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 calculus-single-variablegit 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/calculus-single-variable)<a href="https://agentmods.dev/skills/hamzabellouch/agent-skills/calculus-single-variable"><img src="https://agentmods.dev/badge/skills/hamzabellouch/agent-skills/calculus-single-variable/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/calculus-single-variable"><img src="https://agentmods.dev/badge/skills/hamzabellouch/agent-skills/calculus-single-variable.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 | $0.00051 | $0.00768 |
| Opus 5.5 | $0.00020 | $0.00307 |
| Sonnet 5.5 | $0.00010 | $0.00154 |
| Haiku 4.5 | $0.00005 | $0.00077 |
Grade A, and why
calculus-single-variable scanned grade A with 0 findings 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 today.
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.
Nothing flagged
None of the 26 patterns this scan looks for appear in this file: no shell pipes, no recursive deletes, no credential paths, no hidden text, no instruction-override or anti-refusal phrasing, no agent-config snooping. That is not a guarantee, it is the absence of the things that are checkable.
How it starts
The opening of the file, as written. The whole thing — 34 lines — stays where its author put it; the contents beside it link to each section on GitHub.
Single-Variable Calculus
Limits
- Algebraic simplification, conjugates, squeeze theorem; lim sin x / x = 1; lim (1 + 1/n)^n = e; (1 - cos x)/x^2 -> 1/2.
- L'Hopital for 0/0 or inf/inf; rewrite 0*inf, inf - inf, 1^inf, 0^0 via logs.
- Epsilon-delta definition: for all eps > 0 exists delta > 0 with 0 < |x - a| < delta => |f(x) - L| < eps.
- Continuity, IVT, EVT.
Derivatives
- Rules: product, quotient, chain; (x^n)' = n x^(n-1); (e^x)' = e^x; (ln x)' = 1/x; (a^x)' = a^x ln a; (sin)' = cos; (tan)' = sec^2; (arcsin)' = 1/sqrt(1-x^2); (arctan)' = 1/(1+x^2).
- Implicit and logarithmic differentiation; inverse functions (f^{-1})' = 1/f'(f^{-1}).
- Mean value theorem, Rolle; monotonicity and concavity; critical points, second derivative test.
- Optimization: set derivative to zero, check endpoints and nature. Related rates: differentiate the relation in time.
- Linearization f(x) ~ f(a) + f'(a)(x - a); Newton's method x_{n+1} = x_n - f/f'.
Integrals
- FTC: d/dx integral_a^x f = f(x); integral_a^b f = F(b) - F(a).
- Techniques: substitution; integration by parts (LIATE) integral u dv = uv - integral v du; partial fractions; trig substitution (sqrt(a^2 - x^2): x = a sin t; sqrt(x^2 + a^2): x = a tan t; sqrt(x^2 - a^2): x = a sec t); Weierstrass t = tan(x/2); reduction formulas; symmetry of even/odd functions.
- Improper integrals: integral_1^inf x^-p converges iff p > 1; comparison and limit comparison.
- Applications: area, volumes (disk/shell), arc length integral sqrt(1 + f'^2), surface of revolution, average value, work, probability densities.
Sequences & series
- Tests: divergence, geometric, p-series, integral, comparison, limit comparison, ratio, root, alternating series (Leibniz), absolute vs conditional convergence.
- Power series: radius via ratio test; differentiate/integrate termwise within the radius.
- Taylor: e^x = sum x^n/n!; sin x = x - x^3/3! + ...; cos x = 1 - x^2/2! + ...; ln(1 + x) = x - x^2/2 + ...; 1/(1-x) = sum x^n; (1+x)^a binomial series. Remainder (Lagrange) bounds error.
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.
- today First seen · 34 lines · 51 tokens per session scan A 9885f752df58
calculus-single-variable is a skill published in the GitHub repository hamzabellouch/agent-skills (8 stars, last pushed today), licensed MIT. It adds 51 tokens to every session and 768 once invoked, about $0.0002 per session on Opus 5.5. A static security scan graded it A with 0 findings. No closer match exists in the catalogue, so it is treated as the original; first seen 2026-10-17.
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