Response:
Reasoning:
1. Explicit Euler updates y_{n+1} = y_n + h f(y_n).
2. Here f(y) = -0.4 y, so each step multiplies y by 1 - h*0.4.
3. Apply that update for 3 steps and round the final state.
Final: {"answer": 6.1322, "unit": "state_units"}

Answer: 6.1322

Prompt: Use explicit Euler on dy/dt = -0.4 y with y(0)=63, step size h=1.35, 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) = -0.4 y, so each step multiplies y by 1 - h*0.4.
Apply that update for 3 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(-2.9)=17.19 and f(5.1)=-39.61.
3. The interval width is 8.
Final: {"answer": -89.68, "unit": "area_units"}

Answer: -89.68

Prompt: Use the trapezoid rule with one interval to approximate the integral of f(x)=-7.1x+-3.4 from x=-2.9 to x=5.1. Return the numeric integral estimate.

The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.
Evaluate f(-2.9)=17.19 and f(5.1)=-39.61.
The interval width is 8.

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


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": [1.592, 1.546, -0.034], "unit": "temperature_units"}

Answer: 1.592

Answer: 1.546

Answer: -0.034

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=-1.15; current interior values are [2.95, 2.05, -0.65]. 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. There are 1000 grams in one kilogram.
2. Apply the conversion factor directly to the given value.
3. Compute 24635.0 / 1000.
Final: {"answer": 24.635, "unit": "kg"}

Answer: 24.635

Prompt: Convert 24635 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 24635.0 / 1000.


Response:
Reasoning:
1. The x component is magnitude times cos(theta).
2. The y component is magnitude times sin(theta).
3. Use theta=243 degrees and keep the unit as newtons.
Final: {"answer": [-113.2706, -222.3061], "unit": "N"}

Answer: -113.2706

Answer: -222.3061

Prompt: A vector has magnitude 249.5 N at 243 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=243 degrees and keep the unit as newtons.

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


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, 20.75], "unit": "dimensionless"}

Answer: -4.8

Answer: 20.75

Prompt: A line passes through points (-3.5, 37.55) and (6.5, -10.45). 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. Compare the dimensions on both sides of the equation.
2. volt squared divided by ohm is watt
3. The equation is valid only if both sides have identical dimensions.
Final: {"answer": "consistent"}

Answer: consistent

Prompt: In sensor calibration case 100721, check dimensional consistency for P = V^2 / R. The left side has dimensions W and the right side has dimensions W. Return consistent or inconsistent with a brief reason.

Compare the dimensions on both sides of the equation.
volt squared divided by ohm is watt
The equation is valid only if both sides have identical dimensions.

Answer: consistent


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_000916(x, lo, hi):
    if lo > hi:
        raise ValueError('lo must be <= hi')
    return min(max(x, lo), hi)
```
Final: {"answer": "python_code", "function": "clamp_000916"}

Answer: python_code

Prompt: Write a Python function clamp_000916(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_000916(1, 3, 2)
    raise AssertionError('expected ValueError')
except ValueError:
    pass


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

Answer: INSUFFICIENT_INFO

Prompt: Write a dynamic-programming solver for a routing scoring problem with 174 items and budget 10565, but the recurrence, objective, and tie-breaking rule are all absent. 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: recurrence, objective, tie_breaking_rule.
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 = 19.5 kg and a = 12.25 m/s^2.
3. The unit kg*m/s^2 is one newton.
Final: {"answer": 238.875, "unit": "N"}

Answer: 238.875

Prompt: A cart has mass 19.5 kg and measured acceleration 12.25 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 = 19.5 kg and a = 12.25 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 = 28.5^2 and multiply by 0.5 * 24.35.
3. The unit kg*m^2/s^2 is one joule.
Final: {"answer": 9889.1438, "unit": "J"}

Answer: 9889.1438

Prompt: A body of mass 24.35 kg moves at 28.5 m/s. Find its kinetic energy in joules with unit reasoning.

Kinetic energy is KE = 1/2 m v^2.
Compute v^2 = 28.5^2 and multiply by 0.5 * 24.35.
The unit kg*m^2/s^2 is one joule.


Response:
Reasoning:
1. For level-ground projectile motion, R = v^2 sin(2 theta) / g.
2. Convert theta=58 degrees through the sine of 2 theta.
3. Substitute v=77 m/s and g=9.81 m/s^2.
Final: {"answer": 543.2161, "unit": "m"}

Answer: 543.2161

Prompt: A projectile is launched on level ground with no air resistance at speed 77 m/s and angle 58 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=58 degrees through the sine of 2 theta.
Substitute v=77 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 = 1.27 * 8.314 * 476 / 15.2.
Final: {"answer": 330.6565, "unit": "kPa"}

Answer: 330.6565

Prompt: An ideal gas sample has n=1.27 mol, T=476 K, and V=15.2 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 = 1.27 * 8.314 * 476 / 15.2.


Response:
Reasoning:
1. Use Q = m c DeltaT.
2. The mass is already in grams, matching the specific heat denominator.
3. Compute Q = 1755 * 4.1 * 117.
Final: {"answer": 841873.5, "unit": "J"}

Answer: 841873.5

Prompt: A 1755 g sample has specific heat 4.1 J/(g*K). How much heat is needed to raise its temperature by 117 K?

Use Q = m c DeltaT.
The mass is already in grams, matching the specific heat denominator.
Compute Q = 1755 * 4.1 * 117.


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=177.5 V and R=109.5 ohm.
Final: {"answer": 287.7283, "unit": "W"}

Answer: 287.7283

Prompt: A resistor has resistance 109.5 ohm and voltage 177.5 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=177.5 V and R=109.5 ohm.


Response:
Reasoning:
1. Mass equals amount in moles times molar mass.
2. Use m = 2.44 mol * 100.087 g/mol.
3. The mole unit cancels, leaving grams.
Final: {"answer": 244.2123, "unit": "g"}

Answer: 244.2123

Prompt: A sample contains 2.44 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 = 2.44 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 1860 mL to 1.86 L.
3. Compute M = 1.76 / 1.86.
Final: {"answer": 0.9462, "unit": "mol/L"}

Answer: 0.9462

Prompt: A solution contains 1.76 mol of solute in 1860 mL of solution. Compute the molarity in mol/L.

Molarity is moles of solute divided by solution volume in liters.
Convert 1860 mL to 1.86 L.
Compute M = 1.76 / 1.86.


Response:
Reasoning:
1. Explicit Euler updates y_{n+1} = y_n + h f(y_n).
2. Here f(y) = -0.12 y, so each step multiplies y by 1 - h*0.12.
3. Apply that update for 7 steps and round the final state.
Final: {"answer": 31.0828, "unit": "state_units"}

Answer: 31.0828

Prompt: Use explicit Euler on dy/dt = -0.12 y with y(0)=63, step size h=0.8, 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) = -0.12 y, so each step multiplies y by 1 - h*0.12.
Apply that update for 7 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(-5.4)=-33.42 and f(2.4)=0.12.
3. The interval width is 7.8.
Final: {"answer": -129.87, "unit": "area_units"}

Answer: -129.87

Prompt: Use the trapezoid rule with one interval to approximate the integral of f(x)=4.3x+-10.2 from x=-5.4 to x=2.4. Return the numeric integral estimate.

The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.
Evaluate f(-5.4)=-33.42 and f(2.4)=0.12.
The interval width is 7.8.


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=0.48 and add it to the current value.
Final: {"answer": [0.514, -0.054, 0.562], "unit": "temperature_units"}

Answer: 0.514

Answer: -0.054

Answer: 0.562

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=1.25, right=1.3; current interior values are [-0.35, -0.15, 0.25]. Use r=0.48. 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=0.48 and add it to the current value.


Response:
Reasoning:
1. There are 1000 grams in one kilogram.
2. Apply the conversion factor directly to the given value.
3. Compute 27382.0 / 1000.
Final: {"answer": 27.382, "unit": "kg"}

Answer: 27.382

Prompt: Convert 27382 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 27382.0 / 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": [8.7, 10.75], "unit": "dimensionless"}

Answer: 8.7

Answer: 10.75

Prompt: A line passes through points (9.25, 91.225) and (14.25, 134.725). 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. Compare the dimensions on both sides of the equation.
2. velocity times time gives distance, not acceleration
3. The equation is valid only if both sides have identical dimensions.
Final: {"answer": "inconsistent"}

Answer: inconsistent

Prompt: In simulation spec case 241672, check dimensional consistency for a = v * t. The left side has dimensions m/s^2 and the right side has dimensions m. Return consistent or inconsistent with a brief reason.

Compare the dimensions on both sides of the equation.
velocity times time gives distance, not acceleration
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 = 11.8 kg and a = 9.1 m/s^2.
3. The unit kg*m/s^2 is one newton.
Final: {"answer": 107.38, "unit": "N"}

Answer: 107.38

Prompt: A cart has mass 11.8 kg and measured acceleration 9.1 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 = 11.8 kg and a = 9.1 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 = 29.3^2 and multiply by 0.5 * 28.4.
3. The unit kg*m^2/s^2 is one joule.
Final: {"answer": 12190.558, "unit": "J"}

Answer: 12190.558

Prompt: A body of mass 28.4 kg moves at 29.3 m/s. Find its kinetic energy in joules with unit reasoning.

Kinetic energy is KE = 1/2 m v^2.
Compute v^2 = 29.3^2 and multiply by 0.5 * 28.4.
The unit kg*m^2/s^2 is one joule.


Response:
Reasoning:
1. For level-ground projectile motion, R = v^2 sin(2 theta) / g.
2. Convert theta=59 degrees through the sine of 2 theta.
3. Substitute v=42.7 m/s and g=9.81 m/s^2.
Final: {"answer": 164.1049, "unit": "m"}

Answer: 164.1049

Prompt: A projectile is launched on level ground with no air resistance at speed 42.7 m/s and angle 59 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=59 degrees through the sine of 2 theta.
Substitute v=42.7 m/s and g=9.81 m/s^2.


Response:
Reasoning:
1. Use Q = m c DeltaT.
2. The mass is already in grams, matching the specific heat denominator.
3. Compute Q = 460 * 4.55 * 46.
Final: {"answer": 96278.0, "unit": "J"}

Answer: 96278.0

Prompt: A 460 g sample has specific heat 4.55 J/(g*K). How much heat is needed to raise its temperature by 46 K?

Use Q = m c DeltaT.
The mass is already in grams, matching the specific heat denominator.
Compute Q = 460 * 4.55 * 46.


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=18.4 V and R=114.8 ohm.
Final: {"answer": 2.9491, "unit": "W"}

Answer: 2.9491

Prompt: A resistor has resistance 114.8 ohm and voltage 18.4 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=18.4 V and R=114.8 ohm.


Response:
Reasoning:
1. Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).
2. Use N0=974 mg, t=146 h, and T_half=14.5 h.
3. The remaining amount has the same mass unit as the initial amount.
Final: {"answer": 0.9068, "unit": "mg"}

Answer: 0.9068

Prompt: A radioactive sample starts with 974 mg. Its half-life is 14.5 hours. How many mg remain after 146 hours?

Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).
Use N0=974 mg, t=146 h, and T_half=14.5 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 = 7.65 mol * 58.44 g/mol.
3. The mole unit cancels, leaving grams.
Final: {"answer": 447.066, "unit": "g"}

Answer: 447.066

Prompt: A sample contains 7.65 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 = 7.65 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 4990 mL to 4.99 L.
3. Compute M = 0.615 / 4.99.
Final: {"answer": 0.1232, "unit": "mol/L"}

Answer: 0.1232

Prompt: A solution contains 0.615 mol of solute in 4990 mL of solution. Compute the molarity in mol/L.

Molarity is moles of solute divided by solution volume in liters.
Convert 4990 mL to 4.99 L.
Compute M = 0.615 / 4.99.


Response:
Reasoning:
1. Explicit Euler updates y_{n+1} = y_n + h f(y_n).
2. Here f(y) = -0.52 y, so each step multiplies y by 1 - h*0.52.
3. Apply that update for 5 steps and round the final state.
Final: {"answer": 0.0, "unit": "state_units"}

Answer: 0.0

Prompt: Use explicit Euler on dy/dt = -0.52 y with y(0)=3, step size h=1.75, 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) = -0.52 y, so each step multiplies y by 1 - h*0.52.
Apply that update for 5 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(-0.7)=-18.27 and f(7.2)=-17.48.
3. The interval width is 7.9.
Final: {"answer": -141.2125, "unit": "area_units"}

Answer: -141.2125

Prompt: Use the trapezoid rule with one interval to approximate the integral of f(x)=0.1x+-18.2 from x=-0.7 to x=7.2. Return the numeric integral estimate.

The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.
Evaluate f(-0.7)=-18.27 and f(7.2)=-17.48.
The interval width is 7.9.


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=0.24 and add it to the current value.
Final: {"answer": [1.794, 0.452, -0.27], "unit": "temperature_units"}

Answer: 1.794

Answer: 0.452

Answer: -0.27

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=2.05, right=-0.05; current interior values are [2.55, -0.1, -0.45]. Use r=0.24. 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=0.24 and add it to the current value.


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": [-0.6, 0.0], "unit": "dimensionless"}

Answer: -0.6

Answer: 0.0

Prompt: A line passes through points (-19.25, 11.55) and (-9.5, 5.7). 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. 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 simulation spec case 152139, 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. 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 normalize_000952(values):
    total = sum(values)
    if total == 0:
        raise ValueError('cannot normalize zero-sum values')
    return [v / total for v in values]
```
Final: {"answer": "python_code", "function": "normalize_000952"}

