verify_integral

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

No annotations are provided, so the description must carry the full burden. It mentions the method (differentiating the result) but the return type is only described as 'Verification result' – vague. It does not state whether it returns a boolean, how symbolic equivalence is checked, or potential failure modes. With no annotations, this is a significant gap.

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 structured docstring with clear sections (Args, Returns, Examples). It front-loads the purpose in the first line and avoids unnecessary verbosity.

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?

The tool is simple with only three parameters, and the description covers the purpose, example usage, and parameter semantics. An output schema exists, so return details are not required. However, it could be slightly more explicit about the output type, despite the example implying a boolean.

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?

The description includes an Args section that describes each parameter: integrand, claimed_integral, and variable with its default. Since the schema provides only titles and no descriptions, this compensates completely, giving clear semantics for all parameters.

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?

Description clearly states 'Verify an integral by differentiating the result', which is a specific verb+resource. The example ('x**2' -> 'x**3/3' -> True) reinforces this. It also differentiates from related tools like verify_derivative by explicitly mentioning integration and differentiation.

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?

No explicit guidance on when to use this tool versus alternatives like verify_derivative or verify_equality. The description provides an example but no context about typical use cases, exclusions, or prerequisites.

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