final: {"answer": 0.5264, "unit": "mol/L"}

Answer: 0.5264

Prompt: A solution contains 2.045 mol of solute in 3885 mL of solution. Compute the molarity in mol/L.

Molarity is moles of solute divided by solution volume in liters.
Convert 3885 mL to 3.885 L.
Compute M = 2.045 / 3.885.


Response:
Reasoning:
1. Use the ideal gas law P V = n R T.
2. Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.
3. Compute P = 4.34 * 8.314 * 553 / 55.6.
Final: {"answer": 358.8807, "unit": "kPa"}

Answer: 358.8807

Prompt: An ideal gas sample has n=4.34 mol, T=553 K, and V=55.6 L. Using R=8.314 kPa*L/(mol*K), compute the pressure in kPa.

Use the ideal gas law P V = n R T.
Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.
Compute P = 4.34 * 8.314 * 553 / 55.6.


Response:
Reasoning:
1. Ohm's law gives I = V / R.
2. Power can be written as P = V I = V^2 / R.
3. Substitute V=183.5 V and R=176.9 ohm.
Final: {"answer": 190.3462, "unit": "W"}

Answer: 190.3462

Prompt: A resistor has resistance 176.9 ohm and voltage 183.5 V across it. Compute the dissipated power in watts.

Ohm's law gives I = V / R.
Power can be written as P = V I = V^2 / R.
Substitute V=183.5 V and R=176.9 ohm.


Response:
Reasoning:
1. Explicit Euler updates y_{n+1} = y_n + h f(y_n).
2. Here f(y) = -0.55 y, so each step multiplies y by 1 - h*0.55.
3. Apply that update for 7 steps and round the final state.
Final: {"answer": 30.65, "unit": "state_units"}

Answer: 30.65

Prompt: Use explicit Euler on dy/dt = -0.55 y with y(0)=56, step size h=0.15, for 7 steps. What is y after the final step?

Explicit Euler updates y_{n+1} = y_n + h f(y_n).
Here f(y) = -0.55 y, so each step multiplies y by 1 - h*0.55.
Apply that update for 7 steps and round the final state.


Response:
Reasoning:
1. Ohm's law gives I = V / R.
2. Power can be written as P = V I = V^2 / R.
3. Substitute V=10.7 V and R=135.9 ohm.
Final: {"answer": 0.8425, "unit": "W"}

Answer: 0.8425

Prompt: A resistor has resistance 135.9 ohm and voltage 10.7 V across it. Compute the dissipated power in watts.

Ohm's law gives I = V / R.
Power can be written as P = V I = V^2 / R.
Substitute V=10.7 V and R=135.9 ohm.


Response:
Reasoning:
1. Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).
2. Use N0=383 mg, t=95.5 h, and T_half=23 h.
3. The remaining amount has the same mass unit as the initial amount.
Final: {"answer": 21.5412, "unit": "mg"}

Answer: 21.5412

Prompt: A radioactive sample starts with 383 mg. Its half-life is 23 hours. How many mg remain after 95.5 hours?

Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).
Use N0=383 mg, t=95.5 h, and T_half=23 h.
The remaining amount has the same mass unit as the initial amount.


Response:
Reasoning:
1. The function contract has a normal path and at least one edge case.
2. The implementation checks the edge case before returning the normal result.

```python
def safe_mean_004750(values):
    if not values:
        raise ValueError('safe_mean requires at least one value')
    return sum(values) / len(values)
```
Final: {"answer": "python_code", "function": "safe_mean_004750"}

Answer: python_code

Prompt: Write a Python function safe_mean_004750(values) that returns the arithmetic mean. It must raise ValueError for an empty input and must not mutate the input list. Return a single fenced Python code block.

Identify required edge cases before writing the function.
Implement the shortest total function that satisfies the stated contract.
Avoid global state and return deterministic outputs.

try:
    safe_mean_004750([])
    raise AssertionError('expected ValueError')
except ValueError:
    pass


Response:
Reasoning:
1. Use Q = m c DeltaT.
2. The mass is already in grams, matching the specific heat denominator.
3. Compute Q = 1865 * 0.695 * 100.
Final: {"answer": 129617.5, "unit": "J"}

Answer: 129617.5

Prompt: A 1865 g sample has specific heat 0.695 J/(g*K). How much heat is needed to raise its temperature by 100 K?

