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UK Data: Maths and statistics

calculate_area

Read-onlyIdempotent

Calculates the area of geometric shapes including circle (πr²), triangle (½×base×height), rectangle (length×width), and square (side²). Returns area in square units. (cost: 1 credit)

Input Schema

NameRequiredDescriptionDefault
shapeNostring, required, shape type (circle/triangle/rectangle/square), no unit, no default
measurementsNoobject, required, shape-specific measurements (radius/base/height/length/width/side), appropriate units, no default

Schema Changelog

Changes observed during successful MCP inspections.

  1. First observed

TDQS

A3.9/5.0
Behavior4/5

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

The annotations already establish that this is a read-only, idempotent, non-destructive operation. The description adds useful behavioral detail beyond the annotations by stating the return unit ('square units') and a one-credit cost, though it does not mention precision, rounding, or error behavior.

Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.

Conciseness5/5

Is the description appropriately sized, front-loaded, and free of redundancy?

The description is compact and front-loaded: it names the operation, lists the formulas, states the return unit, and ends with the cost. Every sentence and clause adds useful information with no filler.

Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.

Completeness4/5

Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?

For a simple read-only calculator with full schema coverage and no output schema, the description covers supported cases, formulas, output units, and cost. It leaves only minor gaps around numeric precision, invalid input handling, and measurement formatting.

Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.

Parameters4/5

Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?

Schema coverage is 100%, so the baseline is 3, but the description adds real meaning by mapping each shape to the measurements it expects through the listed formulas. This helps an agent understand what values belong in the generic 'measurements' parameter.

Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.

Purpose4/5

Does the description clearly state what the tool does and how it differs from similar tools?

The description uses a specific verb and resource ('Calculates the area') and enumerates the supported shapes with formulas. It is clear what the tool does, but it does not distinguish itself from sibling geometry tools such as polygon_area_shoelace.

Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.

Usage Guidelines3/5

Does the description explain when to use this tool, when not to, or what alternatives exist?

The supported shape list implies the applicable scope, but there is no explicit when-to-use guidance, no exclusions, and no comparison with alternative area or geometry tools. The agent can infer usage from the formulas but must do the routing itself.

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

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