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

No annotations are provided, so the description carries the full burden of behavioral disclosure. It says one probe returns f(x), but it does not state whether probes are limited, whether calls have side effects, what output format to expect, or what errors may occur when x is outside the domain.

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 definition is a single front-loaded sentence with no extraneous steps. The phrase "black box of a black-box puzzle" is slightly redundant, but the description remains efficient.

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 two-parameter tool with full schema coverage, the description is minimally adequate. However, with no annotations and no output schema, it could do more to explain expected return values and probe limitations.

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 100%, so both parameters are already documented in the schema. The description reinforces that x must be a whole number in the domain stated in the question, but it does not add further meaning for id or clarify domain boundaries beyond the schema.

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 states a specific action: evaluating a black-box function f(x) for a given puzzle input. It clearly distinguishes the operation from puzzle metadata and answer submission, though it does not explicitly name sibling alternatives.

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: this tool is for probing the puzzle function with a whole number in the stated domain. There is no explicit when-to-use versus when-to-use-alternatives guidance, such as when to call probe instead of puzzle_get or puzzle_data.

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