Use Q = m c DeltaT.
The mass is already in grams, matching the specific heat denominator.
Compute Q = 1865 * 0.695 * 100.


Response:
Reasoning:
1. Explicit Euler updates y_{n+1} = y_n + h f(y_n).
2. Here f(y) = -0.22 y, so each step multiplies y by 1 - h*0.22.
3. Apply that update for 6 steps and round the final state.
Final: {"answer": 1.7965, "unit": "state_units"}

Answer: 1.7965

Prompt: Use explicit Euler on dy/dt = -0.22 y with y(0)=37, step size h=1.8, for 6 steps. What is y after the final step?

Explicit Euler updates y_{n+1} = y_n + h f(y_n).
Here f(y) = -0.22 y, so each step multiplies y by 1 - h*0.22.
Apply that update for 6 steps and round the final state.


Response:
Reasoning:
1. The function contract has a normal path and at least one edge case.
2. The implementation checks the edge case before returning the normal result.

```python
def safe_mean_004768(values):
    if not values:
        raise ValueError('safe_mean requires at least one value')
    return sum(values) / len(values)
```
Final: {"answer": "python_code", "function": "safe_mean_004768"}

Answer: python_code

Prompt: Write a Python function safe_mean_004768(values) that returns the arithmetic mean. It must raise ValueError for an empty input and must not mutate the input list. Return a single fenced Python code block.

Identify required edge cases before writing the function.
Implement the shortest total function that satisfies the stated contract.
Avoid global state and return deterministic outputs.

try:
    safe_mean_004768([])
    raise AssertionError('expected ValueError')
except ValueError:
    pass


Response:
Reasoning:
1. Use the ideal gas law P V = n R T.
2. Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.
3. Compute P = 4.15 * 8.314 * 556 / 71.4.
Final: {"answer": 268.6796, "unit": "kPa"}

Answer: 268.6796

Prompt: An ideal gas sample has n=4.15 mol, T=556 K, and V=71.4 L. Using R=8.314 kPa*L/(mol*K), compute the pressure in kPa.

Use the ideal gas law P V = n R T.
Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.
Compute P = 4.15 * 8.314 * 556 / 71.4.


Response:
Reasoning:
1. Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).
2. Use N0=737.5 mg, t=233 h, and T_half=4.5 h.
3. The remaining amount has the same mass unit as the initial amount.
Final: {"answer": 0.0, "unit": "mg"}

Answer: 0.0

Prompt: A radioactive sample starts with 737.5 mg. Its half-life is 4.5 hours. How many mg remain after 233 hours?

Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).
Use N0=737.5 mg, t=233 h, and T_half=4.5 h.
The remaining amount has the same mass unit as the initial amount.


Response:
Reasoning:
1. Molarity is moles of solute divided by solution volume in liters.
2. Convert 4725 mL to 4.725 L.
3. Compute M = 4.17 / 4.725.
Final: {"answer": 0.8825, "unit": "mol/L"}

Answer: 0.8825

Prompt: A solution contains 4.17 mol of solute in 4725 mL of solution. Compute the molarity in mol/L.

Molarity is moles of solute divided by solution volume in liters.
Convert 4725 mL to 4.725 L.
Compute M = 4.17 / 4.725.


Response:
Reasoning:
1. The function contract has a normal path and at least one edge case.
2. The implementation checks the edge case before returning the normal result.

```python
def safe_mean_004786(values):
    if not values:
        raise ValueError('safe_mean requires at least one value')
    return sum(values) / len(values)
```
Final: {"answer": "python_code", "function": "safe_mean_004786"}

Answer: python_code

Prompt: Write a Python function safe_mean_004786(values) that returns the arithmetic mean. It must raise ValueError for an empty input and must not mutate the input list. Return a single fenced Python code block.