Answer: python_code

Prompt: Write a Python function normalize_000952(values) that returns a new list whose values sum to 1. Raise ValueError if the sum 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.

out = normalize_000952([2, 3, 5]); assert len(out) == 3

try:
    normalize_000952([1, -1])
    raise AssertionError('expected ValueError')
except ValueError:
    pass


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=2.19 mol and T=283 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. Kinetic energy is KE = 1/2 m v^2.
2. Compute v^2 = 30.3^2 and multiply by 0.5 * 27.1.
3. The unit kg*m^2/s^2 is one joule.
Final: {"answer": 12440.1195, "unit": "J"}

Answer: 12440.1195

Prompt: A body of mass 27.1 kg moves at 30.3 m/s. Find its kinetic energy in joules with unit reasoning.

Kinetic energy is KE = 1/2 m v^2.
Compute v^2 = 30.3^2 and multiply by 0.5 * 27.1.
The unit kg*m^2/s^2 is one joule.


Response:
Reasoning:
1. For level-ground projectile motion, R = v^2 sin(2 theta) / g.
2. Convert theta=52 degrees through the sine of 2 theta.
3. Substitute v=37.5 m/s and g=9.81 m/s^2.
Final: {"answer": 139.0906, "unit": "m"}

Answer: 139.0906

Prompt: A projectile is launched on level ground with no air resistance at speed 37.5 m/s and angle 52 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=52 degrees through the sine of 2 theta.
Substitute v=37.5 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 = 0.94 * 8.314 * 251 / 51.1.
Final: {"answer": 38.3876, "unit": "kPa"}

Answer: 38.3876

Prompt: An ideal gas sample has n=0.94 mol, T=251 K, and V=51.1 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 = 0.94 * 8.314 * 251 / 51.1.


Response:
Reasoning:
1. Use Q = m c DeltaT.
2. The mass is already in grams, matching the specific heat denominator.
3. Compute Q = 75 * 2.545 * 115.
Final: {"answer": 21950.625, "unit": "J"}

Answer: 21950.625

Prompt: A 75 g sample has specific heat 2.545 J/(g*K). How much heat is needed to raise its temperature by 115 K?

Use Q = m c DeltaT.
The mass is already in grams, matching the specific heat denominator.
Compute Q = 75 * 2.545 * 115.


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=53 V and R=157.1 ohm.
Final: {"answer": 17.8803, "unit": "W"}

Answer: 17.8803

Prompt: A resistor has resistance 157.1 ohm and voltage 53 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=53 V and R=157.1 ohm.


Response:
Reasoning:
1. Molarity is moles of solute divided by solution volume in liters.
2. Convert 4970 mL to 4.97 L.
3. Compute M = 2.27 / 4.97.
Final: {"answer": 0.4567, "unit": "mol/L"}

Answer: 0.4567

Prompt: A solution contains 2.27 mol of solute in 4970 mL of solution. Compute the molarity in mol/L.

Molarity is moles of solute divided by solution volume in liters.
Convert 4970 mL to 4.97 L.
Compute M = 2.27 / 4.97.


