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 = 3.78 * 8.314 * 357 / 76.3.
Final: {"answer": 147.0434, "unit": "kPa"}

Answer: 147.0434

Prompt: An ideal gas sample has n=3.78 mol, T=357 K, and V=76.3 L. Using R=8.314 kPa*L/(mol*K), compute the pressure in kPa.

Use the ideal gas law P V = n R T.
Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.
Compute P = 3.78 * 8.314 * 357 / 76.3.


Response:
Reasoning:
1. Use Q = m c DeltaT.
2. The mass is already in grams, matching the specific heat denominator.
3. Compute Q = 345 * 2.05 * 41.
Final: {"answer": 28997.25, "unit": "J"}

Answer: 28997.25

Prompt: A 345 g sample has specific heat 2.05 J/(g*K). How much heat is needed to raise its temperature by 41 K?

Use Q = m c DeltaT.
The mass is already in grams, matching the specific heat denominator.
Compute Q = 345 * 2.05 * 41.


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=202.4 V and R=123.5 ohm.
Final: {"answer": 331.7066, "unit": "W"}

Answer: 331.7066

Prompt: A resistor has resistance 123.5 ohm and voltage 202.4 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=202.4 V and R=123.5 ohm.


Response:
Reasoning:
1. Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).
2. Use N0=891.5 mg, t=293 h, and T_half=15.5 h.
3. The remaining amount has the same mass unit as the initial amount.
Final: {"answer": 0.0018, "unit": "mg"}

Answer: 0.0018

Prompt: A radioactive sample starts with 891.5 mg. Its half-life is 15.5 hours. How many mg remain after 293 hours?

Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).
Use N0=891.5 mg, t=293 h, and T_half=15.5 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 = 5.54 mol * 180.156 g/mol.
3. The mole unit cancels, leaving grams.
Final: {"answer": 998.0642, "unit": "g"}

Answer: 998.0642

Prompt: A sample contains 5.54 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 = 5.54 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 2890 mL to 2.89 L.
3. Compute M = 0.89 / 2.89.
Final: {"answer": 0.308, "unit": "mol/L"}

Answer: 0.308

Prompt: A solution contains 0.89 mol of solute in 2890 mL of solution. Compute the molarity in mol/L.

Molarity is moles of solute divided by solution volume in liters.
Convert 2890 mL to 2.89 L.
Compute M = 0.89 / 2.89.


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 2 steps and round the final state.
Final: {"answer": 28.9878, "unit": "state_units"}

Answer: 28.9878

Prompt: Use explicit Euler on dy/dt = -0.03 y with y(0)=31, step size h=1.1, for 2 steps. What is y after the final step?

Explicit Euler updates y_{n+1} = y_n + h f(y_n).
Here f(y) = -0.03 y, so each step multiplies y by 1 - h*0.03.
Apply that update for 2 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)=11.4 and f(10.4)=47.12.
3. The interval width is 9.4.
Final: {"answer": 275.044, "unit": "area_units"}

Answer: 275.044

Prompt: Use the trapezoid rule with one interval to approximate the integral of f(x)=3.8x+7.6 from x=1 to x=10.4. Return the numeric integral estimate.

The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.
Evaluate f(1)=11.4 and f(10.4)=47.12.
The interval width is 9.4.

(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": [0.176, 0.766, 0.394], "unit": "temperature_units"}

Answer: 0.176

Answer: 0.766

Answer: 0.394

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=-0.65, right=-1.05; current interior values are [0.05, 1.2, 0.8]. 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. Kelvin equals Celsius plus 273.15.
2. Apply the conversion factor directly to the given value.
3. Compute -22.0 + 273.15.
Final: {"answer": 251.15, "unit": "K"}

Answer: 251.15

Prompt: Convert -22 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 -22.0 + 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=170 degrees and keep the unit as newtons.
Final: {"answer": [-363.8865, 64.163], "unit": "N"}

Answer: -363.8865

Answer: 64.163

Prompt: A vector has magnitude 369.5 N at 170 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=170 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": [-8.9, 25.5], "unit": "dimensionless"}

Answer: -8.9

Answer: 25.5

Prompt: A line passes through points (-15, 159) and (-6, 78.9). Return [slope, intercept] for y = slope*x + intercept.

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


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

Answer: consistent

Prompt: In quality-control check case 71766, 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 safe_mean_001600(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_001600"}

Answer: python_code

Prompt: Write a Python function safe_mean_001600(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_001600([])
    raise AssertionError('expected ValueError')
except ValueError:
    pass


Response:
Reasoning:
1. Use Newton's second law F = m a.
2. Substitute m = 21.85 kg and a = 3.5 m/s^2.
3. The unit kg*m/s^2 is one newton.
Final: {"answer": 76.475, "unit": "N"}

Answer: 76.475

Prompt: A cart has mass 21.85 kg and measured acceleration 3.5 m/s^2. Compute the net force. Check the SI units and give only the final JSON after reasoning.

Use Newton's second law F = m a.
Substitute m = 21.85 kg and a = 3.5 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 = 0.95^2 and multiply by 0.5 * 11.2.
3. The unit kg*m^2/s^2 is one joule.
Final: {"answer": 5.054, "unit": "J"}

Answer: 5.054

Prompt: A body of mass 11.2 kg moves at 0.95 m/s. Find its kinetic energy in joules with unit reasoning.

Kinetic energy is KE = 1/2 m v^2.
Compute v^2 = 0.95^2 and multiply by 0.5 * 11.2.
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=40 degrees through the sine of 2 theta.
3. Substitute v=32 m/s and g=9.81 m/s^2.
Final: {"answer": 102.7975, "unit": "m"}

Answer: 102.7975

Prompt: A projectile is launched on level ground with no air resistance at speed 32 m/s and angle 40 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=40 degrees through the sine of 2 theta.
Substitute v=32 m/s and g=9.81 m/s^2.

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


Response:
Reasoning:
1. Use the ideal gas law P V = n R T.
2. Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.
3. Compute P = 2.46 * 8.314 * 610 / 27.4.
Final: {"answer": 455.328, "unit": "kPa"}

Answer: 455.328

Prompt: An ideal gas sample has n=2.46 mol, T=610 K, and V=27.4 L. Using R=8.314 kPa*L/(mol*K), compute the pressure in kPa.

Use the ideal gas law P V = n R T.
Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.
Compute P = 2.46 * 8.314 * 610 / 27.4.


Response:
Reasoning:
1. Use Q = m c DeltaT.
2. The mass is already in grams, matching the specific heat denominator.
3. Compute Q = 1450 * 0.9 * 109.
Final: {"answer": 142245.0, "unit": "J"}

Answer: 142245.0

Prompt: A 1450 g sample has specific heat 0.9 J/(g*K). How much heat is needed to raise its temperature by 109 K?

Use Q = m c DeltaT.
The mass is already in grams, matching the specific heat denominator.
Compute Q = 1450 * 0.9 * 109.


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=134.5 V and R=10.8 ohm.
Final: {"answer": 1675.0231, "unit": "W"}

Answer: 1675.0231

Prompt: A resistor has resistance 10.8 ohm and voltage 134.5 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=134.5 V and R=10.8 ohm.


Response:
Reasoning:
1. Mass equals amount in moles times molar mass.
2. Use m = 2.29 mol * 18.015 g/mol.
3. The mole unit cancels, leaving grams.
Final: {"answer": 41.2544, "unit": "g"}

Answer: 41.2544

Prompt: A sample contains 2.29 mol of water. Using molar mass 18.015 g/mol, compute the sample mass in grams.

Mass equals amount in moles times molar mass.
Use m = 2.29 mol * 18.015 g/mol.
The mole unit cancels, leaving grams.


Response:
Reasoning:
1. Molarity is moles of solute divided by solution volume in liters.
2. Convert 1495 mL to 1.495 L.
3. Compute M = 1.85 / 1.495.
Final: {"answer": 1.2375, "unit": "mol/L"}

Answer: 1.2375

Prompt: A solution contains 1.85 mol of solute in 1495 mL of solution. Compute the molarity in mol/L.

Molarity is moles of solute divided by solution volume in liters.
Convert 1495 mL to 1.495 L.
Compute M = 1.85 / 1.495.