Identify required edge cases before writing the function.
Implement the shortest total function that satisfies the stated contract.
Avoid global state and return deterministic outputs.

try:
    safe_mean_004786([])
    raise AssertionError('expected ValueError')
except ValueError:
    pass


Response:
Reasoning:
1. Kinetic energy is KE = 1/2 m v^2.
2. Compute v^2 = 9.55^2 and multiply by 0.5 * 22.9.
3. The unit kg*m^2/s^2 is one joule.
Final: {"answer": 1044.2686, "unit": "J"}

Answer: 1044.2686

Prompt: A body of mass 22.9 kg moves at 9.55 m/s. Find its kinetic energy in joules with unit reasoning.

Kinetic energy is KE = 1/2 m v^2.
Compute v^2 = 9.55^2 and multiply by 0.5 * 22.9.
The unit kg*m^2/s^2 is one joule.


Response:
Reasoning:
1. Check whether all variables required by the governing equation or specification are present.
2. The missing required information is: rate_constant, number_of_steps.
3. A numeric or code answer would require inventing unstated assumptions, so abstain.
Final: {"answer": "INSUFFICIENT_INFO", "missing": ["rate_constant", "number_of_steps"]}

Answer: INSUFFICIENT_INFO

Prompt: Use explicit Euler for dy/dt = -k y. The prompt gives y(0)=8 and h=1.05, but omits both k and the number of steps. If there is insufficient information, say so explicitly.

Check whether all variables required by the governing equation or specification are present.
The missing required information is: rate_constant, number_of_steps.
A numeric or code answer would require inventing unstated assumptions, so abstain.


Response:
Reasoning:
1. Compare the dimensions on both sides of the equation.
2. speed squared over acceleration has units of meters
3. The equation is valid only if both sides have identical dimensions.
Final: {"answer": "consistent"}

Answer: consistent

Prompt: In quality-control check case 419600, check dimensional consistency for R = v^2 * sin(theta) / g. The left side has dimensions m and the right side has dimensions m. Return consistent or inconsistent with a brief reason.

Compare the dimensions on both sides of the equation.
speed squared over acceleration has units of meters
The equation is valid only if both sides have identical dimensions.

Answer: consistent


Response:
Reasoning:
1. Check whether all variables required by the governing equation or specification are present.
2. The missing required information is: volume.
3. A numeric or code answer would require inventing unstated assumptions, so abstain.
Final: {"answer": "INSUFFICIENT_INFO", "missing": ["volume"]}

Answer: INSUFFICIENT_INFO

Prompt: Compute pressure from the ideal gas law. The prompt gives n=0.53 mol and T=349 K, but does not give volume. If there is insufficient information, say so explicitly.

Check whether all variables required by the governing equation or specification are present.
The missing required information is: volume.
A numeric or code answer would require inventing unstated assumptions, so abstain.


Response:
Reasoning:
1. Use Q = m c DeltaT.
2. The mass is already in grams, matching the specific heat denominator.
3. Compute Q = 385 * 1.7 * 53.
Final: {"answer": 34688.5, "unit": "J"}

Answer: 34688.5

Prompt: A 385 g sample has specific heat 1.7 J/(g*K). How much heat is needed to raise its temperature by 53 K?

Use Q = m c DeltaT.
The mass is already in grams, matching the specific heat denominator.
Compute Q = 385 * 1.7 * 53.


Response:
Reasoning:
1. Check whether all variables required by the governing equation or specification are present.
2. The missing required information is: required_fields, allowed_transformations.
3. A numeric or code answer would require inventing unstated assumptions, so abstain.
Final: {"answer": "INSUFFICIENT_INFO", "missing": ["required_fields", "allowed_transformations"]}

Answer: INSUFFICIENT_INFO

Prompt: Write a sanitizer for valid field crop records in release 374960, but the prompt does not state which fields are required or which transformations are allowed. If there is insufficient information, say so explicitly.

Check whether all variables required by the governing equation or specification are present.
The missing required information is: required_fields, allowed_transformations.
A numeric or code answer would require inventing unstated assumptions, so abstain.


Response:
Reasoning:
1. Molarity is moles of solute divided by solution volume in liters.
2. Convert 2920 mL to 2.92 L.
3. Compute M = 0.12 / 2.92.
Final: {"answer": 0.0411, "unit": "mol/L"}

Answer: 0.0411

Prompt: A solution contains 0.12 mol of solute in 2920 mL of solution. Compute the molarity in mol/L.