Response:
Reasoning:
1. Explicit Euler updates y_{n+1} = y_n + h f(y_n).
2. Here f(y) = -0.67 y, so each step multiplies y by 1 - h*0.67.
3. Apply that update for 4 steps and round the final state.
Final: {"answer": 18.4488, "unit": "state_units"}

Answer: 18.4488

Prompt: Use explicit Euler on dy/dt = -0.67 y with y(0)=77.5, step size h=0.45, 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) = -0.67 y, so each step multiplies y by 1 - h*0.67.
Apply that update for 4 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(-7.3)=-62.29 and f(0.8)=-11.26.
3. The interval width is 8.1.
Final: {"answer": -297.8775, "unit": "area_units"}

Answer: -297.8775

Prompt: Use the trapezoid rule with one interval to approximate the integral of f(x)=6.3x+-16.3 from x=-7.3 to x=0.8. Return the numeric integral estimate.

The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.
Evaluate f(-7.3)=-62.29 and f(0.8)=-11.26.
The interval width is 8.1.


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": [0.236, 1.804, 1.964], "unit": "temperature_units"}

Answer: 0.236

Answer: 1.804

Answer: 1.964

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=-1.85, right=0.4; current interior values are [-0.1, 2.7, 2.7]. 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. There are 100 centimeters in one meter.
2. Apply the conversion factor directly to the given value.
3. Compute 3818.5 / 100.
Final: {"answer": 38.185, "unit": "m"}

Answer: 38.185

Prompt: Convert 3818.5 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 3818.5 / 100.


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": [-9.25, -23.25], "unit": "dimensionless"}

Answer: -9.25

Answer: -23.25

Prompt: A line passes through points (16, -171.25) and (23.25, -238.312). 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. 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 quality-control check case 545993, 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. 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_000970(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_000970"}

Answer: python_code

Prompt: Write a Python function pairwise_ratios_000970(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_000970([1], [0])
    raise AssertionError('expected ValueError')
except ValueError:
    pass

try:
    pairwise_ratios_000970([1, 2], [1])
    raise AssertionError('expected ValueError')
except ValueError:
    pass


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

Answer: INSUFFICIENT_INFO

Prompt: Solve the 1D heat equation after one finite-difference step. The prompt gives r=0.18 and interior values [0.65, 0.45, 2.15], but gives no boundary values. 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: left_boundary, right_boundary.
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=59 degrees through the sine of 2 theta.
3. Substitute v=12.6 m/s and g=9.81 m/s^2.
Final: {"answer": 14.2892, "unit": "m"}

Answer: 14.2892

Prompt: A projectile is launched on level ground with no air resistance at speed 12.6 m/s and angle 59 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=59 degrees through the sine of 2 theta.
Substitute v=12.6 m/s and g=9.81 m/s^2.


Response:
Reasoning:
1. Use Q = m c DeltaT.
2. The mass is already in grams, matching the specific heat denominator.
3. Compute Q = 695 * 2.105 * 69.
Final: {"answer": 100945.275, "unit": "J"}

Answer: 100945.275

Prompt: A 695 g sample has specific heat 2.105 J/(g*K). How much heat is needed to raise its temperature by 69 K?

Use Q = m c DeltaT.
The mass is already in grams, matching the specific heat denominator.
Compute Q = 695 * 2.105 * 69.


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=63.6 V and R=92.8 ohm.
Final: {"answer": 43.5879, "unit": "W"}

Answer: 43.5879

Prompt: A resistor has resistance 92.8 ohm and voltage 63.6 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=63.6 V and R=92.8 ohm.


Response:
Reasoning:
1. Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).
2. Use N0=264 mg, t=263 h, and T_half=118 h.
3. The remaining amount has the same mass unit as the initial amount.
Final: {"answer": 56.3202, "unit": "mg"}

Answer: 56.3202

Prompt: A radioactive sample starts with 264 mg. Its half-life is 118 hours. How many mg remain after 263 hours?

Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).
Use N0=264 mg, t=263 h, and T_half=118 h.
The remaining amount has the same mass unit as the initial amount.


Response:
Reasoning:
1. Mass equals amount in moles times molar mass.
2. Use m = 4.51 mol * 44.01 g/mol.
3. The mole unit cancels, leaving grams.
Final: {"answer": 198.4851, "unit": "g"}

Answer: 198.4851

Prompt: A sample contains 4.51 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 = 4.51 mol * 44.01 g/mol.
The mole unit cancels, leaving grams.


Response:
Reasoning:
1. Molarity is moles of solute divided by solution volume in liters.
2. Convert 4345 mL to 4.345 L.
3. Compute M = 3.38 / 4.345.
Final: {"answer": 0.7779, "unit": "mol/L"}

Answer: 0.7779

Prompt: A solution contains 3.38 mol of solute in 4345 mL of solution. Compute the molarity in mol/L.

Molarity is moles of solute divided by solution volume in liters.
Convert 4345 mL to 4.345 L.
Compute M = 3.38 / 4.345.


Response:
Reasoning:
1. Explicit Euler updates y_{n+1} = y_n + h f(y_n).
2. Here f(y) = -0.4 y, so each step multiplies y by 1 - h*0.4.
3. Apply that update for 5 steps and round the final state.
Final: {"answer": 3.8725, "unit": "state_units"}

Answer: 3.8725

Prompt: Use explicit Euler on dy/dt = -0.4 y with y(0)=59, step size h=1.05, 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) = -0.4 y, so each step multiplies y by 1 - h*0.4.
Apply that update for 5 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(-2.7)=-27.58 and f(5.1)=22.34.
3. The interval width is 7.8.
Final: {"answer": -20.436, "unit": "area_units"}

Answer: -20.436

Prompt: Use the trapezoid rule with one interval to approximate the integral of f(x)=6.4x+-10.3 from x=-2.7 to x=5.1. Return the numeric integral estimate.

The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.
Evaluate f(-2.7)=-27.58 and f(5.1)=22.34.
The interval width is 7.8.


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=0.1 and add it to the current value.
Final: {"answer": [1.37, 1.445, 1.43], "unit": "temperature_units"}

Answer: 1.37

Answer: 1.445

Answer: 1.43

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=2.25, right=0.05; current interior values are [1.25, 1.45, 1.6]. Use r=0.1. 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=0.1 and add it to the current value.


Response:
Reasoning:
1. Kelvin equals Celsius plus 273.15.
2. Apply the conversion factor directly to the given value.
3. Compute -54.5 + 273.15.
Final: {"answer": 218.65, "unit": "K"}

Answer: 218.65

Prompt: Convert -54.5 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 -54.5 + 273.15.


Response:
Reasoning:
1. The x component is magnitude times cos(theta).
2. The y component is magnitude times sin(theta).
3. Use theta=159 degrees and keep the unit as newtons.
Final: {"answer": [-440.65, 169.1497], "unit": "N"}

Answer: -440.65

Answer: 169.1497

Prompt: A vector has magnitude 472 N at 159 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=159 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": [2.25, 21.75], "unit": "dimensionless"}

Answer: 2.25

Answer: 21.75

Prompt: A line passes through points (-17.25, -17.0625) and (-12.75, -6.9375). 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. Compare the dimensions on both sides of the equation.
2. velocity divided by time is acceleration
3. The equation is valid only if both sides have identical dimensions.
Final: {"answer": "inconsistent"}

Answer: inconsistent

Prompt: In model card equation case 189021, check dimensional consistency for x = v / t. The left side has dimensions m and the right side has dimensions m/s^2. Return consistent or inconsistent with a brief reason.

Compare the dimensions on both sides of the equation.
velocity divided by time is acceleration
The equation is valid only if both sides have identical dimensions.

