CVP verified calculation capability
Composite trapezoid, Simpson 1/3, or Gauss–Legendre of a polynomial, sin, or exp on [a, b]. Not indefinite symbolic integrate.
Math · Numerical Capability ID math.numerical.definite_integral version 1.1.5 CVP VERIFIED CURRENT Core
Trapezoid
h/2 · (y₀ + 2Σ yᵢ + yₙ)h/3 · (y₀ + 4Σ odd + 2Σ even + yₙ)((b−a)/2) Σ wᵢ f(xᵢ)Canonical symbols for this capability. Agent schemas remain the contract.
| Symbol | Quantity | Unit | Role |
|---|---|---|---|
method | Case insensitive; spaces/hyphens normalize to underscores | — | input / output |
integrand | poly / polynomial, sin, exp / e^x | — | input / output |
f | Alias of integrand; supplied aliases must agree | — | input |
a | — | — | input / output |
b | — | — | input / output |
n | — | — | input / output |
coeffs | — | — | input / output |
coefficients | — | — | input |
value | — | — | output |
abs_err | — | — | output |
Inspectable numeric contract for this Capability@Version. Not a rewrite of the engine.
| Field | Declaration |
|---|---|
numeric_domain | real |
exactness | float64 |
algorithm | composite trapezoid / Simpson / Gauss quadrature on a published integrand |
valid_domain | finite decimal [a,b]; sine bounds magnitude at most 1e6; poly degree at most 8, sin, exp; integer panels 2–10000 or Gauss nodes 2–8; decimal aliases must agree |
singularity_policy | Equal bounds return zero; reversed bounds preserve orientation; NUMERICAL_OVERFLOW on nonfinite evaluation or baseline; invalid integrand is coded |
branch_policy | not applicable — real iterate |
tolerance | note: 12 significant digits without an absolute zero floor; exact is a binary64 closed-form baseline; historical abs_err is signed raw quadrature minus baseline, not a certified bound |
convergence | criterion: fixed panels / nodes as published (not adaptive h) |
conditioning | sample overflow/underflow, unresolved nonzero output underflow, and severe quadrature cancellation are rejected; split or rescale; endpoint singularities are out of scope |
rounding | ieee754_round_ties_to_even |
overflow | ieee754_nonfinite_or_coded_error |
reproducibility | deterministic algorithm + Capability@Version |
independent_oracle | cvp:math.numerical.definite_integral O2 / Evidence published cases |
golden_vectors | Evidence golden + boundary + property (and published_reference_case when listed) |
Declared scope for this capability. Do not use it outside this domain.
Assumptions
One numerical check. The calculator page holds worked steps and FAQ.
simpson poly 0,1 on [0,1] → 0.5
CVP VERIFIED · CVP protocol 1.0.0-proposed · Core assurance · all published methods. Computational verification is defined by CVP. Supplemental domain review (internal) and named expert review are defined by the Review policy and do not by themselves determine CVP conformance.
Human page, REST, and MCP share the same engine and calculation_version.
Build verified hashes workspace artifacts only. After deploy, attest:production GETs canonical URLs twice — the public/cached view an Agent actually hits, and origin — including every /capabilities/{id} HTML page. Public Capability HTML version must match catalog before production attestation passes. Live Trust rows above fetch /.well-known/calculatorx-production-attestation.json
and the output schema const. Build hashes: release integrity. That proves currently published page / engine / schema / evidence / MCP agree — not that a historical version is independently immutable. Reference Calculation Standard — Production surface contract 6/6.
curl -sS -X POST 'https://www.calculatorx.com/api/v1/calc/definite-integral' \
-H 'Content-Type: application/json' \
-d '{"inputs":{"method":"simpson","integrand":"poly","coeffs":"0,1","a":0,"b":1,"n":10},"calculation_version":"1.1.5"}'{
"inputs": {
"method": "simpson",
"integrand": "poly",
"coeffs": "0,1",
"a": 0,
"b": 1,
"n": 10
},
"calculation_version": "1.1.5"
}POST /api/v1/calc/definite-integral. This is a POST calculate endpoint — do not GET it.
Full REST contract: REST API docs.
Human-readable sources plus CVP reference evidence classes.
Sources
Reference evidence classes: O1 model · O2 expected_values · O2 numerical_behavior
Inspect, then execute. Same engine as REST and the human calculator.
curl -sS -X POST 'https://www.calculatorx.com/mcp' \
-H 'Content-Type: application/json' \
-H 'MCP-Protocol-Version: 2026-07-28' \
-H 'Mcp-Method: tools/call' \
-H 'Mcp-Name: inspect_capability' \
-d '{"jsonrpc":"2.0","id":1,"method":"tools/call","params":{"name":"inspect_capability","arguments":{"capability_id":"math.numerical.definite_integral"},"_meta":{"io.modelcontextprotocol/protocolVersion":"2026-07-28","io.modelcontextprotocol/clientInfo":{"name":"calculatorx-docs-example","version":"1.0.0"},"io.modelcontextprotocol/clientCapabilities":{}}}}'curl -sS -X POST 'https://www.calculatorx.com/mcp' \
-H 'Content-Type: application/json' \
-H 'MCP-Protocol-Version: 2026-07-28' \
-H 'Mcp-Method: tools/call' \
-H 'Mcp-Name: execute_calculation' \
-d '{"jsonrpc":"2.0","id":2,"method":"tools/call","params":{"name":"execute_calculation","arguments":{"capability_id":"math.numerical.definite_integral","inputs":{"method":"simpson","integrand":"poly","coeffs":"0,1","a":0,"b":1,"n":10},"calculation_version":"1.1.5"},"_meta":{"io.modelcontextprotocol/protocolVersion":"2026-07-28","io.modelcontextprotocol/clientInfo":{"name":"calculatorx-docs-example","version":"1.0.0"},"io.modelcontextprotocol/clientCapabilities":{}}}}'Pin calculation_version (1.1.5) when the result must stay reproducible.
Inspect the trust tier and required assurance level before execution. Full protocol notes: MCP docs.