Molarity is moles of solute divided by solution volume in liters.
Convert 2920 mL to 2.92 L.
Compute M = 0.12 / 2.92.


Response:
Reasoning:
1. Keep the boundary values fixed and update only the three interior grid points.
2. For each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.
3. Multiply each Laplacian by r=0.04 and add it to the current value.
Final: {"answer": [-1.028, 1.854, 2.66], "unit": "temperature_units"}

Answer: -1.028

Answer: 1.854

Answer: 2.66

Prompt: For the 1D heat equation explicit finite-difference step, use u_i(next)=u_i+r*(u_{i-1}-2*u_i+u_{i+1}). Boundary values are left=-0.05, right=2.45; current interior values are [-1.2, 1.95, 2.7]. Use r=0.04. Return the next interior vector.

Keep the boundary values fixed and update only the three interior grid points.
For each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.
Multiply each Laplacian by r=0.04 and add it to the current value.


Response:
Reasoning:
1. Check whether all variables required by the governing equation or specification are present.
2. The missing required information is: required_fields, allowed_transformations.
3. A numeric or code answer would require inventing unstated assumptions, so abstain.
Final: {"answer": "INSUFFICIENT_INFO", "missing": ["required_fields", "allowed_transformations"]}

Answer: INSUFFICIENT_INFO

Prompt: Write a sanitizer for valid field experiment records in release 395122, but the prompt does not state which fields are required or which transformations are allowed. If there is insufficient information, say so explicitly.

Check whether all variables required by the governing equation or specification are present.
The missing required information is: required_fields, allowed_transformations.
A numeric or code answer would require inventing unstated assumptions, so abstain.


Response:
Reasoning:
1. For level-ground projectile motion, R = v^2 sin(2 theta) / g.
2. Convert theta=21 degrees through the sine of 2 theta.
3. Substitute v=81 m/s and g=9.81 m/s^2.
Final: {"answer": 447.5195, "unit": "m"}

Answer: 447.5195

Prompt: A projectile is launched on level ground with no air resistance at speed 81 m/s and angle 21 degrees. Compute the horizontal range in meters using g=9.81 m/s^2.

For level-ground projectile motion, R = v^2 sin(2 theta) / g.
Convert theta=21 degrees through the sine of 2 theta.
Substitute v=81 m/s and g=9.81 m/s^2.


Response:
Reasoning:
1. Molarity is moles of solute divided by solution volume in liters.
2. Convert 4730 mL to 4.73 L.
3. Compute M = 1.95 / 4.73.
Final: {"answer": 0.4123, "unit": "mol/L"}

Answer: 0.4123

Prompt: A solution contains 1.95 mol of solute in 4730 mL of solution. Compute the molarity in mol/L.

Molarity is moles of solute divided by solution volume in liters.
Convert 4730 mL to 4.73 L.
Compute M = 1.95 / 4.73.


Response:
Reasoning:
1. Explicit Euler updates y_{n+1} = y_n + h f(y_n).
2. Here f(y) = -0.2 y, so each step multiplies y by 1 - h*0.2.
3. Apply that update for 9 steps and round the final state.
Final: {"answer": 3.4579, "unit": "state_units"}

Answer: 3.4579

Prompt: Use explicit Euler on dy/dt = -0.2 y with y(0)=66.5, step size h=1.4, for 9 steps. What is y after the final step?

Explicit Euler updates y_{n+1} = y_n + h f(y_n).
Here f(y) = -0.2 y, so each step multiplies y by 1 - h*0.2.
Apply that update for 9 steps and round the final state.


Response:
Reasoning:
1. Kelvin equals Celsius plus 273.15.
2. Apply the conversion factor directly to the given value.
3. Compute -36.0 + 273.15.
Final: {"answer": 237.15, "unit": "K"}

Answer: 237.15

Prompt: Convert -36 degC to K. Return the converted value with unit.

Kelvin equals Celsius plus 273.15.
Apply the conversion factor directly to the given value.
Compute -36.0 + 273.15.


