Newton vs SHARE

Newton is a keyless calculator API deployed as a Vercel serverless function: the operation (simplify, factor, derive, integrate, and more) and expression are both encoded directly in the URL path, and it answers with a small JSON object containing the result. It's a solo open-source project (aunyks/newton-api) rather than a commercial service, so there's no pricing tier or rate limit to opt into.

SHARE (now internally rebranded "trove", version 26.0.0 as of this check) is the Center for Open Science's free aggregator of metadata about research and scholarly activity, pulling in tens of millions of records from sources like CrossRef and OSF and re-indexing them for keyless search. Its v2 API exposes an Elasticsearch-backed search endpoint plus RSS and Atom feeds, all reachable with no registration.