Response:
Reasoning:
1. Explicit Euler updates y_{n+1} = y_n + h f(y_n).
2. Here f(y) = -0.31 y, so each step multiplies y by 1 - h*0.31.
3. Apply that update for 3 steps and round the final state.
Final: {"answer": 27.225, "unit": "state_units"}

Answer: 27.225

Prompt: Use explicit Euler on dy/dt = -0.31 y with y(0)=40.5, step size h=0.4, 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) = -0.31 y, so each step multiplies y by 1 - h*0.31.
Apply that update for 3 steps and round the final state.


Response:
Reasoning:
1. Keep the boundary values fixed and update only the three interior grid points.
2. For each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.
3. Multiply each Laplacian by r=0.06 and add it to the current value.
Final: {"answer": [0.565, 2.239, 0.34], "unit": "temperature_units"}

Answer: 0.565

Answer: 2.239

Answer: 0.34

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=-1.15, right=1.7; current interior values are [0.55, 2.5, 0.1]. 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 1000 grams in one kilogram.
2. Apply the conversion factor directly to the given value.
3. Compute 22276.0 / 1000.
Final: {"answer": 22.276, "unit": "kg"}

Answer: 22.276

Prompt: Convert 22276 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 22276.0 / 1000.


Response:
Reasoning:
1. The x component is magnitude times cos(theta).
2. The y component is magnitude times sin(theta).
3. Use theta=306 degrees and keep the unit as newtons.
Final: {"answer": [281.843, -387.9236], "unit": "N"}

Answer: 281.843

Answer: -387.9236

Prompt: A vector has magnitude 479.5 N at 306 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=306 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": [9.15, 17.75], "unit": "dimensionless"}

Answer: 9.15

Answer: 17.75

Prompt: A line passes through points (-4.5, -23.425) and (-3.25, -11.9875). 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 lab notebook case 833545, 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. 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 threshold_flags_001618(values, threshold):
    return [value >= threshold for value in values]
```
Final: {"answer": "python_code", "function": "threshold_flags_001618"}

Answer: python_code

Prompt: Write a Python function threshold_flags_001618(values, threshold) that returns a list of booleans showing whether each value is greater than or equal to threshold. 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.

assert threshold_flags_001618([1, 2, 3], 2) == [False, True, True]

assert threshold_flags_001618([], 5) == []

assert threshold_flags_001618([-1, 0], 0) == [False, True]


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=0.34 and interior values [-1.95, 0.1, -1.1], 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. Use Newton's second law F = m a.
2. Substitute m = 17.85 kg and a = 3.5 m/s^2.
3. The unit kg*m/s^2 is one newton.
Final: {"answer": 62.475, "unit": "N"}

Answer: 62.475

Prompt: A cart has mass 17.85 kg and measured acceleration 3.5 m/s^2. Compute the net force. Check the SI units and give only the final JSON after reasoning.

Use Newton's second law F = m a.
Substitute m = 17.85 kg and a = 3.5 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 = 12.6^2 and multiply by 0.5 * 0.75.
3. The unit kg*m^2/s^2 is one joule.
Final: {"answer": 59.535, "unit": "J"}

Answer: 59.535

Prompt: A body of mass 0.75 kg moves at 12.6 m/s. Find its kinetic energy in joules with unit reasoning.

Kinetic energy is KE = 1/2 m v^2.
Compute v^2 = 12.6^2 and multiply by 0.5 * 0.75.
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=31 degrees through the sine of 2 theta.
3. Substitute v=37.5 m/s and g=9.81 m/s^2.
Final: {"answer": 126.5693, "unit": "m"}

Answer: 126.5693

Prompt: A projectile is launched on level ground with no air resistance at speed 37.5 m/s and angle 31 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=31 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 = 0.39 * 8.314 * 291 / 88.9.
Final: {"answer": 10.6137, "unit": "kPa"}

Answer: 10.6137

Prompt: An ideal gas sample has n=0.39 mol, T=291 K, and V=88.9 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 = 0.39 * 8.314 * 291 / 88.9.


Response:
Reasoning:
1. Use Q = m c DeltaT.
2. The mass is already in grams, matching the specific heat denominator.
3. Compute Q = 590 * 2.09 * 13.
Final: {"answer": 16030.3, "unit": "J"}

Answer: 16030.3

Prompt: A 590 g sample has specific heat 2.09 J/(g*K). How much heat is needed to raise its temperature by 13 K?

Use Q = m c DeltaT.
The mass is already in grams, matching the specific heat denominator.
Compute Q = 590 * 2.09 * 13.


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=233.9 V and R=145.8 ohm.
Final: {"answer": 375.2346, "unit": "W"}

Answer: 375.2346

Prompt: A resistor has resistance 145.8 ohm and voltage 233.9 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=233.9 V and R=145.8 ohm.


Response:
Reasoning:
1. Mass equals amount in moles times molar mass.
2. Use m = 0.56 mol * 18.015 g/mol.
3. The mole unit cancels, leaving grams.
Final: {"answer": 10.0884, "unit": "g"}

Answer: 10.0884

Prompt: A sample contains 0.56 mol of water. Using molar mass 18.015 g/mol, compute the sample mass in grams.

Mass equals amount in moles times molar mass.
Use m = 0.56 mol * 18.015 g/mol.
The mole unit cancels, leaving grams.


Response:
Reasoning:
1. Molarity is moles of solute divided by solution volume in liters.
2. Convert 3625 mL to 3.625 L.
3. Compute M = 1.365 / 3.625.
Final: {"answer": 0.3766, "unit": "mol/L"}

Answer: 0.3766

Prompt: A solution contains 1.365 mol of solute in 3625 mL of solution. Compute the molarity in mol/L.

Molarity is moles of solute divided by solution volume in liters.
Convert 3625 mL to 3.625 L.
Compute M = 1.365 / 3.625.


Response:
Reasoning:
1. Explicit Euler updates y_{n+1} = y_n + h f(y_n).
2. Here f(y) = -0.15 y, so each step multiplies y by 1 - h*0.15.
3. Apply that update for 12 steps and round the final state.
Final: {"answer": 24.9158, "unit": "state_units"}

Answer: 24.9158

Prompt: Use explicit Euler on dy/dt = -0.15 y with y(0)=63.5, step size h=0.5, 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) = -0.15 y, so each step multiplies y by 1 - h*0.15.
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(4.8)=10.24 and f(7.4)=7.12.
3. The interval width is 2.6.
Final: {"answer": 22.568, "unit": "area_units"}

Answer: 22.568

Prompt: Use the trapezoid rule with one interval to approximate the integral of f(x)=-1.2x+16 from x=4.8 to x=7.4. Return the numeric integral estimate.

The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.
Evaluate f(4.8)=10.24 and f(7.4)=7.12.
The interval width is 2.6.


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": [0.861, 1.756, 1.384], "unit": "temperature_units"}

Answer: 0.861

Answer: 1.756

Answer: 1.384

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=-1.45, right=-0.6; current interior values are [1.4, 1.8, 2.0]. 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 221.0 + 273.15.
Final: {"answer": 494.15, "unit": "K"}

Answer: 494.15

Prompt: Convert 221 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 221.0 + 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=232 degrees and keep the unit as newtons.
Final: {"answer": [-282.2808, -361.3029], "unit": "N"}

Answer: -282.2808

Answer: -361.3029

Prompt: A vector has magnitude 458.5 N at 232 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=232 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": [0.35, 14.5], "unit": "dimensionless"}

Answer: 0.35

Answer: 14.5

Prompt: A line passes through points (4, 15.9) and (15.5, 19.925). 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
import math

def unit_vector_001636(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_001636"}

Answer: python_code

Prompt: Write a Python function unit_vector_001636(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_001636(0, 0)
    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 alignment scoring problem with 1862 items and budget 2500, 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 = 15.55 kg and a = 11.75 m/s^2.
3. The unit kg*m/s^2 is one newton.
Final: {"answer": 182.7125, "unit": "N"}

Answer: 182.7125

Prompt: A cart has mass 15.55 kg and measured acceleration 11.75 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 = 15.55 kg and a = 11.75 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 = 44.6^2 and multiply by 0.5 * 18.3.
3. The unit kg*m^2/s^2 is one joule.
Final: {"answer": 18200.814, "unit": "J"}

Answer: 18200.814

Prompt: A body of mass 18.3 kg moves at 44.6 m/s. Find its kinetic energy in joules with unit reasoning.

Kinetic energy is KE = 1/2 m v^2.
Compute v^2 = 44.6^2 and multiply by 0.5 * 18.3.
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=74 degrees through the sine of 2 theta.
3. Substitute v=81.6 m/s and g=9.81 m/s^2.
Final: {"answer": 359.6839, "unit": "m"}

Answer: 359.6839

Prompt: A projectile is launched on level ground with no air resistance at speed 81.6 m/s and angle 74 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=74 degrees through the sine of 2 theta.
Substitute v=81.6 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 = 0.73 * 8.314 * 563 / 1.8.
Final: {"answer": 1898.3171, "unit": "kPa"}

Answer: 1898.3171

Prompt: An ideal gas sample has n=0.73 mol, T=563 K, and V=1.8 L. Using R=8.314 kPa*L/(mol*K), compute the pressure in kPa.

Use the ideal gas law P V = n R T.
Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.
Compute P = 0.73 * 8.314 * 563 / 1.8.


Response:
Reasoning:
1. Use Q = m c DeltaT.
2. The mass is already in grams, matching the specific heat denominator.
3. Compute Q = 1855 * 1.9 * 89.
Final: {"answer": 313680.5, "unit": "J"}

Answer: 313680.5

Prompt: A 1855 g sample has specific heat 1.9 J/(g*K). How much heat is needed to raise its temperature by 89 K?

Use Q = m c DeltaT.
The mass is already in grams, matching the specific heat denominator.
Compute Q = 1855 * 1.9 * 89.


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=43.8 V and R=142.8 ohm.
Final: {"answer": 13.4345, "unit": "W"}

Answer: 13.4345

Prompt: A resistor has resistance 142.8 ohm and voltage 43.8 V across it. Compute the dissipated power in watts.

Ohm's law gives I = V / R.
Power can be written as P = V I = V^2 / R.
Substitute V=43.8 V and R=142.8 ohm.


Response:
Reasoning:
1. Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).
2. Use N0=683.5 mg, t=131 h, and T_half=33 h.
3. The remaining amount has the same mass unit as the initial amount.
Final: {"answer": 43.6255, "unit": "mg"}

Answer: 43.6255

Prompt: A radioactive sample starts with 683.5 mg. Its half-life is 33 hours. How many mg remain after 131 hours?

Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).
Use N0=683.5 mg, t=131 h, and T_half=33 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 = 0.39 mol * 18.015 g/mol.
3. The mole unit cancels, leaving grams.
Final: {"answer": 7.0259, "unit": "g"}

Answer: 7.0259

Prompt: A sample contains 0.39 mol of water. Using molar mass 18.015 g/mol, compute the sample mass in grams.

Mass equals amount in moles times molar mass.
Use m = 0.39 mol * 18.015 g/mol.
The mole unit cancels, leaving grams.


Response:
Reasoning:
1. Molarity is moles of solute divided by solution volume in liters.
2. Convert 3530 mL to 3.53 L.
3. Compute M = 3.63 / 3.53.
Final: {"answer": 1.0283, "unit": "mol/L"}

Answer: 1.0283

Prompt: A solution contains 3.63 mol of solute in 3530 mL of solution. Compute the molarity in mol/L.

Molarity is moles of solute divided by solution volume in liters.
Convert 3530 mL to 3.53 L.
Compute M = 3.63 / 3.53.


Response:
Reasoning:
1. The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.
2. Evaluate f(-2)=11.6 and f(-0.9)=13.14.
3. The interval width is 1.1.
Final: {"answer": 13.607, "unit": "area_units"}

Answer: 13.607

Prompt: Use the trapezoid rule with one interval to approximate the integral of f(x)=1.4x+14.4 from x=-2 to x=-0.9. Return the numeric integral estimate.

The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.
Evaluate f(-2)=11.6 and f(-0.9)=13.14.
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=0.1 and add it to the current value.
Final: {"answer": [-0.215, 0.0, 1.7], "unit": "temperature_units"}

Answer: -0.215

Answer: 0.0

Answer: 1.7

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=0.8; current interior values are [-0.45, -0.2, 2.05]. 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 118.0 + 273.15.
Final: {"answer": 391.15, "unit": "K"}

Answer: 391.15

Prompt: Convert 118 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 118.0 + 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=43 degrees and keep the unit as newtons.
Final: {"answer": [64.3591, 60.0159], "unit": "N"}

Answer: 64.3591

Answer: 60.0159

Prompt: A vector has magnitude 88 N at 43 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=43 degrees and keep the unit as newtons.


Response:
Reasoning:
1. The slope is (y2-y1)/(x2-x1).
2. The intercept is y1 - slope*x1.
3. Return the pair in [slope, intercept] order.
Final: {"answer": [6.9, 23.75], "unit": "dimensionless"}

Answer: 6.9

Answer: 23.75

Prompt: A line passes through points (-10.5, -48.7) and (-9, -38.35). Return [slope, intercept] for y = slope*x + intercept.

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


Response:
Reasoning:
1. 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 quality-control check case 518667, 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 clamp_001654(x, lo, hi):
    if lo > hi:
        raise ValueError('lo must be <= hi')
    return min(max(x, lo), hi)
```
Final: {"answer": "python_code", "function": "clamp_001654"}