Response:
Reasoning:
1. Check whether all variables required by the governing equation or specification are present.
2. The missing required information is: rate_constant, number_of_steps.
3. A numeric or code answer would require inventing unstated assumptions, so abstain.
Final: {"answer": "INSUFFICIENT_INFO", "missing": ["rate_constant", "number_of_steps"]}

Answer: INSUFFICIENT_INFO

Prompt: Use explicit Euler for dy/dt = -k y. The prompt gives y(0)=24 and h=0.5, but omits both k and the number of steps. If there is insufficient information, say so explicitly.

Check whether all variables required by the governing equation or specification are present.
The missing required information is: rate_constant, number_of_steps.
A numeric or code answer would require inventing unstated assumptions, so abstain.


Response:
Reasoning:
1. Use the ideal gas law P V = n R T.
2. Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.
3. Compute P = 2.79 * 8.314 * 242 / 103.1.
Final: {"answer": 54.4466, "unit": "kPa"}

Answer: 54.4466

Prompt: An ideal gas sample has n=2.79 mol, T=242 K, and V=103.1 L. Using R=8.314 kPa*L/(mol*K), compute the pressure in kPa.

Use the ideal gas law P V = n R T.
Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.
Compute P = 2.79 * 8.314 * 242 / 103.1.


Response:
Reasoning:
1. Use Q = m c DeltaT.
2. The mass is already in grams, matching the specific heat denominator.
3. Compute Q = 530 * 1.1 * 47.
Final: {"answer": 27401.0, "unit": "J"}

Answer: 27401.0

Prompt: A 530 g sample has specific heat 1.1 J/(g*K). How much heat is needed to raise its temperature by 47 K?

Use Q = m c DeltaT.
The mass is already in grams, matching the specific heat denominator.
Compute Q = 530 * 1.1 * 47.


Response:
Reasoning:
1. For level-ground projectile motion, R = v^2 sin(2 theta) / g.
2. Convert theta=5 degrees through the sine of 2 theta.
3. Substitute v=5.3 m/s and g=9.81 m/s^2.
Final: {"answer": 0.4972, "unit": "m"}

Answer: 0.4972

Prompt: A projectile is launched on level ground with no air resistance at speed 5.3 m/s and angle 5 degrees. Compute the horizontal range in meters using g=9.81 m/s^2.

For level-ground projectile motion, R = v^2 sin(2 theta) / g.
Convert theta=5 degrees through the sine of 2 theta.
Substitute v=5.3 m/s and g=9.81 m/s^2.


Response:
Reasoning:
1. Ohm's law gives I = V / R.
2. Power can be written as P = V I = V^2 / R.
3. Substitute V=80.8 V and R=176.5 ohm.
Final: {"answer": 36.9895, "unit": "W"}

Answer: 36.9895

Prompt: A resistor has resistance 176.5 ohm and voltage 80.8 V across it. Compute the dissipated power in watts.

Ohm's law gives I = V / R.
Power can be written as P = V I = V^2 / R.
Substitute V=80.8 V and R=176.5 ohm.


Response:
Reasoning:
1. The slope is (y2-y1)/(x2-x1).
2. The intercept is y1 - slope*x1.
3. Return the pair in [slope, intercept] order.
Final: {"answer": [-5.35, 11.25], "unit": "dimensionless"}

Answer: -5.35

Answer: 11.25

Prompt: A line passes through points (6.75, -24.8625) and (9, -36.9). Return [slope, intercept] for y = slope*x + intercept.

The slope is (y2-y1)/(x2-x1).
The intercept is y1 - slope*x1.
Return the pair in [slope, intercept] order.


Response:
Reasoning:
1. The function contract has a normal path and at least one edge case.
2. The implementation checks the edge case before returning the normal result.

```python
def clamp_005056(x, lo, hi):
    if lo > hi:
        raise ValueError('lo must be <= hi')
    return min(max(x, lo), hi)
```
Final: {"answer": "python_code", "function": "clamp_005056"}

Answer: python_code

Prompt: Write a Python function clamp_005056(x, lo, hi) that clips x into the inclusive interval [lo, hi]. It must raise ValueError if lo > hi. Return a single fenced Python code block.