Answer: inconsistent


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
import math

def unit_vector_000988(x, y):
    norm = math.hypot(x, y)
    if norm == 0:
        raise ValueError('zero vector has no direction')
    return (x / norm, y / norm)
```
Final: {"answer": "python_code", "function": "unit_vector_000988"}

Answer: python_code

Prompt: Write a Python function unit_vector_000988(x, y) that returns the 2D unit vector as a tuple. Raise ValueError for the zero vector. 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:
    unit_vector_000988(0, 0)
    raise AssertionError('expected ValueError')
except ValueError:
    pass


Response:
Reasoning:
1. Use Newton's second law F = m a.
2. Substitute m = 14.5 kg and a = 10.85 m/s^2.
3. The unit kg*m/s^2 is one newton.
Final: {"answer": 157.325, "unit": "N"}

Answer: 157.325

Prompt: A cart has mass 14.5 kg and measured acceleration 10.85 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 = 14.5 kg and a = 10.85 m/s^2.
The unit kg*m/s^2 is one newton.


Response:
Reasoning:
1. For level-ground projectile motion, R = v^2 sin(2 theta) / g.
2. Convert theta=80 degrees through the sine of 2 theta.
3. Substitute v=50.1 m/s and g=9.81 m/s^2.
Final: {"answer": 87.5101, "unit": "m"}

Answer: 87.5101

Prompt: A projectile is launched on level ground with no air resistance at speed 50.1 m/s and angle 80 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=80 degrees through the sine of 2 theta.
Substitute v=50.1 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 = 5.36 * 8.314 * 409 / 37.9.
Final: {"answer": 480.9046, "unit": "kPa"}

Answer: 480.9046

Prompt: An ideal gas sample has n=5.36 mol, T=409 K, and V=37.9 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 = 5.36 * 8.314 * 409 / 37.9.


Response:
Reasoning:
1. Use Q = m c DeltaT.
2. The mass is already in grams, matching the specific heat denominator.
3. Compute Q = 1135 * 1.39 * 23.
Final: {"answer": 36285.95, "unit": "J"}

Answer: 36285.95

Prompt: A 1135 g sample has specific heat 1.39 J/(g*K). How much heat is needed to raise its temperature by 23 K?

Use Q = m c DeltaT.
The mass is already in grams, matching the specific heat denominator.
Compute Q = 1135 * 1.39 * 23.


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=131.3 V and R=31.8 ohm.
Final: {"answer": 542.1286, "unit": "W"}

Answer: 542.1286

Prompt: A resistor has resistance 31.8 ohm and voltage 131.3 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=131.3 V and R=31.8 ohm.


Response:
Reasoning:
1. Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).
2. Use N0=944 mg, t=343 h, and T_half=42.5 h.
3. The remaining amount has the same mass unit as the initial amount.
Final: {"answer": 3.5114, "unit": "mg"}

Answer: 3.5114

Prompt: A radioactive sample starts with 944 mg. Its half-life is 42.5 hours. How many mg remain after 343 hours?

Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).
Use N0=944 mg, t=343 h, and T_half=42.5 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 4020 mL to 4.02 L.
3. Compute M = 2.91 / 4.02.
Final: {"answer": 0.7239, "unit": "mol/L"}

Answer: 0.7239

Prompt: A solution contains 2.91 mol of solute in 4020 mL of solution. Compute the molarity in mol/L.

Molarity is moles of solute divided by solution volume in liters.
Convert 4020 mL to 4.02 L.
Compute M = 2.91 / 4.02.


Response:
Reasoning:
1. The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.
2. Evaluate f(-4.8)=39.68 and f(-1.7)=23.87.
3. The interval width is 3.1.
Final: {"answer": 98.5025, "unit": "area_units"}

Answer: 98.5025

Prompt: Use the trapezoid rule with one interval to approximate the integral of f(x)=-5.1x+15.2 from x=-4.8 to x=-1.7. Return the numeric integral estimate.

The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.
Evaluate f(-4.8)=39.68 and f(-1.7)=23.87.
The interval width is 3.1.


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=0.06 and add it to the current value.
Final: {"answer": [1.908, 0.338, 2.518], "unit": "temperature_units"}

Answer: 1.908

Answer: 0.338

Answer: 2.518

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=0.95, right=0.85; current interior values are [2.1, 0.05, 2.8]. Use r=0.06. 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=0.06 and add it to the current value.


Response:
Reasoning:
1. There are 100 centimeters in one meter.
2. Apply the conversion factor directly to the given value.
3. Compute 1643.5 / 100.
Final: {"answer": 16.435, "unit": "m"}

Answer: 16.435

Prompt: Convert 1643.5 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 1643.5 / 100.


Response:
Reasoning:
1. The x component is magnitude times cos(theta).
2. The y component is magnitude times sin(theta).
3. Use theta=40 degrees and keep the unit as newtons.
Final: {"answer": [41.3664, 34.7105], "unit": "N"}

Answer: 41.3664

Answer: 34.7105

Prompt: A vector has magnitude 54 N at 40 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=40 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": [-0.8, -22.0], "unit": "dimensionless"}

Answer: -0.8

Answer: -22.0

Prompt: A line passes through points (14.25, -33.4) and (27.5, -44). 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. Compare the dimensions on both sides of the equation.
2. velocity times time gives distance, not acceleration
3. The equation is valid only if both sides have identical dimensions.
Final: {"answer": "inconsistent"}

Answer: inconsistent

Prompt: In field worksheet case 728386, check dimensional consistency for a = v * t. The left side has dimensions m/s^2 and the right side has dimensions m. Return consistent or inconsistent with a brief reason.

Compare the dimensions on both sides of the equation.
velocity times time gives distance, not acceleration
The equation is valid only if both sides have identical dimensions.

Answer: inconsistent


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_001006(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_001006"}

Answer: python_code

Prompt: Write a Python function safe_mean_001006(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_001006([])
    raise AssertionError('expected ValueError')
except ValueError:
    pass


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 invoice records in release 625555, 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. Kinetic energy is KE = 1/2 m v^2.
2. Compute v^2 = 4.8^2 and multiply by 0.5 * 7.3.
3. The unit kg*m^2/s^2 is one joule.
Final: {"answer": 84.096, "unit": "J"}

Answer: 84.096

Prompt: A body of mass 7.3 kg moves at 4.8 m/s. Find its kinetic energy in joules with unit reasoning.

Kinetic energy is KE = 1/2 m v^2.
Compute v^2 = 4.8^2 and multiply by 0.5 * 7.3.
The unit kg*m^2/s^2 is one joule.


Response:
Reasoning:
1. For level-ground projectile motion, R = v^2 sin(2 theta) / g.
2. Convert theta=77 degrees through the sine of 2 theta.
3. Substitute v=61.5 m/s and g=9.81 m/s^2.
Final: {"answer": 169.0142, "unit": "m"}

Answer: 169.0142

Prompt: A projectile is launched on level ground with no air resistance at speed 61.5 m/s and angle 77 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=77 degrees through the sine of 2 theta.
Substitute v=61.5 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=113.7 V and R=120.5 ohm.
Final: {"answer": 107.2837, "unit": "W"}

Answer: 107.2837

Prompt: A resistor has resistance 120.5 ohm and voltage 113.7 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=113.7 V and R=120.5 ohm.


Response:
Reasoning:
1. Molarity is moles of solute divided by solution volume in liters.
2. Convert 2130 mL to 2.13 L.
3. Compute M = 3.82 / 2.13.
Final: {"answer": 1.7934, "unit": "mol/L"}

Answer: 1.7934

Prompt: A solution contains 3.82 mol of solute in 2130 mL of solution. Compute the molarity in mol/L.

Molarity is moles of solute divided by solution volume in liters.
Convert 2130 mL to 2.13 L.
Compute M = 3.82 / 2.13.


Response:
Reasoning:
1. Explicit Euler updates y_{n+1} = y_n + h f(y_n).
2. Here f(y) = -0.73 y, so each step multiplies y by 1 - h*0.73.
3. Apply that update for 11 steps and round the final state.
Final: {"answer": 0.0, "unit": "state_units"}

Answer: 0.0

Prompt: Use explicit Euler on dy/dt = -0.73 y with y(0)=52.5, step size h=1.25, for 11 steps. What is y after the final step?

Explicit Euler updates y_{n+1} = y_n + h f(y_n).
Here f(y) = -0.73 y, so each step multiplies y by 1 - h*0.73.
Apply that update for 11 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(9.8)=60.08 and f(14.8)=93.08.
3. The interval width is 5.
Final: {"answer": 382.9, "unit": "area_units"}

Answer: 382.9

Prompt: Use the trapezoid rule with one interval to approximate the integral of f(x)=6.6x+-4.6 from x=9.8 to x=14.8. Return the numeric integral estimate.

The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.
Evaluate f(9.8)=60.08 and f(14.8)=93.08.
The interval width is 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=0.22 and add it to the current value.
Final: {"answer": [0.793, 1.829, 1.003], "unit": "temperature_units"}

Answer: 0.793

Answer: 1.829

Answer: 1.003

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=-0.55, right=-1.25; current interior values are [0.65, 2.5, 1.3]. Use r=0.22. 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=0.22 and add it to the current value.


Response:
Reasoning:
1. There are 1000 grams in one kilogram.
2. Apply the conversion factor directly to the given value.
3. Compute 26986.0 / 1000.
Final: {"answer": 26.986, "unit": "kg"}

Answer: 26.986

Prompt: Convert 26986 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 26986.0 / 1000.


Response:
Reasoning:
1. The x component is magnitude times cos(theta).
2. The y component is magnitude times sin(theta).
3. Use theta=22 degrees and keep the unit as newtons.
Final: {"answer": [94.5728, 38.2099], "unit": "N"}

Answer: 94.5728

Answer: 38.2099

Prompt: A vector has magnitude 102 N at 22 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=22 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": [-3.9, 3.5], "unit": "dimensionless"}

Answer: -3.9

Answer: 3.5

Prompt: A line passes through points (12.5, -45.25) and (13, -47.2). 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. 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 simulation spec case 255729, 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. 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 normalize_001024(values):
    total = sum(values)
    if total == 0:
        raise ValueError('cannot normalize zero-sum values')
    return [v / total for v in values]
```
Final: {"answer": "python_code", "function": "normalize_001024"}