Answer: python_code

Prompt: Write a Python function clamp_001654(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_001654(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 alignment scoring problem with 2297 items and budget 20930, 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 = 4.4 kg and a = 7.6 m/s^2.
3. The unit kg*m/s^2 is one newton.
Final: {"answer": 33.44, "unit": "N"}

Answer: 33.44

Prompt: A cart has mass 4.4 kg and measured acceleration 7.6 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 = 4.4 kg and a = 7.6 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 = 34.55^2 and multiply by 0.5 * 19.
3. The unit kg*m^2/s^2 is one joule.
Final: {"answer": 11340.1737, "unit": "J"}

Answer: 11340.1737

Prompt: A body of mass 19 kg moves at 34.55 m/s. Find its kinetic energy in joules with unit reasoning.

Kinetic energy is KE = 1/2 m v^2.
Compute v^2 = 34.55^2 and multiply by 0.5 * 19.
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=24 degrees through the sine of 2 theta.
3. Substitute v=24.6 m/s and g=9.81 m/s^2.
Final: {"answer": 45.8432, "unit": "m"}

Answer: 45.8432

Prompt: A projectile is launched on level ground with no air resistance at speed 24.6 m/s and angle 24 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=24 degrees through the sine of 2 theta.
Substitute v=24.6 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 = 3.9 * 8.314 * 254 / 38.4.
Final: {"answer": 214.4752, "unit": "kPa"}

Answer: 214.4752

Prompt: An ideal gas sample has n=3.9 mol, T=254 K, and V=38.4 L. Using R=8.314 kPa*L/(mol*K), compute the pressure in kPa.

Use the ideal gas law P V = n R T.
Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.
Compute P = 3.9 * 8.314 * 254 / 38.4.


Response:
Reasoning:
1. Use Q = m c DeltaT.
2. The mass is already in grams, matching the specific heat denominator.
3. Compute Q = 790 * 4.11 * 86.
Final: {"answer": 279233.4, "unit": "J"}

Answer: 279233.4

Prompt: A 790 g sample has specific heat 4.11 J/(g*K). How much heat is needed to raise its temperature by 86 K?

Use Q = m c DeltaT.
The mass is already in grams, matching the specific heat denominator.
Compute Q = 790 * 4.11 * 86.


Response:
Reasoning:
1. Ohm's law gives I = V / R.
2. Power can be written as P = V I = V^2 / R.
3. Substitute V=100.6 V and R=121.3 ohm.
Final: {"answer": 83.4325, "unit": "W"}

Answer: 83.4325

Prompt: A resistor has resistance 121.3 ohm and voltage 100.6 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=100.6 V and R=121.3 ohm.