Identify required edge cases before writing the function.
Implement the shortest total function that satisfies the stated contract.
Avoid global state and return deterministic outputs.

try:
    clamp_005056(1, 3, 2)
    raise AssertionError('expected ValueError')
except ValueError:
    pass


Response:
Reasoning:
1. Kinetic energy is KE = 1/2 m v^2.
2. Compute v^2 = 30.8^2 and multiply by 0.5 * 10.6.
3. The unit kg*m^2/s^2 is one joule.
Final: {"answer": 5027.792, "unit": "J"}

Answer: 5027.792

Prompt: A body of mass 10.6 kg moves at 30.8 m/s. Find its kinetic energy in joules with unit reasoning.

Kinetic energy is KE = 1/2 m v^2.
Compute v^2 = 30.8^2 and multiply by 0.5 * 10.6.
The unit kg*m^2/s^2 is one joule.


Response:
Reasoning:
1. Mass equals amount in moles times molar mass.
2. Use m = 7.93 mol * 44.01 g/mol.
3. The mole unit cancels, leaving grams.
Final: {"answer": 348.9993, "unit": "g"}

Answer: 348.9993

Prompt: A sample contains 7.93 mol of carbon dioxide. Using molar mass 44.01 g/mol, compute the sample mass in grams.

Mass equals amount in moles times molar mass.
Use m = 7.93 mol * 44.01 g/mol.
The mole unit cancels, leaving grams.


Response:
Reasoning:
1. The x component is magnitude times cos(theta).
2. The y component is magnitude times sin(theta).
3. Use theta=203 degrees and keep the unit as newtons.
Final: {"answer": [-297.3231, -126.2062], "unit": "N"}

Answer: -297.3231

Answer: -126.2062

Prompt: A vector has magnitude 323 N at 203 degrees counterclockwise from the +x axis. Return its [x, y] components in newtons.

The x component is magnitude times cos(theta).
The y component is magnitude times sin(theta).
Use theta=203 degrees and keep the unit as newtons.


Response:
Reasoning:
1. The slope is (y2-y1)/(x2-x1).
2. The intercept is y1 - slope*x1.
3. Return the pair in [slope, intercept] order.
Final: {"answer": [-4.25, 0.25], "unit": "dimensionless"}

Answer: -4.25

Answer: 0.25

Prompt: A line passes through points (14, -59.25) and (18.25, -77.3125). Return [slope, intercept] for y = slope*x + intercept.

The slope is (y2-y1)/(x2-x1).
The intercept is y1 - slope*x1.
Return the pair in [slope, intercept] order.


Response:
Reasoning:
1. Molarity is moles of solute divided by solution volume in liters.
2. Convert 4645 mL to 4.645 L.
3. Compute M = 4.76 / 4.645.
Final: {"answer": 1.0248, "unit": "mol/L"}

Answer: 1.0248

Prompt: A solution contains 4.76 mol of solute in 4645 mL of solution. Compute the molarity in mol/L.

Molarity is moles of solute divided by solution volume in liters.
Convert 4645 mL to 4.645 L.
Compute M = 4.76 / 4.645.


Response:
Reasoning:
1. Check whether all variables required by the governing equation or specification are present.
2. The missing required information is: target_schema, valid_examples.
3. A numeric or code answer would require inventing unstated assumptions, so abstain.
Final: {"answer": "INSUFFICIENT_INFO", "missing": ["target_schema", "valid_examples"]}

Answer: INSUFFICIENT_INFO

Prompt: Write a parser that converts each warehouse ledger record from batch 691332 into the correct schema, but the prompt does not include the target schema or examples. If there is insufficient information, say so explicitly.

Check whether all variables required by the governing equation or specification are present.
The missing required information is: target_schema, valid_examples.
A numeric or code answer would require inventing unstated assumptions, so abstain.


Response:
Reasoning:
1. Use the ideal gas law P V = n R T.
2. Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.
3. Compute P = 2.32 * 8.314 * 586 / 18.1.
Final: {"answer": 624.4779, "unit": "kPa"}

Answer: 624.4779

Prompt: An ideal gas sample has n=2.32 mol, T=586 K, and V=18.1 L. Using R=8.314 kPa*L/(mol*K), compute the pressure in kPa.

