Scientific Calculator

Numerical Integral Calculator

calculator_numerical_integral

Read-only

Numerical definite integral via trapezoidal or Simpson's rule.

Tool call template

Replace each placeholder with a value matching the input schema. Only required parameters are included; add optional parameters as needed.

{
  "id": 1,
  "jsonrpc": "2.0",
  "method": "tools/call",
  "params": {
    "arguments": {
      "expression": "<expression>",
      "lower": "<lower>",
      "upper": "<upper>"
    },
    "name": "calculator_numerical_integral"
  }
}

Input Schema

Name	Required	Description	Default
`lower`	Yes	Lower limit.
`upper`	Yes	Upper limit.
`method`	No	trapezoidal or simpson (default).	simpson
`variable`	No	Variable (default x).	x
`expression`	Yes	Integrand.
`n_intervals`	No	Number of intervals (default 1000).

Output Schema

Name	Required	Description	Default
`method`	No
`result`	Yes
`expression`	Yes

Schema Changelog

Changes observed during successful MCP inspections.

First observedOct 23, 2026

TDQS

B3.2/5.0

Behavior3/5

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

Annotations already declare readOnlyHint, destructiveHint=false and openWorldHint=false, so the safety profile is covered. The description adds only the algorithmic families, with no notes on accuracy, interval count effects, or handling of singular integrands.

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

Conciseness4/5

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

One short, waste-free sentence that front-loads the core purpose. It is terse to the point of omitting useful method-choice guidance, but nothing in it is filler.

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

Completeness3/5

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

An output schema exists so return values need no explanation, and all parameters are documented in the schema. For a 6-parameter numeric tool, however, the description omits method tradeoffs and precision considerations that would help an agent call it well.

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

Parameters3/5

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

Schema description coverage is 100%, so the baseline is 3. The description contributes nothing beyond the schema on expression syntax, variable semantics, or how n_intervals interacts with the chosen method.

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?

States a specific verb+resource ('numerical definite integral') and names the two supported rules, so it is distinguishable from the symbolic calculator_integral sibling. It does not explicitly point at that sibling, so it stops short of a 5.

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

Usage Guidelines2/5

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

There is no when-to-use, when-not-to-use, or prerequisites statement. The description never says to prefer this over calculator_integral for definite numeric results, nor when to pick trapezoidal vs Simpson's rule.

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

All Scientific Calculator tools Inspect

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