# Sampled-Series Integration via Composite Trapezoidal Rule

> 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.

## Facts

- Endpoint: POST https://www.mahastrategies.com/api/v1/compute/numerics/integration?utm_source=zero.xyz
- Price: $0.018501/call
- Payment: x402
- Status: unknown
- Last checked: 2026-10-15
- Activations on Zero: 0
- Tags: x402
- Canonical page: https://www.zero.xyz/c/sampled-series-integration-via-composite-trapezoidal-rule-4c8d5a38
- Structured record (JSON): https://api.zero.xyz/v1/capabilities/cap_q1cDYzoIKD58DqUuVLgsp

Status and success rate cover calls made through Zero and Zero's own probes. Third-party monitors may report differently.

## How to call it through Zero

Zero handles the 402 payment challenge and records the run. With the Zero CLI installed (`npm i -g @zeroxyz/cli`):

```sh
zero fetch --capability sampled-series-integration-via-composite-trapezoidal-rule-4c8d5a38 -d '<json body>'
```

Example prompt: Integrate these 8 equally spaced samples — [0, 3, 7, 12, 10, 6, 4, 1] — with a spacing of 0.5 seconds (x-unit: seconds, y-unit: volts), classified as synthetic data, and give me the exact rational result with a receipt.

## When to prefer this

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.

## Known failure modes

- 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

## 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.

## Request schema (JSON Schema)

```json
{
 "type": "object",
 "properties": {
  "xUnit": {
   "type": "string",
   "maxLength": 32,
   "minLength": 1
  },
  "yUnit": {
   "type": "string",
   "maxLength": 32,
   "minLength": 1
  },
  "spacing": {
   "type": "string",
   "maxLength": 19
  },
  "dataClass": {
   "enum": [
    "public",
    "synthetic"
   ],
   "type": "string"
  },
  "ordinates": {
   "type": "array",
   "maxItems": 128,
   "minItems": 1
  }
 }
}
```

## More

- Live health (JSON, refreshed every minute): https://www.zero.xyz/c/sampled-series-integration-via-composite-trapezoidal-rule-4c8d5a38/health.json
- [Zero catalog index](https://www.zero.xyz/llms.txt)
- [Other services from www.mahastrategies.com](https://www.zero.xyz/host/www.mahastrategies.com/llms.txt)