Use the ideal gas law P V = n R T.
Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.
Compute P = 2.32 * 8.314 * 586 / 18.1.


Response:
Reasoning:
1. Molarity is moles of solute divided by solution volume in liters.
2. Convert 4960 mL to 4.96 L.
3. Compute M = 2.025 / 4.96.
Final: {"answer": 0.4083, "unit": "mol/L"}

Answer: 0.4083

Prompt: A solution contains 2.025 mol of solute in 4960 mL of solution. Compute the molarity in mol/L.

Molarity is moles of solute divided by solution volume in liters.
Convert 4960 mL to 4.96 L.
Compute M = 2.025 / 4.96.


Response:
Reasoning:
1. The slope is (y2-y1)/(x2-x1).
2. The intercept is y1 - slope*x1.
3. Return the pair in [slope, intercept] order.
Final: {"answer": [4.8, -11.25], "unit": "dimensionless"}

Answer: 4.8

Answer: -11.25

Prompt: A line passes through points (12, 46.35) and (15.75, 64.35). Return [slope, intercept] for y = slope*x + intercept.

The slope is (y2-y1)/(x2-x1).
The intercept is y1 - slope*x1.
Return the pair in [slope, intercept] order.


Response:
Reasoning:
1. The x component is magnitude times cos(theta).
2. The y component is magnitude times sin(theta).
3. Use theta=137 degrees and keep the unit as newtons.
Final: {"answer": [-177.7189, 165.7256], "unit": "N"}

Answer: -177.7189

Answer: 165.7256

Prompt: A vector has magnitude 243 N at 137 degrees counterclockwise from the +x axis. Return its [x, y] components in newtons.

The x component is magnitude times cos(theta).
The y component is magnitude times sin(theta).
Use theta=137 degrees and keep the unit as newtons.


Response:
Reasoning:
1. Kinetic energy is KE = 1/2 m v^2.
2. Compute v^2 = 24.5^2 and multiply by 0.5 * 24.05.
3. The unit kg*m^2/s^2 is one joule.
Final: {"answer": 7218.0063, "unit": "J"}

Answer: 7218.0063

Prompt: A body of mass 24.05 kg moves at 24.5 m/s. Find its kinetic energy in joules with unit reasoning.

Kinetic energy is KE = 1/2 m v^2.
Compute v^2 = 24.5^2 and multiply by 0.5 * 24.05.
The unit kg*m^2/s^2 is one joule.


Response:
Reasoning:
1. Explicit Euler updates y_{n+1} = y_n + h f(y_n).
2. Here f(y) = -0.41 y, so each step multiplies y by 1 - h*0.41.
3. Apply that update for 4 steps and round the final state.
Final: {"answer": 1.3113, "unit": "state_units"}

Answer: 1.3113

Prompt: Use explicit Euler on dy/dt = -0.41 y with y(0)=48.5, step size h=1.45, for 4 steps. What is y after the final step?

Explicit Euler updates y_{n+1} = y_n + h f(y_n).
Here f(y) = -0.41 y, so each step multiplies y by 1 - h*0.41.
Apply that update for 4 steps and round the final state.


Response:
Reasoning:
1. Keep the boundary values fixed and update only the three interior grid points.
2. For each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.
3. Multiply each Laplacian by r=0.32 and add it to the current value.
Final: {"answer": [0.668, 1.17, 0.452], "unit": "temperature_units"}

Answer: 0.668

Answer: 1.17

Answer: 0.452

Prompt: For the 1D heat equation explicit finite-difference step, use u_i(next)=u_i+r*(u_{i-1}-2*u_i+u_{i+1}). Boundary values are left=0.8, right=-1.45; current interior values are [1.1, 0.05, 2.5]. Use r=0.32. Return the next interior vector.

Keep the boundary values fixed and update only the three interior grid points.
For each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.
Multiply each Laplacian by r=0.32 and add it to the current value.