Response:
Reasoning:
1. Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).
2. Use N0=265.5 mg, t=324 h, and T_half=39.5 h.
3. The remaining amount has the same mass unit as the initial amount.
Final: {"answer": 0.9013, "unit": "mg"}

Answer: 0.9013

Prompt: A radioactive sample starts with 265.5 mg. Its half-life is 39.5 hours. How many mg remain after 324 hours?

Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).
Use N0=265.5 mg, t=324 h, and T_half=39.5 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 = 6.63 mol * 44.01 g/mol.
3. The mole unit cancels, leaving grams.
Final: {"answer": 291.7863, "unit": "g"}

Answer: 291.7863

Prompt: A sample contains 6.63 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 = 6.63 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 2915 mL to 2.915 L.
3. Compute M = 0.575 / 2.915.
Final: {"answer": 0.1973, "unit": "mol/L"}

Answer: 0.1973

Prompt: A solution contains 0.575 mol of solute in 2915 mL of solution. Compute the molarity in mol/L.

Molarity is moles of solute divided by solution volume in liters.
Convert 2915 mL to 2.915 L.
Compute M = 0.575 / 2.915.


Response:
Reasoning:
1. Explicit Euler updates y_{n+1} = y_n + h f(y_n).
2. Here f(y) = -0.13 y, so each step multiplies y by 1 - h*0.13.
3. Apply that update for 7 steps and round the final state.
Final: {"answer": 1.9547, "unit": "state_units"}

Answer: 1.9547

Prompt: Use explicit Euler on dy/dt = -0.13 y with y(0)=10, step size h=1.6, 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) = -0.13 y, so each step multiplies y by 1 - h*0.13.
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(7)=-44.6 and f(13.9)=-69.44.
3. The interval width is 6.9.
Final: {"answer": -393.438, "unit": "area_units"}

Answer: -393.438

Prompt: Use the trapezoid rule with one interval to approximate the integral of f(x)=-3.6x+-19.4 from x=7 to x=13.9. Return the numeric integral estimate.

The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.
Evaluate f(7)=-44.6 and f(13.9)=-69.44.
The interval width is 6.9.


Response:
Reasoning:
1. There are 100 centimeters in one meter.
2. Apply the conversion factor directly to the given value.
3. Compute 4698.0 / 100.
Final: {"answer": 46.98, "unit": "m"}

Answer: 46.98

Prompt: Convert 4698 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 4698.0 / 100.


Response:
Reasoning:
1. The x component is magnitude times cos(theta).
2. The y component is magnitude times sin(theta).
3. Use theta=318 degrees and keep the unit as newtons.
Final: {"answer": [82.8606, -74.6081], "unit": "N"}

Answer: 82.8606

Answer: -74.6081

Prompt: A vector has magnitude 111.5 N at 318 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=318 degrees and keep the unit as newtons.


Response:
Reasoning:
1. Kinetic energy is KE = 1/2 m v^2.
2. Compute v^2 = 31.75^2 and multiply by 0.5 * 11.6.
3. The unit kg*m^2/s^2 is one joule.
Final: {"answer": 5846.7625, "unit": "J"}

Answer: 5846.7625

Prompt: A body of mass 11.6 kg moves at 31.75 m/s. Find its kinetic energy in joules with unit reasoning.

Kinetic energy is KE = 1/2 m v^2.
Compute v^2 = 31.75^2 and multiply by 0.5 * 11.6.
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=35 degrees through the sine of 2 theta.
3. Substitute v=73.2 m/s and g=9.81 m/s^2.
Final: {"answer": 513.2618, "unit": "m"}

Answer: 513.2618

Prompt: A projectile is launched on level ground with no air resistance at speed 73.2 m/s and angle 35 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=35 degrees through the sine of 2 theta.
Substitute v=73.2 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 = 4.45 * 8.314 * 435 / 102.7.
Final: {"answer": 156.7072, "unit": "kPa"}

Answer: 156.7072

Prompt: An ideal gas sample has n=4.45 mol, T=435 K, and V=102.7 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 = 4.45 * 8.314 * 435 / 102.7.


Response:
Reasoning:
1. Use Q = m c DeltaT.
2. The mass is already in grams, matching the specific heat denominator.
3. Compute Q = 1890 * 0.675 * 58.
Final: {"answer": 73993.5, "unit": "J"}

Answer: 73993.5

Prompt: A 1890 g sample has specific heat 0.675 J/(g*K). How much heat is needed to raise its temperature by 58 K?

Use Q = m c DeltaT.
The mass is already in grams, matching the specific heat denominator.
Compute Q = 1890 * 0.675 * 58.


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=158.3 V and R=105.4 ohm.
Final: {"answer": 237.7504, "unit": "W"}

Answer: 237.7504

Prompt: A resistor has resistance 105.4 ohm and voltage 158.3 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=158.3 V and R=105.4 ohm.


Response:
Reasoning:
1. Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).
2. Use N0=808.5 mg, t=242 h, and T_half=86 h.
3. The remaining amount has the same mass unit as the initial amount.
Final: {"answer": 114.9729, "unit": "mg"}

Answer: 114.9729

Prompt: A radioactive sample starts with 808.5 mg. Its half-life is 86 hours. How many mg remain after 242 hours?

Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).
Use N0=808.5 mg, t=242 h, and T_half=86 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) = -0.43 y, so each step multiplies y by 1 - h*0.43.
3. Apply that update for 5 steps and round the final state.
Final: {"answer": 19.2784, "unit": "state_units"}

Answer: 19.2784

Prompt: Use explicit Euler on dy/dt = -0.43 y with y(0)=56.5, step size h=0.45, 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) = -0.43 y, so each step multiplies y by 1 - h*0.43.
Apply that update for 5 steps and round the final state.


Response:
Reasoning:
1. Keep the boundary values fixed and update only the three interior grid points.
2. For each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.
3. Multiply each Laplacian by r=0.04 and add it to the current value.
Final: {"answer": [1.522, 0.964, 2.638], "unit": "temperature_units"}

Answer: 1.522

Answer: 0.964

Answer: 2.638

Prompt: For the 1D heat equation explicit finite-difference step, use u_i(next)=u_i+r*(u_{i-1}-2*u_i+u_{i+1}). Boundary values are left=-0.75, right=-1.6; current interior values are [1.65, 0.85, 2.9]. Use r=0.04. Return the next interior vector.

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


Response:
Reasoning:
1. There are 1000 grams in one kilogram.
2. Apply the conversion factor directly to the given value.
3. Compute 9636.0 / 1000.
Final: {"answer": 9.636, "unit": "kg"}

Answer: 9.636

Prompt: Convert 9636 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 9636.0 / 1000.


Response:
Reasoning:
1. The x component is magnitude times cos(theta).
2. The y component is magnitude times sin(theta).
3. Use theta=244 degrees and keep the unit as newtons.
Final: {"answer": [-181.2665, -371.6513], "unit": "N"}

Answer: -181.2665

Answer: -371.6513

Prompt: A vector has magnitude 413.5 N at 244 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=244 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": [9.35, -29.75], "unit": "dimensionless"}

Answer: 9.35

Answer: -29.75

Prompt: A line passes through points (16.75, 126.862) and (20.75, 164.262). Return [slope, intercept] for y = slope*x + intercept.

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


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

Answer: INSUFFICIENT_INFO

Prompt: Write a parser that converts each laboratory survey record from batch 434024 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 = 7.65 kg and a = 3.5 m/s^2.
3. The unit kg*m/s^2 is one newton.
Final: {"answer": 26.775, "unit": "N"}

Answer: 26.775

Prompt: A cart has mass 7.65 kg and measured acceleration 3.5 m/s^2. Compute the net force. Check the SI units and give only the final JSON after reasoning.

Use Newton's second law F = m a.
Substitute m = 7.65 kg and a = 3.5 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 = 26.25^2 and multiply by 0.5 * 15.8.
3. The unit kg*m^2/s^2 is one joule.
Final: {"answer": 5443.5938, "unit": "J"}

Answer: 5443.5938

Prompt: A body of mass 15.8 kg moves at 26.25 m/s. Find its kinetic energy in joules with unit reasoning.