Answer: python_code

Prompt: Write a Python function normalize_001024(values) that returns a new list whose values sum to 1. Raise ValueError if the sum 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.

out = normalize_001024([2, 3, 5]); assert len(out) == 3

try:
    normalize_001024([1, -1])
    raise AssertionError('expected ValueError')
except ValueError:
    pass


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 53.8 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 = 19.45 kg and a = 2.75 m/s^2.
3. The unit kg*m/s^2 is one newton.
Final: {"answer": 53.4875, "unit": "N"}

Answer: 53.4875

Prompt: A cart has mass 19.45 kg and measured acceleration 2.75 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 = 19.45 kg and a = 2.75 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 = 4.2^2 and multiply by 0.5 * 22.6.
3. The unit kg*m^2/s^2 is one joule.
Final: {"answer": 199.332, "unit": "J"}

Answer: 199.332

Prompt: A body of mass 22.6 kg moves at 4.2 m/s. Find its kinetic energy in joules with unit reasoning.

Kinetic energy is KE = 1/2 m v^2.
Compute v^2 = 4.2^2 and multiply by 0.5 * 22.6.
The unit kg*m^2/s^2 is one joule.


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=41.1 m/s and g=9.81 m/s^2.
Final: {"answer": 106.0124, "unit": "m"}

Answer: 106.0124

Prompt: A projectile is launched on level ground with no air resistance at speed 41.1 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=41.1 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 = 2.71 * 8.314 * 369 / 78.7.
Final: {"answer": 105.6406, "unit": "kPa"}

Answer: 105.6406

Prompt: An ideal gas sample has n=2.71 mol, T=369 K, and V=78.7 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 = 2.71 * 8.314 * 369 / 78.7.


Response:
Reasoning:
1. Use Q = m c DeltaT.
2. The mass is already in grams, matching the specific heat denominator.
3. Compute Q = 1985 * 3.205 * 38.
Final: {"answer": 241753.15, "unit": "J"}

Answer: 241753.15

Prompt: A 1985 g sample has specific heat 3.205 J/(g*K). How much heat is needed to raise its temperature by 38 K?

Use Q = m c DeltaT.
The mass is already in grams, matching the specific heat denominator.
Compute Q = 1985 * 3.205 * 38.


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=236.4 V and R=99 ohm.
Final: {"answer": 564.4945, "unit": "W"}

Answer: 564.4945

Prompt: A resistor has resistance 99 ohm and voltage 236.4 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=236.4 V and R=99 ohm.


Response:
Reasoning:
1. Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).
2. Use N0=85.5 mg, t=204 h, and T_half=119 h.
3. The remaining amount has the same mass unit as the initial amount.
Final: {"answer": 26.0564, "unit": "mg"}

Answer: 26.0564

Prompt: A radioactive sample starts with 85.5 mg. Its half-life is 119 hours. How many mg remain after 204 hours?

Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).
Use N0=85.5 mg, t=204 h, and T_half=119 h.
The remaining amount has the same mass unit as the initial amount.


Response:
Reasoning:
1. Mass equals amount in moles times molar mass.
2. Use m = 7.68 mol * 180.156 g/mol.
3. The mole unit cancels, leaving grams.
Final: {"answer": 1383.5981, "unit": "g"}

Answer: 1383.5981

Prompt: A sample contains 7.68 mol of glucose. Using molar mass 180.156 g/mol, compute the sample mass in grams.

Mass equals amount in moles times molar mass.
Use m = 7.68 mol * 180.156 g/mol.
The mole unit cancels, leaving grams.


Response:
Reasoning:
1. Molarity is moles of solute divided by solution volume in liters.
2. Convert 4665 mL to 4.665 L.
3. Compute M = 3.17 / 4.665.
Final: {"answer": 0.6795, "unit": "mol/L"}

Answer: 0.6795

Prompt: A solution contains 3.17 mol of solute in 4665 mL of solution. Compute the molarity in mol/L.

Molarity is moles of solute divided by solution volume in liters.
Convert 4665 mL to 4.665 L.
Compute M = 3.17 / 4.665.


Response:
Reasoning:
1. Explicit Euler updates y_{n+1} = y_n + h f(y_n).
2. Here f(y) = -0.9 y, so each step multiplies y by 1 - h*0.9.
3. Apply that update for 11 steps and round the final state.
Final: {"answer": -0.4007, "unit": "state_units"}

Answer: -0.4007

Prompt: Use explicit Euler on dy/dt = -0.9 y with y(0)=77, step size h=1.8, for 11 steps. What is y after the final step?

Explicit Euler updates y_{n+1} = y_n + h f(y_n).
Here f(y) = -0.9 y, so each step multiplies y by 1 - h*0.9.
Apply that update for 11 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(-7.5)=-18.25 and f(-3.6)=-5.38.
3. The interval width is 3.9.
Final: {"answer": -46.0785, "unit": "area_units"}

Answer: -46.0785

Prompt: Use the trapezoid rule with one interval to approximate the integral of f(x)=3.3x+6.5 from x=-7.5 to x=-3.6. Return the numeric integral estimate.

The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.
Evaluate f(-7.5)=-18.25 and f(-3.6)=-5.38.
The interval width is 3.9.


Response:
Reasoning:
1. There are 1000 grams in one kilogram.
2. Apply the conversion factor directly to the given value.
3. Compute 3410.0 / 1000.
Final: {"answer": 3.41, "unit": "kg"}

Answer: 3.41

Prompt: Convert 3410 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 3410.0 / 1000.


Response:
Reasoning:
1. The x component is magnitude times cos(theta).
2. The y component is magnitude times sin(theta).
3. Use theta=289 degrees and keep the unit as newtons.
Final: {"answer": [129.5761, -376.3164], "unit": "N"}

Answer: 129.5761

Answer: -376.3164

Prompt: A vector has magnitude 398 N at 289 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=289 degrees and keep the unit as newtons.


