SageMath MCP Server

Integrate Expression

integrate_expression

Idempotent

Compute indefinite or definite integrals of mathematical expressions with respect to a specified variable. Provide bounds for definite integration; supports infinity and symbolic limits.

Instructions

Integrate an expression (indefinite or definite with bounds)

Input Schema

TableJSON Schema

Name	Required	Description	Default
`session`	No	Workspace to use, as a name or a portable handle. Workspaces have independent variables. A name is scoped to this MCP session; a handle returned by start_sage_session (workspace_token) reaches the same workspace across reconnects and is a bearer credential -- keep it secret. Omit for 'default'.	default
`variable`	No	Integration variable	x
`expression`	Yes	Expression to integrate
`lower_bound`	No	Lower bound for definite integral (e.g., '0', '-oo')
`upper_bound`	No	Upper bound for definite integral (e.g., '1', 'oo')

Output Schema

TableJSON Schema

Name	Required	Description	Default
No arguments

Schema Changelog

Changes observed during successful MCP inspections.

Changed1 schema field changedv0.7.0Sep 12, 2026

changedInput schema / properties / session / description

Previous value: -"Named workspace to use. Workspaces have independent variables; omit for 'default'."New value: +"Workspace to use, as a name or a portable handle. Workspaces have independent variables. A name is scoped to this MCP session; a handle returned by start_sage_session (workspace_token) reaches the same workspace across reconnects and is a bearer credential -- keep it secret. Omit for 'default'."

Changed1 schema field changedv0.5.0Aug 14, 2026

addedInput schema / properties / session

Added value: +{
+  "default": "default",
+  "description": "Named workspace to use. Workspaces have independent variables; omit for 'default'.",
+  "type": "string"
+}

First observedv0.3.1Jul 31, 2026

TDQS

A3.8/5.0

Behavior3/5

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

Annotations already convey idempotency and non-destructiveness, and the description adds the useful distinction between indefinite and definite integration. However, it does not disclose subtler behavior such as how malformed bounds or mismatched variable references are handled; descriptions here do not contradict 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.

Conciseness5/5

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

The description is a single, front-loaded sentence with no filler. It communicates the operation and the key mode distinction (indefinite vs definite) in minimal space.

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?

Given the rich input schema, output schema, and annotations, the description is sufficient for an agent to select and invoke the tool. The only minor gap is that it does not explicitly state that both lower_bound and upper_bound are needed for a definite integral, but 'with bounds' reasonably implies this.

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%, and every parameter (session, variable, expression, lower_bound, upper_bound) is fully documented in the schema. The tool description itself adds no parameter-specific meaning beyond the schema, so the baseline of 3 applies.

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

Purpose5/5

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

The description uses a specific verb ('Integrate') and resource ('an expression'), and immediately clarifies the two modes: indefinite or definite with bounds. This clearly separates it from siblings like differentiate_expression, calculate_expression, and symbolic_sum by naming the core operation.

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?

Usage context is implied rather than stated: an agent can infer this tool is for integration from the name and description, but there is no explicit guidance on when to prefer it over related siblings such as differentiate_expression or calculate_expression. No exclusions or alternative routing are provided.

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