{"uid":"cap_-OWKVqFlT7hOpctlTaL5v","slug":"numora-calculus-integral-api-cc83c467","name":"Numora Calculus Integral API","description":"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.","url":"https://numormo.vercel.app/api/calculus/integral","method":"POST","headers":{},"bodySchema":{"type":"object","required":["a","b","fn"],"properties":{"a":{"type":"number"},"b":{"type":"number"},"fn":{"type":"string"},"method":{"enum":["simpson","trapezoid","gauss"],"type":"string"}}},"responseSchema":{"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"}}},"example":null,"exampleRequest":null,"tags":["x402"],"displayCostAmount":"0.1","displayCostAsset":"USDC","priceDynamic":false,"priceHint":null,"priceStatus":"priced","priceSource":"registry","requiresHandshake":false,"reviewCount":0,"rating":{"score":"0.00","successRate":"0.00","reviews":0,"stars":null,"state":"unrated"},"availabilityStatus":"unknown","priceObserved":null,"sessionDeposit":null,"pricing":{"kind":"static","summary":"$0.1/call","primary":{"kind":"static","protocol":"x402","network":"base","amountUsd":"0.1","per":"call","confidence":"exact"},"accepted":[{"kind":"static","protocol":"x402","network":"base","amountUsd":"0.1","per":"call","confidence":"exact"}]},"paymentMethods":[{"uid":"pm_0u6SRiT4qfgayUaxd9Jrb","protocol":"x402","methodType":"crypto","chain":"base","mode":"charge","costAmount":"0.1","costPer":"request","priority":0,"asset":null,"unit":"request","depositMicros":null,"planRef":null}],"brandName":null,"brandSlug":null,"brandBaseUrl":null,"brandDocsUrl":null,"whatItDoes":"Numerically integrates a mathematical function over a specified interval using Simpson's, trapezoid, or Gauss quadrature methods","exampleAgentPrompt":"Can you numerically integrate the function x^2 + 3*x from a=0 to b=5 using Simpson's method?","exampleUseCases":[{"title":"Physics simulation area under curve","prompt":"I need the definite integral of sin(x) from 0 to 3.14159 — use the Gauss method to evaluate it."},{"title":"Financial curve area calculation","prompt":"Calculate the integral of 0.05*e^(0.03*x) from x=0 to x=10 using the trapezoid method — I'm modeling a continuously compounding growth curve."},{"title":"Engineering load distribution integral","prompt":"Can you integrate the function 4*x^3 - 2*x + 7 from a=1 to b=8 using Simpson's rule so I can find the total load over that range?"}],"resultDescription":"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.","failureModes":["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"],"whenToPreferThis":"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.","instructions":null,"reviewSummary":null,"reviewSummaryHighlights":null,"reviewSummaryConcerns":null,"reviewSummaryGeneratedAt":null,"activationCount":0,"lastUsedAt":null,"lastSuccessfullyRanAt":null,"lastHealthCheckAt":"2026-09-15T00:51:10.892Z","isFirstParty":false}