Student's t distribution with df degrees of freedom (> 0). `function` selects the density (pdf), cumulative distribution (cdf) or quantile / inverse-CDF.

Diameter, circumference and area of a circle from its radius.

Creates an image from scratch from a text description. Choose the quality tier with image_generator_version: hd, genius, or super_genius for the highest detail at 2k output. The genius tier also takes an art style in genius_preference: classic, anime, photography, graphic, or cinematic. Returns a link to the generated image.

OpenAI-compatible chat completion, priced by counted input tokens + max output tokens at per-model rates

The n-th Catalan number Cₙ = C(2n, n)/(n+1), counting balanced bracketings, binary trees, and many other structures. Requires n ≤ 10000.

Creates an image from scratch from a text description. Choose the quality tier with image_generator_version: hd, genius, or super_genius for the highest detail at 2k output. The genius tier also takes an art style in genius_preference: classic, anime, photography, graphic, or cinematic. Returns a link to the generated image.

Solve the linear system A·x = b for a square coefficient matrix A and vector b via Gaussian elimination with partial pivoting. A non-square A or a b of the wrong length is a clean 400. A singular system is NOT an error — it returns a successful { solvable:false, solution:null }.

Convert an amount from one currency to another using reference rates (latest or a historical date). Amount defaults to 1.

Creates an image from scratch from a text description. Choose the quality tier with image_generator_version: hd, genius, or super_genius for the highest detail at 2k output. The genius tier also takes an art style in genius_preference: classic, anime, photography, graphic, or cinematic. Returns a link to the generated image.

IP threat intelligence from first-party honeypot observations (not scraped blocklists): was this IP seen scanning, brute-forcing or probing a live honeypot, which traps it triggered (credential stuffing, webshell, exploit scans, scrapers), bot category and confidence. Works for IPv4 and IPv6.

Enriched context for a single match: the teams, venue, status, and surrounding tournament state, addressable by event, event URN, or team and opponent on a date.

Generate one or more lexicographically sortable ULIDs (monotonic within a call).

Generate cryptographically-secure random bytes, returned as hex, base64 or base64url.

TraceFast live Ethereum data: the validator activation and exit queues as of the newest sampled epoch — how many validators wait on each side, how much capital they hold, the churn rates, the trailing 7-day and 30-day averages, recent exit and deposit flow, and the active set's total effective balance. Docs: https://docs.tracefast.xyz/api/consensus-current.md

Creates an image from scratch from a text description. Choose the quality tier with image_generator_version: hd, genius, or super_genius for the highest detail at 2k output. The genius tier also takes an art style in genius_preference: classic, anime, photography, graphic, or cinematic. Returns a link to the generated image.

Generate a secure random password (characters) or a wordlist passphrase.

List every ISO 3166-1 alpha-2 country code for which a postal-code pattern is available.

Break a User-Agent string into browser, engine, operating system (each with a version) and device type. Unidentifiable components are reported as null.

Creates an image from scratch from a text description. Choose the quality tier with image_generator_version: hd, genius, or super_genius for the highest detail at 2k output. The genius tier also takes an art style in genius_preference: classic, anime, photography, graphic, or cinematic. Returns a link to the generated image.

Creates an image from scratch from a text description. Choose the quality tier with image_generator_version: hd, genius, or super_genius for the highest detail at 2k output. The genius tier also takes an art style in genius_preference: classic, anime, photography, graphic, or cinematic. Returns a link to the generated image.