Kinetic energy is KE = 1/2 m v^2.
Compute v^2 = 26.25^2 and multiply by 0.5 * 15.8.
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=83 degrees through the sine of 2 theta.
3. Substitute v=36.9 m/s and g=9.81 m/s^2.
Final: {"answer": 33.5783, "unit": "m"}

Answer: 33.5783

Prompt: A projectile is launched on level ground with no air resistance at speed 36.9 m/s and angle 83 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=83 degrees through the sine of 2 theta.
Substitute v=36.9 m/s and g=9.81 m/s^2.


Response:
Reasoning:
1. Ohm's law gives I = V / R.
2. Power can be written as P = V I = V^2 / R.
3. Substitute V=73 V and R=197.3 ohm.
Final: {"answer": 27.0096, "unit": "W"}

Answer: 27.0096

Prompt: A resistor has resistance 197.3 ohm and voltage 73 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=73 V and R=197.3 ohm.


Response:
Reasoning:
1. Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).
2. Use N0=884 mg, t=91 h, and T_half=84.5 h.
3. The remaining amount has the same mass unit as the initial amount.
Final: {"answer": 419.0503, "unit": "mg"}

Answer: 419.0503

Prompt: A radioactive sample starts with 884 mg. Its half-life is 84.5 hours. How many mg remain after 91 hours?

Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).
Use N0=884 mg, t=91 h, and T_half=84.5 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 = 2.2 mol * 100.087 g/mol.
3. The mole unit cancels, leaving grams.
Final: {"answer": 220.1914, "unit": "g"}

Answer: 220.1914

Prompt: A sample contains 2.2 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 = 2.2 mol * 100.087 g/mol.
The mole unit cancels, leaving grams.


Response:
Reasoning:
1. Explicit Euler updates y_{n+1} = y_n + h f(y_n).
2. Here f(y) = -0.24 y, so each step multiplies y by 1 - h*0.24.
3. Apply that update for 11 steps and round the final state.
Final: {"answer": 0.3429, "unit": "state_units"}

Answer: 0.3429

Prompt: Use explicit Euler on dy/dt = -0.24 y with y(0)=31, step size h=1.4, 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) = -0.24 y, so each step multiplies y by 1 - h*0.24.
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(1.1)=2.09 and f(11.1)=-48.91.
3. The interval width is 10.
Final: {"answer": -234.1, "unit": "area_units"}

Answer: -234.1

Prompt: Use the trapezoid rule with one interval to approximate the integral of f(x)=-5.1x+7.7 from x=1.1 to x=11.1. Return the numeric integral estimate.

The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.
Evaluate f(1.1)=2.09 and f(11.1)=-48.91.
The interval width is 10.


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": [-0.545, 0.775, 1.625], "unit": "temperature_units"}

Answer: -0.545

Answer: 0.775

Answer: 1.625

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=0.1, right=1.4; current interior values are [-0.8, 0.85, 1.75]. 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. There are 100 centimeters in one meter.
2. Apply the conversion factor directly to the given value.
3. Compute 2555.5 / 100.
Final: {"answer": 25.555, "unit": "m"}

Answer: 25.555

Prompt: Convert 2555.5 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 2555.5 / 100.


Response:
Reasoning:
1. The x component is magnitude times cos(theta).
2. The y component is magnitude times sin(theta).
3. Use theta=75 degrees and keep the unit as newtons.
Final: {"answer": [36.7523, 137.1615], "unit": "N"}

Answer: 36.7523

Answer: 137.1615

Prompt: A vector has magnitude 142 N at 75 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=75 degrees and keep the unit as newtons.


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 882824, 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 weighted_sum_001708(values, weights):
    if len(values) != len(weights):
        raise ValueError('length mismatch')
    return sum(value * weight for value, weight in zip(values, weights))
```
Final: {"answer": "python_code", "function": "weighted_sum_001708"}

Answer: python_code

Prompt: Write a Python function weighted_sum_001708(values, weights) that returns sum(value*weight). Raise ValueError when the two inputs have different lengths. 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:
    weighted_sum_001708([1], [1, 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: 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=3.95 mol and T=475 K, but does not give volume. If there is insufficient information, say so explicitly.

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


Response:
Reasoning:
1. Use Newton's second law F = m a.
2. Substitute m = 2.6 kg and a = 8.8 m/s^2.
3. The unit kg*m/s^2 is one newton.
Final: {"answer": 22.88, "unit": "N"}

Answer: 22.88

Prompt: A cart has mass 2.6 kg and measured acceleration 8.8 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 = 2.6 kg and a = 8.8 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 = 32.65^2 and multiply by 0.5 * 18.
3. The unit kg*m^2/s^2 is one joule.
Final: {"answer": 9594.2025, "unit": "J"}

Answer: 9594.2025

Prompt: A body of mass 18 kg moves at 32.65 m/s. Find its kinetic energy in joules with unit reasoning.

Kinetic energy is KE = 1/2 m v^2.
Compute v^2 = 32.65^2 and multiply by 0.5 * 18.
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=25 degrees through the sine of 2 theta.
3. Substitute v=75.1 m/s and g=9.81 m/s^2.
Final: {"answer": 440.4178, "unit": "m"}

Answer: 440.4178

Prompt: A projectile is launched on level ground with no air resistance at speed 75.1 m/s and angle 25 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=25 degrees through the sine of 2 theta.
Substitute v=75.1 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 = 0.86 * 8.314 * 453 / 114.8.
Final: {"answer": 28.214, "unit": "kPa"}

Answer: 28.214

Prompt: An ideal gas sample has n=0.86 mol, T=453 K, and V=114.8 L. Using R=8.314 kPa*L/(mol*K), compute the pressure in kPa.

Use the ideal gas law P V = n R T.
Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.
Compute P = 0.86 * 8.314 * 453 / 114.8.


Response:
Reasoning:
1. Use Q = m c DeltaT.
2. The mass is already in grams, matching the specific heat denominator.
3. Compute Q = 735 * 2.945 * 8.
Final: {"answer": 17316.6, "unit": "J"}

Answer: 17316.6

Prompt: A 735 g sample has specific heat 2.945 J/(g*K). How much heat is needed to raise its temperature by 8 K?

Use Q = m c DeltaT.
The mass is already in grams, matching the specific heat denominator.
Compute Q = 735 * 2.945 * 8.


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=150.5 V and R=57.4 ohm.
Final: {"answer": 394.6037, "unit": "W"}

Answer: 394.6037

Prompt: A resistor has resistance 57.4 ohm and voltage 150.5 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=150.5 V and R=57.4 ohm.


Response:
Reasoning:
1. Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).
2. Use N0=744.5 mg, t=198 h, and T_half=61 h.
3. The remaining amount has the same mass unit as the initial amount.
Final: {"answer": 78.4785, "unit": "mg"}

Answer: 78.4785

Prompt: A radioactive sample starts with 744.5 mg. Its half-life is 61 hours. How many mg remain after 198 hours?

Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).
Use N0=744.5 mg, t=198 h, and T_half=61 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 = 4.48 mol * 180.156 g/mol.
3. The mole unit cancels, leaving grams.
Final: {"answer": 807.0989, "unit": "g"}

Answer: 807.0989

Prompt: A sample contains 4.48 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 = 4.48 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 4810 mL to 4.81 L.
3. Compute M = 0.41 / 4.81.
Final: {"answer": 0.0852, "unit": "mol/L"}

Answer: 0.0852

Prompt: A solution contains 0.41 mol of solute in 4810 mL of solution. Compute the molarity in mol/L.

Molarity is moles of solute divided by solution volume in liters.
Convert 4810 mL to 4.81 L.
Compute M = 0.41 / 4.81.


Response:
Reasoning:
1. Explicit Euler updates y_{n+1} = y_n + h f(y_n).
2. Here f(y) = -0.49 y, so each step multiplies y by 1 - h*0.49.
3. Apply that update for 8 steps and round the final state.
Final: {"answer": 8.2138, "unit": "state_units"}

Answer: 8.2138

Prompt: Use explicit Euler on dy/dt = -0.49 y with y(0)=37, step size h=0.35, for 8 steps. What is y after the final step?

Explicit Euler updates y_{n+1} = y_n + h f(y_n).
Here f(y) = -0.49 y, so each step multiplies y by 1 - h*0.49.
Apply that update for 8 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(5.5)=-44.65 and f(9.3)=-71.63.
3. The interval width is 3.8.
Final: {"answer": -220.932, "unit": "area_units"}

Answer: -220.932

Prompt: Use the trapezoid rule with one interval to approximate the integral of f(x)=-7.1x+-5.6 from x=5.5 to x=9.3. Return the numeric integral estimate.

The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.
Evaluate f(5.5)=-44.65 and f(9.3)=-71.63.
The interval width is 3.8.


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=0.42 and add it to the current value.
Final: {"answer": [0.568, 1.253, 1.254], "unit": "temperature_units"}

Answer: 0.568

Answer: 1.253

Answer: 1.254

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=1.5, right=3; current interior values are [1.45, -0.7, 1.8]. Use r=0.42. 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=0.42 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 42998.0 / 1000.
Final: {"answer": 42.998, "unit": "kg"}

Answer: 42.998

Prompt: Convert 42998 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 42998.0 / 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": [-4.7, -18.5], "unit": "dimensionless"}

Answer: -4.7

Answer: -18.5

Prompt: A line passes through points (-15.75, 55.525) and (-10.5, 30.85). 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. grams cancel with J/(g*K), and kelvin cancels, leaving joules
3. The equation is valid only if both sides have identical dimensions.
Final: {"answer": "consistent"}

Answer: consistent

Prompt: In simulation spec case 376371, check dimensional consistency for Q = m * c * DeltaT. The left side has dimensions J and the right side has dimensions J. Return consistent or inconsistent with a brief reason.

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

Answer: consistent


Response:
Reasoning:
1. 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 running_total_001726(values):
    total = 0
    out = []
    for value in values:
        total += value
        out.append(total)
    return out
```
Final: {"answer": "python_code", "function": "running_total_001726"}