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_001042(x, lo, hi):
    if lo > hi:
        raise ValueError('lo must be <= hi')
    return min(max(x, lo), hi)
```
Final: {"answer": "python_code", "function": "clamp_001042"}

Answer: python_code

Prompt: Write a Python function clamp_001042(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_001042(1, 3, 2)
    raise AssertionError('expected ValueError')
except ValueError:
    pass


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 billing experiment record from batch 794094 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 Newton's second law F = m a.
2. Substitute m = 7.7 kg and a = 8.25 m/s^2.
3. The unit kg*m/s^2 is one newton.
Final: {"answer": 63.525, "unit": "N"}

Answer: 63.525

Prompt: A cart has mass 7.7 kg and measured acceleration 8.25 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 = 7.7 kg and a = 8.25 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 = 37.5^2 and multiply by 0.5 * 21.45.
3. The unit kg*m^2/s^2 is one joule.
Final: {"answer": 15082.0312, "unit": "J"}

Answer: 15082.0312

Prompt: A body of mass 21.45 kg moves at 37.5 m/s. Find its kinetic energy in joules with unit reasoning.

Kinetic energy is KE = 1/2 m v^2.
Compute v^2 = 37.5^2 and multiply by 0.5 * 21.45.
The unit kg*m^2/s^2 is one joule.


Response:
Reasoning:
1. For level-ground projectile motion, R = v^2 sin(2 theta) / g.
2. Convert theta=33 degrees through the sine of 2 theta.
3. Substitute v=78.6 m/s and g=9.81 m/s^2.
Final: {"answer": 575.3157, "unit": "m"}

Answer: 575.3157

Prompt: A projectile is launched on level ground with no air resistance at speed 78.6 m/s and angle 33 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=33 degrees through the sine of 2 theta.
Substitute v=78.6 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 = 2.88 * 8.314 * 337 / 65.2.
Final: {"answer": 123.7613, "unit": "kPa"}

Answer: 123.7613

Prompt: An ideal gas sample has n=2.88 mol, T=337 K, and V=65.2 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 = 2.88 * 8.314 * 337 / 65.2.


Response:
Reasoning:
1. Use Q = m c DeltaT.
2. The mass is already in grams, matching the specific heat denominator.
3. Compute Q = 1115 * 4.375 * 2.
Final: {"answer": 9756.25, "unit": "J"}

Answer: 9756.25

Prompt: A 1115 g sample has specific heat 4.375 J/(g*K). How much heat is needed to raise its temperature by 2 K?

Use Q = m c DeltaT.
The mass is already in grams, matching the specific heat denominator.
Compute Q = 1115 * 4.375 * 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=149.5 V and R=41.4 ohm.
Final: {"answer": 539.8611, "unit": "W"}

Answer: 539.8611

Prompt: A resistor has resistance 41.4 ohm and voltage 149.5 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=149.5 V and R=41.4 ohm.


Response:
Reasoning:
1. Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).
2. Use N0=387 mg, t=134.5 h, and T_half=38.5 h.
3. The remaining amount has the same mass unit as the initial amount.
Final: {"answer": 34.3606, "unit": "mg"}

Answer: 34.3606

Prompt: A radioactive sample starts with 387 mg. Its half-life is 38.5 hours. How many mg remain after 134.5 hours?

Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).
Use N0=387 mg, t=134.5 h, and T_half=38.5 h.
The remaining amount has the same mass unit as the initial amount.


Response:
Reasoning:
1. Mass equals amount in moles times molar mass.
2. Use m = 0.75 mol * 44.01 g/mol.
3. The mole unit cancels, leaving grams.
Final: {"answer": 33.0075, "unit": "g"}

Answer: 33.0075

Prompt: A sample contains 0.75 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 = 0.75 mol * 44.01 g/mol.
The mole unit cancels, leaving grams.


Response:
Reasoning:
1. Molarity is moles of solute divided by solution volume in liters.
2. Convert 4510 mL to 4.51 L.
3. Compute M = 2.615 / 4.51.
Final: {"answer": 0.5798, "unit": "mol/L"}

Answer: 0.5798

Prompt: A solution contains 2.615 mol of solute in 4510 mL of solution. Compute the molarity in mol/L.

Molarity is moles of solute divided by solution volume in liters.
Convert 4510 mL to 4.51 L.
Compute M = 2.615 / 4.51.


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 12 steps and round the final state.
Final: {"answer": 28.533, "unit": "state_units"}

Answer: 28.533

Prompt: Use explicit Euler on dy/dt = -0.03 y with y(0)=54.5, step size h=1.75, 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) = -0.03 y, so each step multiplies y by 1 - h*0.03.
Apply that update for 12 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 33.0 + 273.15.
Final: {"answer": 306.15, "unit": "K"}

Answer: 306.15

Prompt: Convert 33 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 33.0 + 273.15.


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": [0.1, -29.0], "unit": "dimensionless"}

Answer: 0.1

Answer: -29.0

Prompt: A line passes through points (-18.75, -30.875) and (-14, -30.4). 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 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_001060(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_001060"}

Answer: python_code

Prompt: Write a Python function safe_mean_001060(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_001060([])
    raise AssertionError('expected ValueError')
except ValueError:
    pass


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 82.9 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. Use Newton's second law F = m a.
2. Substitute m = 20.85 kg and a = 4.3 m/s^2.
3. The unit kg*m/s^2 is one newton.
Final: {"answer": 89.655, "unit": "N"}

Answer: 89.655

Prompt: A cart has mass 20.85 kg and measured acceleration 4.3 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 = 20.85 kg and a = 4.3 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 = 11.95^2 and multiply by 0.5 * 28.2.
3. The unit kg*m^2/s^2 is one joule.
Final: {"answer": 2013.5152, "unit": "J"}

Answer: 2013.5152

Prompt: A body of mass 28.2 kg moves at 11.95 m/s. Find its kinetic energy in joules with unit reasoning.

Kinetic energy is KE = 1/2 m v^2.
Compute v^2 = 11.95^2 and multiply by 0.5 * 28.2.
The unit kg*m^2/s^2 is one joule.


Response:
Reasoning:
1. For level-ground projectile motion, R = v^2 sin(2 theta) / g.
2. Convert theta=43 degrees through the sine of 2 theta.
3. Substitute v=48.4 m/s and g=9.81 m/s^2.
Final: {"answer": 238.2114, "unit": "m"}

Answer: 238.2114

Prompt: A projectile is launched on level ground with no air resistance at speed 48.4 m/s and angle 43 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=43 degrees through the sine of 2 theta.
Substitute v=48.4 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 = 3.51 * 8.314 * 378 / 38.0.
Final: {"answer": 290.2855, "unit": "kPa"}

Answer: 290.2855

Prompt: An ideal gas sample has n=3.51 mol, T=378 K, and V=38.0 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 = 3.51 * 8.314 * 378 / 38.0.


Response:
Reasoning:
1. Use Q = m c DeltaT.
2. The mass is already in grams, matching the specific heat denominator.
3. Compute Q = 55 * 0.595 * 7.
Final: {"answer": 229.075, "unit": "J"}

Answer: 229.075

Prompt: A 55 g sample has specific heat 0.595 J/(g*K). How much heat is needed to raise its temperature by 7 K?

Use Q = m c DeltaT.
The mass is already in grams, matching the specific heat denominator.
Compute Q = 55 * 0.595 * 7.


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=174.2 V and R=180 ohm.
Final: {"answer": 168.5869, "unit": "W"}

Answer: 168.5869

Prompt: A resistor has resistance 180 ohm and voltage 174.2 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=174.2 V and R=180 ohm.


Response:
Reasoning:
1. Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).
2. Use N0=594 mg, t=45.5 h, and T_half=118.5 h.
3. The remaining amount has the same mass unit as the initial amount.
Final: {"answer": 455.1988, "unit": "mg"}

Answer: 455.1988

Prompt: A radioactive sample starts with 594 mg. Its half-life is 118.5 hours. How many mg remain after 45.5 hours?

Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).
Use N0=594 mg, t=45.5 h, and T_half=118.5 h.
The remaining amount has the same mass unit as the initial amount.


Response:
Reasoning:
1. Mass equals amount in moles times molar mass.
2. Use m = 2.74 mol * 58.44 g/mol.
3. The mole unit cancels, leaving grams.
Final: {"answer": 160.1256, "unit": "g"}

Answer: 160.1256

Prompt: A sample contains 2.74 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 = 2.74 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 2020 mL to 2.02 L.
3. Compute M = 0.16 / 2.02.
Final: {"answer": 0.0792, "unit": "mol/L"}

Answer: 0.0792

Prompt: A solution contains 0.16 mol of solute in 2020 mL of solution. Compute the molarity in mol/L.

Molarity is moles of solute divided by solution volume in liters.
Convert 2020 mL to 2.02 L.
Compute M = 0.16 / 2.02.


Response:
Reasoning:
1. Explicit Euler updates y_{n+1} = y_n + h f(y_n).
2. Here f(y) = -0.88 y, so each step multiplies y by 1 - h*0.88.
3. Apply that update for 12 steps and round the final state.
Final: {"answer": 0.096, "unit": "state_units"}

Answer: 0.096

Prompt: Use explicit Euler on dy/dt = -0.88 y with y(0)=25.5, step size h=1.85, 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) = -0.88 y, so each step multiplies y by 1 - h*0.88.
Apply that update for 12 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(1.9)=7.68 and f(7.5)=-2.4.
3. The interval width is 5.6.
Final: {"answer": 14.784, "unit": "area_units"}

Answer: 14.784

Prompt: Use the trapezoid rule with one interval to approximate the integral of f(x)=-1.8x+11.1 from x=1.9 to x=7.5. Return the numeric integral estimate.

The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.
Evaluate f(1.9)=7.68 and f(7.5)=-2.4.
The interval width is 5.6.


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=0.22 and add it to the current value.
Final: {"answer": [-0.017, 0.056, -0.968], "unit": "temperature_units"}

Answer: -0.017

Answer: 0.056

Answer: -0.968

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=1.65, right=-1.4; current interior values are [-1.15, 1.2, -1.65]. Use r=0.22. 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=0.22 and add it to the current value.


Response:
Reasoning:
1. Kelvin equals Celsius plus 273.15.
2. Apply the conversion factor directly to the given value.
3. Compute -6.5 + 273.15.
Final: {"answer": 266.65, "unit": "K"}

Answer: 266.65

Prompt: Convert -6.5 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 -6.5 + 273.15.


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": [-0.5, 25.25], "unit": "dimensionless"}

Answer: -0.5

Answer: 25.25

Prompt: A line passes through points (-18, 34.25) and (-6.5, 28.5). 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. Compare the dimensions on both sides of the equation.
2. lever arm times force has torque dimensions
3. The equation is valid only if both sides have identical dimensions.
Final: {"answer": "consistent"}

Answer: consistent

Prompt: In lab notebook case 845667, check dimensional consistency for tau = r * F. The left side has dimensions N*m and the right side has dimensions N*m. Return consistent or inconsistent with a brief reason.

Compare the dimensions on both sides of the equation.
lever arm times force has torque dimensions
The equation is valid only if both sides have identical dimensions.

Answer: consistent


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_001078(x, lo, hi):
    if lo > hi:
        raise ValueError('lo must be <= hi')
    return min(max(x, lo), hi)
```
Final: {"answer": "python_code", "function": "clamp_001078"}

