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

No annotations exist, so the description carries the full burden. It usefully discloses the boundary behavior ('0 outside it') and adds payment context ('5 free trial calls per signed wallet'), which is genuinely beyond the schema. It does not, however, state that this is a deterministic, side-effect-free pure computation, nor anything about auth beyond the wallet mention.

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?

The functional sentence is front-loaded and dense with no wasted words; the math semantics ('at x', 'range from a to b', 'or 0 outside it') are packed efficiently. The trailing trial-call promo is extra but brief and arguably relevant context rather than padding.

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 simple pure-math tool with no output schema and no annotations, the description covers the computation and the boundary case adequately. It falls short on input typing/format for the string-typed a/b/x parameters, which is the one thing an agent could plausibly get wrong when calling it.

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 coverage is 0% and the schema gives only three untyped-looking string properties. The description partially compensates by mapping x to the evaluation point and a/b to the range bounds, which is real added meaning. But with all params typed as strings at 0% coverage, nothing clarifies number format, precision, or ordering assumptions.

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 and resource ('Returns the uniform probability density at x for a range from a to b, or 0 outside it'). The word 'uniform' plus the explicit distribution semantics distinguish it from siblings like x402-normal-pdf, x402-exponential-pdf, and x402-geometric-pmf without needing to open the 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?

Usage is implied by the mathematical definition (call it to evaluate a uniform PDF), and the 'or 0 outside it' clause tells the agent what happens for out-of-range x. However, it never names or steers away from the competing PDF/PMF siblings in this large family, so there is no explicit when-to-use-this-vs-alternative guidance.

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