Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?

Goes well beyond the readOnly/idempotent annotations by disclosing pricing ($0.001 USDC per successful call via x402 on Solana), the HTTPS fallback endpoint, and the precision rule (decimal string past 15 digits). It does not describe error behavior for out-of-range n or response shape beyond the precision note, so not a full 5.

Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.

Is the description appropriately sized, front-loaded, and free of redundancy?

Front-loads the formula and examples before the operational details (range, precision, pricing, endpoint). Dense but each sentence carries information; the range restatement is the only mild redundancy against the schema.

Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.

Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?

For a single-parameter computational tool with no output schema, the description covers the formula, domain, expected outputs, return-format threshold, and payment/auth context. Only the failure mode for invalid n is unstated.

Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.

Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?

Schema description coverage is 0%, so the description must carry the burden; it defines n as the number of terms and anchors it with worked examples (1 term = 1, 2 terms = 10, 4 terms = 84). The 0–1000000 range is merely repeated from the schema, but the meaning of n and the expected scale of output are genuinely added.

Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.

Does the description clearly state what the tool does and how it differs from similar tools?

States a specific verb+resource ('The sum of the first n odd squares') and disambiguates precisely with the closed form n(4n^2-1)/3 plus concrete terms. An agent can distinguish it from neighbors like square_sum or odd_goldbach without inspecting any schema.

Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.

Does the description explain when to use this tool, when not to, or what alternatives exist?

The mathematical definition implies when the tool applies, but there is no explicit when-to-use/when-not guidance and no sibling is named (e.g. square_sum, cube_sum). Domain of n is given, which constrains usage, but alternative selection is left to inference.

Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.