Answer: python_code

Prompt: Write a Python function clamp_001078(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_001078(1, 3, 2)
    raise AssertionError('expected ValueError')
except ValueError:
    pass


Response:
Reasoning:
1. Use Newton's second law F = m a.
2. Substitute m = 14.75 kg and a = 7 m/s^2.
3. The unit kg*m/s^2 is one newton.
Final: {"answer": 103.25, "unit": "N"}

Answer: 103.25

Prompt: A cart has mass 14.75 kg and measured acceleration 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 = 14.75 kg and a = 7 m/s^2.
The unit kg*m/s^2 is one newton.


Response:
Reasoning:
1. For level-ground projectile motion, R = v^2 sin(2 theta) / g.
2. Convert theta=11 degrees through the sine of 2 theta.
3. Substitute v=35.6 m/s and g=9.81 m/s^2.
Final: {"answer": 48.3957, "unit": "m"}

Answer: 48.3957

Prompt: A projectile is launched on level ground with no air resistance at speed 35.6 m/s and angle 11 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=11 degrees through the sine of 2 theta.
Substitute v=35.6 m/s and g=9.81 m/s^2.


Response:
Reasoning:
1. Use Q = m c DeltaT.
2. The mass is already in grams, matching the specific heat denominator.
3. Compute Q = 1320 * 4.275 * 16.
Final: {"answer": 90288.0, "unit": "J"}

Answer: 90288.0

Prompt: A 1320 g sample has specific heat 4.275 J/(g*K). How much heat is needed to raise its temperature by 16 K?

Use Q = m c DeltaT.
The mass is already in grams, matching the specific heat denominator.
Compute Q = 1320 * 4.275 * 16.


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=1.9 V and R=97.7 ohm.
Final: {"answer": 0.0369, "unit": "W"}

Answer: 0.0369

Prompt: A resistor has resistance 97.7 ohm and voltage 1.9 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=1.9 V and R=97.7 ohm.


Response:
Reasoning:
1. Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).
2. Use N0=969.5 mg, t=173 h, and T_half=46 h.
3. The remaining amount has the same mass unit as the initial amount.
Final: {"answer": 71.5177, "unit": "mg"}

Answer: 71.5177

Prompt: A radioactive sample starts with 969.5 mg. Its half-life is 46 hours. How many mg remain after 173 hours?

Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).
Use N0=969.5 mg, t=173 h, and T_half=46 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 475 mL to 0.475 L.
3. Compute M = 2.725 / 0.475.
Final: {"answer": 5.7368, "unit": "mol/L"}

Answer: 5.7368

Prompt: A solution contains 2.725 mol of solute in 475 mL of solution. Compute the molarity in mol/L.

Molarity is moles of solute divided by solution volume in liters.
Convert 475 mL to 0.475 L.
Compute M = 2.725 / 0.475.


Response:
Reasoning:
1. Explicit Euler updates y_{n+1} = y_n + h f(y_n).
2. Here f(y) = -0.1 y, so each step multiplies y by 1 - h*0.1.
3. Apply that update for 3 steps and round the final state.
Final: {"answer": 41.5892, "unit": "state_units"}

Answer: 41.5892

Prompt: Use explicit Euler on dy/dt = -0.1 y with y(0)=60, step size h=1.15, 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) = -0.1 y, so each step multiplies y by 1 - h*0.1.
Apply that update for 3 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(8.5)=-32.1 and f(17.6)=-64.86.
3. The interval width is 9.1.
Final: {"answer": -441.168, "unit": "area_units"}

Answer: -441.168

Prompt: Use the trapezoid rule with one interval to approximate the integral of f(x)=-3.6x+-1.5 from x=8.5 to x=17.6. Return the numeric integral estimate.

The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.
Evaluate f(8.5)=-32.1 and f(17.6)=-64.86.
The interval width is 9.1.


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=0.44 and add it to the current value.
Final: {"answer": [1.59, 1.566, 0.152], "unit": "temperature_units"}

Answer: 1.59

Answer: 1.566

Answer: 0.152

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=1.95, right=-1.85; current interior values are [0.6, 1.5, 2.55]. Use r=0.44. 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=0.44 and add it to the current value.


Response:
Reasoning:
1. There are 100 centimeters in one meter.
2. Apply the conversion factor directly to the given value.
3. Compute 1181.5 / 100.
Final: {"answer": 11.815, "unit": "m"}

Answer: 11.815

Prompt: Convert 1181.5 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 1181.5 / 100.


Response:
Reasoning:
1. The x component is magnitude times cos(theta).
2. The y component is magnitude times sin(theta).
3. Use theta=18 degrees and keep the unit as newtons.
Final: {"answer": [452.7029, 147.0921], "unit": "N"}

Answer: 452.7029

Answer: 147.0921

Prompt: A vector has magnitude 476 N at 18 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=18 degrees and keep the unit as newtons.


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 lab notebook case 644349, 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: 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)=53.5 and h=0.8, 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 Newton's second law F = m a.
2. Substitute m = 3.25 kg and a = 15.45 m/s^2.
3. The unit kg*m/s^2 is one newton.
Final: {"answer": 50.2125, "unit": "N"}

Answer: 50.2125

Prompt: A cart has mass 3.25 kg and measured acceleration 15.45 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 = 3.25 kg and a = 15.45 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 = 44.05^2 and multiply by 0.5 * 23.8.
3. The unit kg*m^2/s^2 is one joule.
Final: {"answer": 23090.7897, "unit": "J"}

Answer: 23090.7897

Prompt: A body of mass 23.8 kg moves at 44.05 m/s. Find its kinetic energy in joules with unit reasoning.

Kinetic energy is KE = 1/2 m v^2.
Compute v^2 = 44.05^2 and multiply by 0.5 * 23.8.
The unit kg*m^2/s^2 is one joule.


Response:
Reasoning:
1. For level-ground projectile motion, R = v^2 sin(2 theta) / g.
2. Convert theta=30 degrees through the sine of 2 theta.
3. Substitute v=8.5 m/s and g=9.81 m/s^2.
Final: {"answer": 6.3782, "unit": "m"}

Answer: 6.3782

Prompt: A projectile is launched on level ground with no air resistance at speed 8.5 m/s and angle 30 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=30 degrees through the sine of 2 theta.
Substitute v=8.5 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 = 1.74 * 8.314 * 249 / 99.1.
Final: {"answer": 36.3484, "unit": "kPa"}

Answer: 36.3484

Prompt: An ideal gas sample has n=1.74 mol, T=249 K, and V=99.1 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 = 1.74 * 8.314 * 249 / 99.1.


