SageMath MCP Server

integrate_expression

Idempotent

Compute symbolic indefinite or definite integrals of expressions, with optional variable and lower/upper bounds.

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

C2.9/5.0

Behavior2/5

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

Annotations already declare idempotentHint=true and destructiveHint=false, so safety is partly covered, but readOnlyHint=false is unusual for a compute operation and the description does nothing to clarify it. The description omits session-state effects and the fact that workspace variables persist, which the schema mentions but the description ignores.

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?

A single front-loaded sentence with no wasted words, and the indefinite/definite distinction is front-loaded. It is arguably under-specified for a tool with session and bound semantics rather than over-long.

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 not be explained, and the required/optional parameter split is clear from the schema. However, for a symbolic-computation tool with session reuse and bound handling, the description is minimally complete and omits behavioral context an agent would want.

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 (expression, variable, bounds, session) is documented there. The description adds no syntax, format, or default-value meaning beyond the schema, so baseline 3 applies.

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 (integrate) and resource (expression) and even distinguishes the two operating modes (indefinite vs definite with bounds). It does not name or contrast any sibling tool explicitly, so it stops short of the top score.

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?

The parenthetical hints at indefinite vs definite modes but gives no guidance on when to choose this over alternatives like symbolic_sum, limit_expression, or evaluate_sage. No prerequisites, no when-not-to-use conditions.

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