Response:
Reasoning:
1. Explicit Euler updates y_{n+1} = y_n + h f(y_n).
2. Here f(y) = -0.51 y, so each step multiplies y by 1 - h*0.51.
3. Apply that update for 4 steps and round the final state.
Final: {"answer": 0.2128, "unit": "state_units"}

Answer: 0.2128

Prompt: Use explicit Euler on dy/dt = -0.51 y with y(0)=16.5, step size h=1.3, for 4 steps. What is y after the final step?

Explicit Euler updates y_{n+1} = y_n + h f(y_n).
Here f(y) = -0.51 y, so each step multiplies y by 1 - h*0.51.
Apply that update for 4 steps and round the final state.


Response:
Reasoning:
1. Compare the dimensions on both sides of the equation.
2. grams cancel with J/(g*K), and kelvin cancels, leaving joules
3. The equation is valid only if both sides have identical dimensions.
Final: {"answer": "consistent"}

Answer: consistent

Prompt: In field worksheet case 396990, check dimensional consistency for Q = m * c * DeltaT. The left side has dimensions J and the right side has dimensions J. Return consistent or inconsistent with a brief reason.

Compare the dimensions on both sides of the equation.
grams cancel with J/(g*K), and kelvin cancels, leaving joules
The equation is valid only if both sides have identical dimensions.

Answer: consistent


Response:
Reasoning:
1. Use Newton's second law F = m a.
2. Substitute m = 20.7 kg and a = 8.05 m/s^2.
3. The unit kg*m/s^2 is one newton.
Final: {"answer": 166.635, "unit": "N"}

Answer: 166.635

Prompt: A cart has mass 20.7 kg and measured acceleration 8.05 m/s^2. Compute the net force. Check the SI units and give only the final JSON after reasoning.

Use Newton's second law F = m a.
Substitute m = 20.7 kg and a = 8.05 m/s^2.
The unit kg*m/s^2 is one newton.


Response:
Reasoning:
1. Keep the boundary values fixed and update only the three interior grid points.
2. For each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.
3. Multiply each Laplacian by r=0.28 and add it to the current value.
Final: {"answer": [0.248, 1.202, 2.27], "unit": "temperature_units"}

Answer: 0.248

Answer: 1.202

Answer: 2.27

Prompt: For the 1D heat equation explicit finite-difference step, use u_i(next)=u_i+r*(u_{i-1}-2*u_i+u_{i+1}). Boundary values are left=1.6, right=1.75; current interior values are [-1.95, 2.35, 2.55]. Use r=0.28. Return the next interior vector.

Keep the boundary values fixed and update only the three interior grid points.
For each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.
Multiply each Laplacian by r=0.28 and add it to the current value.


Response:
Reasoning:
1. Mass equals amount in moles times molar mass.
2. Use m = 3.87 mol * 100.087 g/mol.
3. The mole unit cancels, leaving grams.
Final: {"answer": 387.3367, "unit": "g"}

Answer: 387.3367

Prompt: A sample contains 3.87 mol of calcium carbonate. Using molar mass 100.087 g/mol, compute the sample mass in grams.

Mass equals amount in moles times molar mass.
Use m = 3.87 mol * 100.087 g/mol.
The mole unit cancels, leaving grams.


Response:
Reasoning:
1. The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.
2. Evaluate f(-2.5)=11.8 and f(4.5)=-37.2.
3. The interval width is 7.
Final: {"answer": -88.9, "unit": "area_units"}

Answer: -88.9

Prompt: Use the trapezoid rule with one interval to approximate the integral of f(x)=-7x+-5.7 from x=-2.5 to x=4.5. Return the numeric integral estimate.

The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.
Evaluate f(-2.5)=11.8 and f(4.5)=-37.2.
The interval width is 7.


Response:
Reasoning:
1. The x component is magnitude times cos(theta).
2. The y component is magnitude times sin(theta).
3. Use theta=153 degrees and keep the unit as newtons.
Final: {"answer": [-15.5926, 7.9448], "unit": "N"}

Answer: -15.5926

Answer: 7.9448

Prompt: A vector has magnitude 17.5 N at 153 degrees counterclockwise from the +x axis. Return its [x, y] components in newtons.

The x component is magnitude times cos(theta).
The y component is magnitude times sin(theta).
Use theta=153 degrees and keep the unit as newtons.