Answer: python_code

Prompt: Write a Python function running_total_001726(values) that returns cumulative sums as a new list. It 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.


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

Answer: INSUFFICIENT_INFO

Prompt: Write a parser that converts each laboratory crop record from batch 154673 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 = 19 kg and a = 10.1 m/s^2.
3. The unit kg*m/s^2 is one newton.
Final: {"answer": 191.9, "unit": "N"}

Answer: 191.9

Prompt: A cart has mass 19 kg and measured acceleration 10.1 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 = 19 kg and a = 10.1 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 = 25.05^2 and multiply by 0.5 * 5.25.
3. The unit kg*m^2/s^2 is one joule.
Final: {"answer": 1647.1941, "unit": "J"}

Answer: 1647.1941

Prompt: A body of mass 5.25 kg moves at 25.05 m/s. Find its kinetic energy in joules with unit reasoning.

Kinetic energy is KE = 1/2 m v^2.
Compute v^2 = 25.05^2 and multiply by 0.5 * 5.25.
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=23 degrees through the sine of 2 theta.
3. Substitute v=28.7 m/s and g=9.81 m/s^2.
Final: {"answer": 60.3989, "unit": "m"}

Answer: 60.3989

Prompt: A projectile is launched on level ground with no air resistance at speed 28.7 m/s and angle 23 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=23 degrees through the sine of 2 theta.
Substitute v=28.7 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 = 415 * 4.165 * 57.
Final: {"answer": 98523.075, "unit": "J"}

Answer: 98523.075

Prompt: A 415 g sample has specific heat 4.165 J/(g*K). How much heat is needed to raise its temperature by 57 K?

Use Q = m c DeltaT.
The mass is already in grams, matching the specific heat denominator.
Compute Q = 415 * 4.165 * 57.


Response:
Reasoning:
1. Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).
2. Use N0=553.5 mg, t=206 h, and T_half=13 h.
3. The remaining amount has the same mass unit as the initial amount.
Final: {"answer": 0.0094, "unit": "mg"}

Answer: 0.0094

Prompt: A radioactive sample starts with 553.5 mg. Its half-life is 13 hours. How many mg remain after 206 hours?

Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).
Use N0=553.5 mg, t=206 h, and T_half=13 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 = 7.04 mol * 100.087 g/mol.
3. The mole unit cancels, leaving grams.
Final: {"answer": 704.6125, "unit": "g"}

Answer: 704.6125

Prompt: A sample contains 7.04 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 = 7.04 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 1930 mL to 1.93 L.
3. Compute M = 2.545 / 1.93.
Final: {"answer": 1.3187, "unit": "mol/L"}

Answer: 1.3187

Prompt: A solution contains 2.545 mol of solute in 1930 mL of solution. Compute the molarity in mol/L.

Molarity is moles of solute divided by solution volume in liters.
Convert 1930 mL to 1.93 L.
Compute M = 2.545 / 1.93.


Response:
Reasoning:
1. Explicit Euler updates y_{n+1} = y_n + h f(y_n).
2. Here f(y) = -0.15 y, so each step multiplies y by 1 - h*0.15.
3. Apply that update for 7 steps and round the final state.
Final: {"answer": 17.4156, "unit": "state_units"}

Answer: 17.4156

Prompt: Use explicit Euler on dy/dt = -0.15 y with y(0)=79.5, step size h=1.3, 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) = -0.15 y, so each step multiplies y by 1 - h*0.15.
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(1.5)=13.75 and f(5.3)=17.17.
3. The interval width is 3.8.
Final: {"answer": 58.748, "unit": "area_units"}

Answer: 58.748

Prompt: Use the trapezoid rule with one interval to approximate the integral of f(x)=0.9x+12.4 from x=1.5 to x=5.3. Return the numeric integral estimate.

The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.
Evaluate f(1.5)=13.75 and f(5.3)=17.17.
The interval width is 3.8.


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=0.32 and add it to the current value.
Final: {"answer": [-0.322, -0.202, 0.682], "unit": "temperature_units"}

Answer: -0.322

Answer: -0.202

Answer: 0.682

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=1.95; current interior values are [-0.45, -1.45, 1.45]. 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. Kelvin equals Celsius plus 273.15.
2. Apply the conversion factor directly to the given value.
3. Compute 173.0 + 273.15.
Final: {"answer": 446.15, "unit": "K"}

Answer: 446.15

Prompt: Convert 173 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 173.0 + 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=357 degrees and keep the unit as newtons.
Final: {"answer": [30.4582, -1.5962], "unit": "N"}

Answer: 30.4582

Answer: -1.5962

Prompt: A vector has magnitude 30.5 N at 357 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=357 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": [-8.95, -21.5], "unit": "dimensionless"}

Answer: -8.95

Answer: -21.5

Prompt: A line passes through points (-2.5, 0.875) and (2, -39.4). 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. 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 947620, 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_001744(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_001744"}

Answer: python_code

Prompt: Write a Python function pairwise_ratios_001744(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_001744([1], [0])
    raise AssertionError('expected ValueError')
except ValueError:
    pass

try:
    pairwise_ratios_001744([1, 2], [1])
    raise AssertionError('expected ValueError')
except ValueError:
    pass


Response:
Reasoning:
1. Kinetic energy is KE = 1/2 m v^2.
2. Compute v^2 = 42.1^2 and multiply by 0.5 * 18.15.
3. The unit kg*m^2/s^2 is one joule.
Final: {"answer": 16084.6208, "unit": "J"}

Answer: 16084.6208

Prompt: A body of mass 18.15 kg moves at 42.1 m/s. Find its kinetic energy in joules with unit reasoning.

Kinetic energy is KE = 1/2 m v^2.
Compute v^2 = 42.1^2 and multiply by 0.5 * 18.15.
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=18 degrees through the sine of 2 theta.
3. Substitute v=36.2 m/s and g=9.81 m/s^2.
Final: {"answer": 78.5176, "unit": "m"}

Answer: 78.5176

Prompt: A projectile is launched on level ground with no air resistance at speed 36.2 m/s and angle 18 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=18 degrees through the sine of 2 theta.
Substitute v=36.2 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 = 2.72 * 8.314 * 302 / 59.3.
Final: {"answer": 115.1678, "unit": "kPa"}

Answer: 115.1678

Prompt: An ideal gas sample has n=2.72 mol, T=302 K, and V=59.3 L. Using R=8.314 kPa*L/(mol*K), compute the pressure in kPa.

