Getting it into your agent
One page per mod, every tool's command on it. A separate URL per tool would split the same page into five that compete with each other.
npx skills add hamzabellouch/agent-skills --skill multivariable-calculusgit clone --depth 1 https://github.com/hamzabellouch/agent-skillsWrote this? Show the measurements
A badge with what this costs and how it scanned, read live from this page, so it follows the numbers instead of freezing them. Markdown for a README, HTML for a documentation site or a project page.
[](https://agentmods.dev/skills/hamzabellouch/agent-skills/multivariable-calculus)<a href="https://agentmods.dev/skills/hamzabellouch/agent-skills/multivariable-calculus"><img src="https://agentmods.dev/badge/skills/hamzabellouch/agent-skills/multivariable-calculus/github.svg" alt="Measured on agentmods" height="20"></a>Or the 80×15 button, for a site that already has a row of RSS and ATOM ones. Only the verdict fits; the numbers stay here.
<a href="https://agentmods.dev/skills/hamzabellouch/agent-skills/multivariable-calculus"><img src="https://agentmods.dev/badge/skills/hamzabellouch/agent-skills/multivariable-calculus.svg" alt="Reviewed on agentmods" width="80" height="20"></a>What it costs to keep this loaded
Counted locally with the o200k_base tokenizer, which is exact for GPT models; Claude uses its own tokenizer and its counts differ. Treat this as one consistent yardstick across the catalogue rather than a bill. Prices are per million input tokens.
| Model | Per session | Once invoked |
|---|---|---|
| Fable 5.1 | $0.00027 | $0.00272 |
| Opus 5.5 | $0.00011 | $0.00109 |
| Sonnet 5.5 | $0.00005 | $0.00054 |
| Haiku 4.5 | $0.00003 | $0.00027 |
Grade A, and why
multivariable-calculus scanned grade A with 1 finding against 26 rules in 11 categories — prompt injection, anti-refusal, data exfiltration, privilege escalation, supply chain, agent snooping, system-prompt leakage, SSRF and excessive agency — measured 7d ago.
A static scan of the body, not an audit. Every finding is printed with the line that produced it so you can judge whether it matters here. A mod is markdown that instructs an agent; that is exactly why what it instructs is worth reading.
Makes network callslowCapability
Not a fault in itself. Listed so you know the mod talks to something, and to what.
- Divergence, curl, Laplacian What it actually says
Multivariable Calculus
Domain
Calculus in ℝⁿ.
Core Concepts
- Partial derivatives, gradients, directional derivatives
- Multiple integrals (double, triple)
- Line and surface integrals
- Divergence, curl, Laplacian
- Jacobian and change of variables
Key Methods
- Lagrange multipliers for constrained extrema
- Green's, Stokes', and Divergence theorems
- Polar/spherical/cylindrical coordinates
- Hessian for second-order tests
Canonical Examples
- ∇f for f(x,y)=x²y → (2xy, x²).
- ∬_D (x²+y²) dA over unit disk = π/2.
- Stokes: ∮ F·dr = ∬ (∇×F)·dS.
Common Pitfalls
- Forgetting the Jacobian in substitutions
- Confusing divergence (scalar) with curl (vector)
- Boundary orientation errors in Stokes/Green
Related Skills
Linear Algebra, PDEs, Differential Geometry
What ships with it
1 file beside SKILL.md in the same directory: the scripts, references and assets a skill reads on demand. Not counted in the per-session cost; read them before you install if any of them is executable.
What this file has done since we first saw it
Hashed on every crawl. A supply-chain change to an agent config is a question of when, not whether, so the history is kept rather than the latest state alone.
- 7d ago First seen · 38 lines · 27 tokens per session scan A 25aa5c433395
multivariable-calculus is a skill published in the GitHub repository hamzabellouch/agent-skills (8 stars, last pushed today), licensed MIT. It adds 27 tokens to every session and 272 once invoked, about $0.0001 per session on Opus 5.5. A static security scan graded it A with 1 finding (makes network calls). No closer match exists in the catalogue, so it is treated as the original; first seen 2026-10-10.
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