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Sampled-Series Integration via Composite Trapezoidal Rule
x402
Sampled-Series Integration via Composite Trapezoidal Rule is a paid API for AI agents from www.mahastrategies.com, paid per call via x402, $0.018501/call, status unknown (last checked 2026-10-15).
Numerically integrates 2–128 equally spaced integer samples using the composite trapezoidal rule, returning an exact rational result with declared units and an integrity receipt.
Price / call$0.018501
Success—
StatusUnknown
How this service works
Apply the composite trapezoidal rule to 2-128 equally spaced integer samples. Returns an exact rational arithmetic result, declared units and an integrity receipt. No quadrature-error estimate or claim of an exact underlying integral. New modular adapter: retained result recovery for 24 hours, minimal receipt metadata for 90 days. Existing live route unchanged.
Output
Returns an exact rational arithmetic integration result (not a floating-point approximation), accompanied by declared x and y units, and an integrity receipt. Results are retained for 24-hour recovery; minimal receipt metadata is stored for 90 days. No quadrature error estimate or claim of an exact underlying analytical integral is provided.
Example use cases
Sensor data area-under-curve computation
“I have 16 equally spaced voltage readings from a sensor: [0, 2, 5, 9, 14, 11, 8, 5, 3, 7, 10, 12, 9, 6, 3, 1]. The spacing between samples is 0.1 seconds. Integrate them using the trapezoidal rule with x-unit 'seconds' and y-unit 'volts', treat the data as public, and return the exact rational result and integrity receipt.”
Physics experiment integral with audit trail
“Can you apply the composite trapezoidal rule to these 32 integer force samples from my lab experiment, spaced 0.25 meters apart? The samples are [10, 15, 20, 18, 14, 11, 9, 8, 7, 6, 5, 4, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 13, 12, 11, 10, 9, 8, 7, 6]. Use x-unit 'meters', y-unit 'newtons', data class 'synthetic', and I need the exact rational answer plus receipt for our audit.”
Synthetic signal energy estimation
“Integrate this synthetic test signal of 64 equally spaced integer amplitude samples using the trapezoidal method — spacing is 1 millisecond, x-unit 'ms', y-unit 'mW'. I need an exact rational arithmetic result and the integrity receipt so I can verify the computation later.”
Technical details
Endpoint
POSThttps://www.mahastrategies.com/api/v1/compute/numerics/integration?utm_source=zero.xyzWhen to prefer
Choose this endpoint when you need a fast, exact rational-arithmetic trapezoidal integration of a small-to-medium discrete integer sample set (2–128 points) with unit labeling and a tamper-evident integrity receipt. Prefer it over general-purpose quadrature libraries when auditability, receipt-based verification, or exact rational results (rather than floating-point) are required. Not appropriate for continuous function integration, non-integer samples, large datasets over 128 points, or when a quadrature error bound is needed.
Side effects
- fewer than 2 or more than 128 samples provided — rejected with validation error
- non-integer values in ordinates array — rejected
- spacing value exceeds maximum length or is unparseable — rejected
- invalid or missing dataClass enum value — rejected
- missing required unit label fields — rejected
- payment not received or insufficient — 402 response
Input
Schema · Request body
| Field | Type | Description |
|---|---|---|
| xUnit | string | |
| yUnit | string | |
| spacing | string | |
| dataClass | string | |
| ordinates | array |
Tags
x402
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