Use the ideal gas law P V = n R T.
Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.
Compute P = 2.72 * 8.314 * 302 / 59.3.


Response:
Reasoning:
1. Use Q = m c DeltaT.
2. The mass is already in grams, matching the specific heat denominator.
3. Compute Q = 885 * 1.47 * 101.
Final: {"answer": 131395.95, "unit": "J"}

Answer: 131395.95

Prompt: A 885 g sample has specific heat 1.47 J/(g*K). How much heat is needed to raise its temperature by 101 K?

Use Q = m c DeltaT.
The mass is already in grams, matching the specific heat denominator.
Compute Q = 885 * 1.47 * 101.


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=90.3 V and R=175.9 ohm.
Final: {"answer": 46.3564, "unit": "W"}

Answer: 46.3564

Prompt: A resistor has resistance 175.9 ohm and voltage 90.3 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=90.3 V and R=175.9 ohm.


Response:
Reasoning:
1. Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).
2. Use N0=550 mg, t=73 h, and T_half=76 h.
3. The remaining amount has the same mass unit as the initial amount.
Final: {"answer": 282.6282, "unit": "mg"}

Answer: 282.6282

Prompt: A radioactive sample starts with 550 mg. Its half-life is 76 hours. How many mg remain after 73 hours?

Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).
Use N0=550 mg, t=73 h, and T_half=76 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 = 6.38 mol * 180.156 g/mol.
3. The mole unit cancels, leaving grams.
Final: {"answer": 1149.3953, "unit": "g"}

Answer: 1149.3953

Prompt: A sample contains 6.38 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 = 6.38 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 4725 mL to 4.725 L.
3. Compute M = 2.66 / 4.725.
Final: {"answer": 0.563, "unit": "mol/L"}

Answer: 0.563

Prompt: A solution contains 2.66 mol of solute in 4725 mL of solution. Compute the molarity in mol/L.

Molarity is moles of solute divided by solution volume in liters.
Convert 4725 mL to 4.725 L.
Compute M = 2.66 / 4.725.


Response:
Reasoning:
1. Explicit Euler updates y_{n+1} = y_n + h f(y_n).
2. Here f(y) = -0.3 y, so each step multiplies y by 1 - h*0.3.
3. Apply that update for 6 steps and round the final state.
Final: {"answer": 0.09, "unit": "state_units"}

Answer: 0.09

Prompt: Use explicit Euler on dy/dt = -0.3 y with y(0)=6.5, step size h=1.7, for 6 steps. What is y after the final step?

Explicit Euler updates y_{n+1} = y_n + h f(y_n).
Here f(y) = -0.3 y, so each step multiplies y by 1 - h*0.3.
Apply that update for 6 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(-4.4)=-33.68 and f(5.3)=21.61.
3. The interval width is 9.7.
Final: {"answer": -58.5395, "unit": "area_units"}

Answer: -58.5395

Prompt: Use the trapezoid rule with one interval to approximate the integral of f(x)=5.7x+-8.6 from x=-4.4 to x=5.3. Return the numeric integral estimate.

The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.
Evaluate f(-4.4)=-33.68 and f(5.3)=21.61.
The interval width is 9.7.


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=0.38 and add it to the current value.
Final: {"answer": [1.575, 0.354, 0.443], "unit": "temperature_units"}

Answer: 1.575

Answer: 0.354

Answer: 0.443

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=2.7, right=-1.1; current interior values are [-0.8, 1.95, 0.5]. Use r=0.38. 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=0.38 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 57.5 / 100.
Final: {"answer": 0.575, "unit": "m"}

Answer: 0.575

Prompt: Convert 57.5 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 57.5 / 100.


Response:
Reasoning:
1. The x component is magnitude times cos(theta).
2. The y component is magnitude times sin(theta).
3. Use theta=78 degrees and keep the unit as newtons.
Final: {"answer": [65.3882, 307.6274], "unit": "N"}

Answer: 65.3882

Answer: 307.6274

Prompt: A vector has magnitude 314.5 N at 78 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=78 degrees and keep the unit as newtons.


Response:
Reasoning:
1. The slope is (y2-y1)/(x2-x1).
2. The intercept is y1 - slope*x1.
3. Return the pair in [slope, intercept] order.
Final: {"answer": [6.8, -9.25], "unit": "dimensionless"}

Answer: 6.8

Answer: -9.25

Prompt: A line passes through points (-3.25, -31.35) and (5.5, 28.15). Return [slope, intercept] for y = slope*x + intercept.

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


Response:
Reasoning:
1. Compare the dimensions on both sides of the equation.
2. coulomb per second is ampere
3. The equation is valid only if both sides have identical dimensions.
Final: {"answer": "consistent"}

Answer: consistent

Prompt: In student derivation case 837786, check dimensional consistency for I = Q / t. The left side has dimensions A and the right side has dimensions A. Return consistent or inconsistent with a brief reason.

Compare the dimensions on both sides of the equation.
coulomb per second is ampere
The equation is valid only if both sides have identical dimensions.

Answer: consistent


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

Answer: INSUFFICIENT_INFO

Prompt: Write a parser that converts each warehouse experiment record from batch 587497 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 = 2.25 kg and a = 7.05 m/s^2.
3. The unit kg*m/s^2 is one newton.
Final: {"answer": 15.8625, "unit": "N"}

Answer: 15.8625

Prompt: A cart has mass 2.25 kg and measured acceleration 7.05 m/s^2. Compute the net force. Check the SI units and give only the final JSON after reasoning.

Use Newton's second law F = m a.
Substitute m = 2.25 kg and a = 7.05 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 = 38.3^2 and multiply by 0.5 * 25.55.
3. The unit kg*m^2/s^2 is one joule.
Final: {"answer": 18739.5197, "unit": "J"}

Answer: 18739.5197

Prompt: A body of mass 25.55 kg moves at 38.3 m/s. Find its kinetic energy in joules with unit reasoning.

Kinetic energy is KE = 1/2 m v^2.
Compute v^2 = 38.3^2 and multiply by 0.5 * 25.55.
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 = 4.72 * 8.314 * 274 / 107.5.
Final: {"answer": 100.0217, "unit": "kPa"}

Answer: 100.0217

Prompt: An ideal gas sample has n=4.72 mol, T=274 K, and V=107.5 L. Using R=8.314 kPa*L/(mol*K), compute the pressure in kPa.

Use the ideal gas law P V = n R T.
Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.
Compute P = 4.72 * 8.314 * 274 / 107.5.


Response:
Reasoning:
1. Use Q = m c DeltaT.
2. The mass is already in grams, matching the specific heat denominator.
3. Compute Q = 1530 * 0.74 * 57.
Final: {"answer": 64535.4, "unit": "J"}

Answer: 64535.4

Prompt: A 1530 g sample has specific heat 0.74 J/(g*K). How much heat is needed to raise its temperature by 57 K?

Use Q = m c DeltaT.
The mass is already in grams, matching the specific heat denominator.
Compute Q = 1530 * 0.74 * 57.


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=211.7 V and R=73.1 ohm.
Final: {"answer": 613.0902, "unit": "W"}

Answer: 613.0902

Prompt: A resistor has resistance 73.1 ohm and voltage 211.7 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=211.7 V and R=73.1 ohm.


Response:
Reasoning:
1. Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).
2. Use N0=660.5 mg, t=122.5 h, and T_half=73 h.
3. The remaining amount has the same mass unit as the initial amount.
Final: {"answer": 206.4048, "unit": "mg"}

Answer: 206.4048

Prompt: A radioactive sample starts with 660.5 mg. Its half-life is 73 hours. How many mg remain after 122.5 hours?

Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).
Use N0=660.5 mg, t=122.5 h, and T_half=73 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 = 6.5 mol * 100.087 g/mol.
3. The mole unit cancels, leaving grams.
Final: {"answer": 650.5655, "unit": "g"}

Answer: 650.5655

Prompt: A sample contains 6.5 mol of calcium carbonate. Using molar mass 100.087 g/mol, compute the sample mass in grams.

