Two public demo endpoints on api.nope.net. No API key, no account, nothing to install. They're rate-limited to 10 requests/minute per IP and don't count toward any quota.
Both take either {"text": "..."} or {"messages": [{"role": "user"|"assistant", "content": "..."}]}.
curl -sS -X POST https://api.nope.net/v1/try/evaluate \