calculus

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

Annotations already indicate the tool is read-only, idempotent, and non-destructive. The description adds the crucial behavioral detail that all operations are symbolic, which affects user expectations about output type and computational nature. It also clarifies operation-specific parameter requirements, going beyond the annotations.

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 extremely concise, consisting of two sentences that front-load the core functionality. Every sentence adds value, and the parameter guidance is embedded naturally without waste. It achieves high information density without becoming bulky.

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 the tool's complexity (9 parameters, 4 operations) and the presence of an output schema, the description covers the most critical usage aspects: which parameters are needed for each operation and what `order` means. It does not mention `direction` or `precision`, but those are less critical and have schema defaults/enums. Overall, it is sufficient for an agent to invoke the tool correctly for typical calculus tasks.

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 compensate. It explains `order` (derivative order vs series terms), and implicitly clarifies `lower_bound`/`upper_bound` for definite integrals and `point` for limits/series. It does not explain `direction` (for one-sided limits) or `precision`, but the main non-obvious parameters are handled well given the tool's complexity.

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 clearly states the tool's purpose: it performs symbolic differentiation, integration, limits, and series expansion. The verb 'Differentiate, integrate, take a limit, or expand a series' is specific and distinguishes it from sibling tools like calculate or solve. The scope is precisely defined and not a tautology.

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 description gives concrete usage instructions: for definite integrals provide bounds, for limits/series provide a point, and `order` has operation-specific meaning. This helps the agent invoke it correctly. It does not explicitly exclude alternatives (e.g., numeric vs symbolic) but the context is clear enough for a specialized calculus tool.

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