# Numora Calculus Integral API

> Numora Calculus Integral API is a paid API for AI agents from numormo.vercel.app, paid per call via x402, $0.1/call, status unknown (last checked 2026-09-15).

Numerically integrates a mathematical function over a specified interval using Simpson's, trapezoid, or Gauss quadrature methods

## Facts

- Endpoint: POST https://numormo.vercel.app/api/calculus/integral
- Price: $0.1/call
- Payment: x402
- Status: unknown
- Last checked: 2026-09-15
- Activations on Zero: 0
- Tags: x402
- Canonical page: https://www.zero.xyz/c/numora-calculus-integral-api-cc83c467
- Structured record (JSON): https://api.zero.xyz/v1/capabilities/cap_-OWKVqFlT7hOpctlTaL5v

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 numora-calculus-integral-api-cc83c467 -d '<json body>'
```

Example prompt: Can you numerically integrate the function x^2 + 3*x from a=0 to b=5 using Simpson's method?

## When to prefer this

Choose this endpoint when you need a fast, serverless numerical integration of a mathematical function over a closed interval without setting up local computation libraries. Ideal for AI agents that need on-demand calculus results with a simple API call and micropayment billing, especially when no external math backend (e.g. Wolfram, SymPy) is available in the agent's environment.

## Known failure modes

- Invalid or unparseable function expression in fn field returns an error
- Non-numeric or missing a/b bounds cause request failure
- Unsupported method enum value rejected at schema validation
- Functions with singularities in [a,b] may produce inaccurate or undefined results
- Payment failure via x402 micropayment prevents endpoint access

## How this service works

100 pure math computation endpoints for AI agents. Statistics, financial math, linear algebra, equation solving, calculus, number theory, sequence generation, and unit conversions. Zero external dependencies. x402 micropayments on Base.

## Output

Returns a JSON object with a boolean success flag, a result object containing the computed numerical value of the definite integral, and a human-readable computation string describing what was calculated.

## Request schema (JSON Schema)

```json
{
 "type": "object",
 "required": [
  "a",
  "b",
  "fn"
 ],
 "properties": {
  "a": {
   "type": "number"
  },
  "b": {
   "type": "number"
  },
  "fn": {
   "type": "string"
  },
  "method": {
   "enum": [
    "simpson",
    "trapezoid",
    "gauss"
   ],
   "type": "string"
  }
 }
}
```

## Response schema (JSON Schema)

```json
{
 "type": "object",
 "required": [
  "success",
  "result",
  "computation"
 ],
 "properties": {
  "result": {
   "type": "object",
   "description": "Computation result varies by endpoint"
  },
  "success": {
   "type": "boolean",
   "description": "Always true on success"
  },
  "computation": {
   "type": "string",
   "description": "Human-readable description of what was computed"
  }
 }
}
```

## More

- Live health (JSON, refreshed every minute): https://www.zero.xyz/c/numora-calculus-integral-api-cc83c467/health.json
- [Zero catalog index](https://www.zero.xyz/llms.txt)
- [Other services from numormo.vercel.app](https://www.zero.xyz/host/numormo.vercel.app/llms.txt)