Mass equals amount in moles times molar mass.
Use m = 6.5 mol * 100.087 g/mol.
The mole unit cancels, leaving grams.


Response:
Reasoning:
1. Explicit Euler updates y_{n+1} = y_n + h f(y_n).
2. Here f(y) = -0.59 y, so each step multiplies y by 1 - h*0.59.
3. Apply that update for 3 steps and round the final state.
Final: {"answer": 1.0191, "unit": "state_units"}

Answer: 1.0191

Prompt: Use explicit Euler on dy/dt = -0.59 y with y(0)=18.5, step size h=1.05, 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) = -0.59 y, so each step multiplies y by 1 - h*0.59.
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(5)=-35.3 and f(10.8)=-79.38.
3. The interval width is 5.8.
Final: {"answer": -332.572, "unit": "area_units"}

Answer: -332.572

Prompt: Use the trapezoid rule with one interval to approximate the integral of f(x)=-7.6x+2.7 from x=5 to x=10.8. Return the numeric integral estimate.

The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.
Evaluate f(5)=-35.3 and f(10.8)=-79.38.
The interval width is 5.8.


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=0.16 and add it to the current value.
Final: {"answer": [1.946, 0.412, 0.004], "unit": "temperature_units"}

Answer: 1.946

Answer: 0.412

Answer: 0.004

Prompt: For the 1D heat equation explicit finite-difference step, use u_i(next)=u_i+r*(u_{i-1}-2*u_i+u_{i+1}). Boundary values are left=-0.05, right=2.9; current interior values are [2.85, 0.1, -0.7]. Use r=0.16. Return the next interior vector.

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


Response:
Reasoning:
1. Kelvin equals Celsius plus 273.15.
2. Apply the conversion factor directly to the given value.
3. Compute 15.0 + 273.15.
Final: {"answer": 288.15, "unit": "K"}

Answer: 288.15

Prompt: Convert 15 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 15.0 + 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": [10.0, -8.0], "unit": "dimensionless"}

Answer: 10.0

Answer: -8.0

Prompt: A line passes through points (2.5, 17) and (11.75, 109.5). 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. 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_001780(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_001780"}

Answer: python_code

Prompt: Write a Python function normalize_001780(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_001780([2, 3, 5]); assert len(out) == 3

try:
    normalize_001780([1, -1])
    raise AssertionError('expected ValueError')
except ValueError:
    pass


Response:
Reasoning:
1. Use Newton's second law F = m a.
2. Substitute m = 19.45 kg and a = 4.75 m/s^2.
3. The unit kg*m/s^2 is one newton.
Final: {"answer": 92.3875, "unit": "N"}

Answer: 92.3875

Prompt: A cart has mass 19.45 kg and measured acceleration 4.75 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 = 4.75 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=79 degrees through the sine of 2 theta.
3. Substitute v=11.7 m/s and g=9.81 m/s^2.
Final: {"answer": 5.2273, "unit": "m"}

Answer: 5.2273

Prompt: A projectile is launched on level ground with no air resistance at speed 11.7 m/s and angle 79 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=79 degrees through the sine of 2 theta.
Substitute v=11.7 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 = 2.12 * 8.314 * 252 / 104.7.
Final: {"answer": 42.4228, "unit": "kPa"}

Answer: 42.4228

Prompt: An ideal gas sample has n=2.12 mol, T=252 K, and V=104.7 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 = 2.12 * 8.314 * 252 / 104.7.


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=190.1 V and R=198.7 ohm.
Final: {"answer": 181.8722, "unit": "W"}

Answer: 181.8722

Prompt: A resistor has resistance 198.7 ohm and voltage 190.1 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=190.1 V and R=198.7 ohm.


Response:
Reasoning:
1. Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).
2. Use N0=709.5 mg, t=258.5 h, and T_half=39 h.
3. The remaining amount has the same mass unit as the initial amount.
Final: {"answer": 7.1724, "unit": "mg"}

Answer: 7.1724

Prompt: A radioactive sample starts with 709.5 mg. Its half-life is 39 hours. How many mg remain after 258.5 hours?

Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).
Use N0=709.5 mg, t=258.5 h, and T_half=39 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 = 5.95 mol * 44.01 g/mol.
3. The mole unit cancels, leaving grams.
Final: {"answer": 261.8595, "unit": "g"}

Answer: 261.8595

Prompt: A sample contains 5.95 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 = 5.95 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 1185 mL to 1.185 L.
3. Compute M = 3.065 / 1.185.
Final: {"answer": 2.5865, "unit": "mol/L"}

Answer: 2.5865

Prompt: A solution contains 3.065 mol of solute in 1185 mL of solution. Compute the molarity in mol/L.

Molarity is moles of solute divided by solution volume in liters.
Convert 1185 mL to 1.185 L.
Compute M = 3.065 / 1.185.


Response:
Reasoning:
1. Explicit Euler updates y_{n+1} = y_n + h f(y_n).
2. Here f(y) = -0.36 y, so each step multiplies y by 1 - h*0.36.
3. Apply that update for 11 steps and round the final state.
Final: {"answer": 8.3518, "unit": "state_units"}

Answer: 8.3518

Prompt: Use explicit Euler on dy/dt = -0.36 y with y(0)=19, step size h=0.2, 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) = -0.36 y, so each step multiplies y by 1 - h*0.36.
Apply that update for 11 steps and round the final state.


Response:
Reasoning:
1. Keep the boundary values fixed and update only the three interior grid points.
2. For each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.
3. Multiply each Laplacian by r=0.26 and add it to the current value.
Final: {"answer": [0.464, 0.243, 0.581], "unit": "temperature_units"}

Answer: 0.464

Answer: 0.243

Answer: 0.581

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=0.85, right=2.5; current interior values are [0.1, 0.75, -0.55]. Use r=0.26. 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=0.26 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 5544.0 / 1000.
Final: {"answer": 5.544, "unit": "kg"}

Answer: 5.544

Prompt: Convert 5544 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 5544.0 / 1000.


Response:
Reasoning:
1. The x component is magnitude times cos(theta).
2. The y component is magnitude times sin(theta).
3. Use theta=209 degrees and keep the unit as newtons.
Final: {"answer": [-167.927, -93.0834], "unit": "N"}

Answer: -167.927

Answer: -93.0834

Prompt: A vector has magnitude 192 N at 209 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=209 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": [9.0, -19.75], "unit": "dimensionless"}

Answer: 9.0

Answer: -19.75

Prompt: A line passes through points (-5.75, -71.5) and (-5.5, -69.25). 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 quality-control check case 108090, 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. 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 3129 items and budget 5970, 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 = 12.5 kg and a = 7.7 m/s^2.
3. The unit kg*m/s^2 is one newton.
Final: {"answer": 96.25, "unit": "N"}

Answer: 96.25

Prompt: A cart has mass 12.5 kg and measured acceleration 7.7 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 = 12.5 kg and a = 7.7 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 = 40.8^2 and multiply by 0.5 * 1.15.
3. The unit kg*m^2/s^2 is one joule.
Final: {"answer": 957.168, "unit": "J"}

Answer: 957.168

Prompt: A body of mass 1.15 kg moves at 40.8 m/s. Find its kinetic energy in joules with unit reasoning.

Kinetic energy is KE = 1/2 m v^2.
Compute v^2 = 40.8^2 and multiply by 0.5 * 1.15.
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=44 degrees through the sine of 2 theta.
3. Substitute v=61.7 m/s and g=9.81 m/s^2.
Final: {"answer": 387.8258, "unit": "m"}

Answer: 387.8258

Prompt: A projectile is launched on level ground with no air resistance at speed 61.7 m/s and angle 44 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=44 degrees through the sine of 2 theta.
Substitute v=61.7 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 = 5.58 * 8.314 * 492 / 43.1.
Final: {"answer": 529.5806, "unit": "kPa"}

Answer: 529.5806

Prompt: An ideal gas sample has n=5.58 mol, T=492 K, and V=43.1 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 = 5.58 * 8.314 * 492 / 43.1.