numerical_integrate

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

No annotations are provided, so the description carries the full behavioral burden. It states the available methods but says nothing about accuracy, convergence, computational cost, invalid inputs, or whether intervals must satisfy method-specific constraints. It also omits any description of the return value despite the absence of an output schema.

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 description is a single, front-loaded sentence that states the operation and method choices with no filler. Every clause earns its place. It is not verbose or poorly structured.

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?

Given a five-parameter numerical tool with no output schema and no annotations, the description is incomplete. It does not explain what the tool returns, how accurate the result is, or how the interval count affects precision. The rich schema covers parameters, but the missing behavioral and output context leaves material gaps.

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 100%, so all five parameters are already documented in the input schema, including defaults for method and intervals. The description only repeats the method options and adds no syntax, format, or constraint details beyond what the schema supplies. The baseline score of 3 applies.

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?

The description names a specific operation (numerical integration), the resource (a math expression), and the available methods (Simpson's rule, trapezoid, midpoint). It is clear enough to distinguish from numerical_diff or ode_solve, though it does not explicitly name those siblings. The purpose is unambiguous.

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?

There is no guidance on when to choose this tool over alternatives like numerical_diff, ode_solve, or root_find. No prerequisites, exclusions, or conditions are stated. Usage is only implied by the word 'integration'.

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