Response:
Reasoning:
1. Use Q = m c DeltaT.
2. The mass is already in grams, matching the specific heat denominator.
3. Compute Q = 1615 * 0.91 * 60.
Final: {"answer": 88179.0, "unit": "J"}

Answer: 88179.0

Prompt: A 1615 g sample has specific heat 0.91 J/(g*K). How much heat is needed to raise its temperature by 60 K?

Use Q = m c DeltaT.
The mass is already in grams, matching the specific heat denominator.
Compute Q = 1615 * 0.91 * 60.


Response:
Reasoning:
1. Mass equals amount in moles times molar mass.
2. Use m = 2.89 mol * 100.087 g/mol.
3. The mole unit cancels, leaving grams.
Final: {"answer": 289.2514, "unit": "g"}

Answer: 289.2514

Prompt: A sample contains 2.89 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 = 2.89 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 90 mL to 0.09 L.
3. Compute M = 4.425 / 0.09.
Final: {"answer": 49.1667, "unit": "mol/L"}

Answer: 49.1667

Prompt: A solution contains 4.425 mol of solute in 90 mL of solution. Compute the molarity in mol/L.

Molarity is moles of solute divided by solution volume in liters.
Convert 90 mL to 0.09 L.
Compute M = 4.425 / 0.09.


Response:
Reasoning:
1. The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.
2. Evaluate f(8.8)=1.18 and f(9.9)=3.49.
3. The interval width is 1.1.
Final: {"answer": 2.5685, "unit": "area_units"}

Answer: 2.5685

Prompt: Use the trapezoid rule with one interval to approximate the integral of f(x)=2.1x+-17.3 from x=8.8 to x=9.9. Return the numeric integral estimate.

The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.
Evaluate f(8.8)=1.18 and f(9.9)=3.49.
The interval width is 1.1.


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=0.3 and add it to the current value.
Final: {"answer": [1.96, 2.06, 1.365], "unit": "temperature_units"}

Answer: 1.96

Answer: 2.06

Answer: 1.365

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=2.5, right=-0.95; current interior values are [1.75, 1.7, 2.85]. Use r=0.3. 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=0.3 and add it to the current value.


Response:
Reasoning:
1. There are 1000 grams in one kilogram.
2. Apply the conversion factor directly to the given value.
3. Compute 16846.0 / 1000.
Final: {"answer": 16.846, "unit": "kg"}

Answer: 16.846

Prompt: Convert 16846 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 16846.0 / 1000.


Response:
Reasoning:
1. The x component is magnitude times cos(theta).
2. The y component is magnitude times sin(theta).
3. Use theta=30 degrees and keep the unit as newtons.
Final: {"answer": [175.3701, 101.25], "unit": "N"}

Answer: 175.3701

Answer: 101.25

Prompt: A vector has magnitude 202.5 N at 30 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=30 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": [0.4, 2.0], "unit": "dimensionless"}

Answer: 0.4

Answer: 2.0

Prompt: A line passes through points (-6, -0.4) and (2.5, 3). 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. Compare the dimensions on both sides of the equation.
2. energy divided by length is force, not spring constant
3. The equation is valid only if both sides have identical dimensions.
Final: {"answer": "inconsistent"}

Answer: inconsistent

Prompt: In student derivation case 248715, check dimensional consistency for k = E / x. The left side has dimensions N/m and the right side has dimensions J/m. Return consistent or inconsistent with a brief reason.

Compare the dimensions on both sides of the equation.
energy divided by length is force, not spring constant
The equation is valid only if both sides have identical dimensions.

Answer: inconsistent


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_001114(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_001114"}

Answer: python_code

Prompt: Write a Python function pairwise_ratios_001114(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_001114([1], [0])
    raise AssertionError('expected ValueError')
except ValueError:
    pass

try:
    pairwise_ratios_001114([1, 2], [1])
    raise AssertionError('expected ValueError')
except ValueError:
    pass


Response:
Reasoning:
1. Use Newton's second law F = m a.
2. Substitute m = 1.6 kg and a = 10.3 m/s^2.
3. The unit kg*m/s^2 is one newton.
Final: {"answer": 16.48, "unit": "N"}

Answer: 16.48

Prompt: A cart has mass 1.6 kg and measured acceleration 10.3 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 = 1.6 kg and a = 10.3 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 = 42.15^2 and multiply by 0.5 * 2.8.
3. The unit kg*m^2/s^2 is one joule.
Final: {"answer": 2487.2715, "unit": "J"}

Answer: 2487.2715

Prompt: A body of mass 2.8 kg moves at 42.15 m/s. Find its kinetic energy in joules with unit reasoning.

Kinetic energy is KE = 1/2 m v^2.
Compute v^2 = 42.15^2 and multiply by 0.5 * 2.8.
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 = 2.05 * 8.314 * 271 / 57.2.
Final: {"answer": 80.749, "unit": "kPa"}

Answer: 80.749

Prompt: An ideal gas sample has n=2.05 mol, T=271 K, and V=57.2 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 = 2.05 * 8.314 * 271 / 57.2.


Response:
Reasoning:
1. Use Q = m c DeltaT.
2. The mass is already in grams, matching the specific heat denominator.
3. Compute Q = 565 * 1.65 * 30.
Final: {"answer": 27967.5, "unit": "J"}

Answer: 27967.5

Prompt: A 565 g sample has specific heat 1.65 J/(g*K). How much heat is needed to raise its temperature by 30 K?

Use Q = m c DeltaT.
The mass is already in grams, matching the specific heat denominator.
Compute Q = 565 * 1.65 * 30.


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=124.1 V and R=69.7 ohm.
Final: {"answer": 220.9585, "unit": "W"}

Answer: 220.9585

Prompt: A resistor has resistance 69.7 ohm and voltage 124.1 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=124.1 V and R=69.7 ohm.


Response:
Reasoning:
1. Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).
2. Use N0=439.5 mg, t=48 h, and T_half=26 h.
3. The remaining amount has the same mass unit as the initial amount.
Final: {"answer": 122.2394, "unit": "mg"}

Answer: 122.2394

Prompt: A radioactive sample starts with 439.5 mg. Its half-life is 26 hours. How many mg remain after 48 hours?

Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).
Use N0=439.5 mg, t=48 h, and T_half=26 h.
The remaining amount has the same mass unit as the initial amount.


Response:
Reasoning:
1. Explicit Euler updates y_{n+1} = y_n + h f(y_n).
2. Here f(y) = -0.76 y, so each step multiplies y by 1 - h*0.76.
3. Apply that update for 5 steps and round the final state.
Final: {"answer": 1.132, "unit": "state_units"}

Answer: 1.132

Prompt: Use explicit Euler on dy/dt = -0.76 y with y(0)=77, step size h=0.75, 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) = -0.76 y, so each step multiplies y by 1 - h*0.76.
Apply that update for 5 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 659.0 / 100.
Final: {"answer": 6.59, "unit": "m"}

Answer: 6.59

Prompt: Convert 659 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 659.0 / 100.


Response:
Reasoning:
1. The x component is magnitude times cos(theta).
2. The y component is magnitude times sin(theta).
3. Use theta=37 degrees and keep the unit as newtons.
Final: {"answer": [248.3756, 187.1645], "unit": "N"}

Answer: 248.3756

Answer: 187.1645

Prompt: A vector has magnitude 311 N at 37 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=37 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": [-4.85, 7.5], "unit": "dimensionless"}

Answer: -4.85

Answer: 7.5

Prompt: A line passes through points (13.5, -57.975) and (16.25, -71.3125). 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. 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 752000, 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. Check whether all variables required by the governing equation or specification are present.
2. The missing required information is: left_boundary, right_boundary.
3. A numeric or code answer would require inventing unstated assumptions, so abstain.
Final: {"answer": "INSUFFICIENT_INFO", "missing": ["left_boundary", "right_boundary"]}

Answer: INSUFFICIENT_INFO

Prompt: Solve the 1D heat equation after one finite-difference step. The prompt gives r=0.42 and interior values [1.75, -0.2, -0.45], but gives no boundary values. 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: left_boundary, right_boundary.
A numeric or code answer would require inventing unstated assumptions, so abstain.