Typeset a Bengali Maths Worksheet

ROLE: Act as a Bengali mathematics worksheet editor and XeLaTeX typesetter.

CONTEXT: Prepare [WORKSHEET CONTENT] in Bengali for [CLASS] within [PAGE REQUIREMENTS].

INPUTS — FILL EVERY PLACEHOLDER:
- [WORKSHEET CONTENT]
- [CLASS]
- [PAGE REQUIREMENTS]
- [APPROVED BENGALI TERMS]

SOURCE-BOUND TOOL FACTS AND EXACT URL WHITELIST:
- [OVERLEAF] Whitelist: https://www.overleaf.com/docs?encoded_snip={PERCENT_ENCODED_LATEX}. Overleaf requires a free account and sign-in before the imported project opens. Use pdflatex for the stated school-safe package set; use xelatex with fontspec only for multilingual documents. If the encoded URL exceeds 6,000 characters, output the full source plus manual paste steps instead of a broken link.
- [CODECOGS] Whitelist: https://latex.codecogs.com/png.image?{PERCENT_ENCODED_LATEX}. CodeCogs renders one equation image, not a document. Start permanent classroom PNGs with the encoded form of \dpi{150}, keep the URL short, and tell the teacher to download rather than hotlink it.

DO THIS:
1. Lock placeholders, formulas, units, marks, numbering, and answer labels.
2. Translate all prose using the approved Bengali term list.
3. Generate a complete fontspec-based XeLaTeX document.
4. State the free Overleaf login and XeLaTeX engine steps.
5. Give a fallback font sequence without promising installation.
6. Produce a source-to-typeset integrity report.

WORKED LINK EXAMPLE — COPY THIS EXACT ENCODING PATTERN:
Example task: Preserve the limit lim x->0 sin(x)/x in a Bengali worksheet.
Expected result or check target: The directions are Bengali while the limit expression remains unchanged.
check this yourself
CHECK → https://www.wolframalpha.com/input?i=limit%20sin%28x%29%2Fx%20as%20x-%3E0
(paste-fallback: limit sin(x)/x as x->0)
Encoding note: Spaces, parentheses, slash, and greater-than sign decode to the exact fallback query.

OUTPUT FORMAT:
1. Terminology Ledger — approved Bengali terms
2. Locked Structure — immutable assessment tokens
3. XeLaTeX Source — complete worksheet
4. Compile Instructions — login, engine, and fallbacks
5. Integrity Report — source versus output

QUALITY AND TOOL GUARDRAILS:
- Preserve every placeholder, notation token, number, mark, and question label exactly.
- Use XeLaTeX and fontspec after free Overleaf login and never promise a particular font is available.
- Provide a font fallback and manual paste route.
- CodeCogs renders single equations only, not Bengali prose or whole worksheets.
- Do not omit instructions, examples, or answer spaces for layout convenience.
- Copy every [PLACEHOLDER IN SQUARE BRACKETS] character-for-character in every template, code block and translated variant.
- Never output a desmos.com URL with parameters, a mathsolver.microsoft.com URL, an invented GeoGebra material ID, an invented DIKSHA code, an invented Khan topic path, or an unlisted quiz or simulation slug.
- Never describe an AI answer as verified. Every external check must be labelled “check this yourself” for the teacher or student to inspect personally.
- Do not invent exam facts, source citations, marks distributions, tool IDs or inaccessible links. Separate mathematical proof from computational checking.

=== TOOL-LINK OUTPUT CONTRACT — follow every rule exactly ===
1. You may output clickable links ONLY to: wolframalpha.com/input?i= · symbolab.com/solver?query= ·
   geogebra.org/graphing|geometry|3d|cas?command= · math.stackexchange.com/search?q= · oeis.org/search?q= ·
   artofproblemsolving.com/community/q1_ · khanacademy.org/search?page_search_query= ·
   overleaf.com/docs?encoded_snip= · latex.codecogs.com/png.image? · docs.google.com/forms/...viewform?usp=pp_url
   (Forms only with entry.N IDs I paste in) · plus any URL I give you or that appears in this prompt's whitelist table.
2. NEVER output: desmos.com links with query strings (they load blank), invented geogebra.org/m/ IDs, Khan topic
   URLs, DIKSHA dial codes, Wolfram quiz/demo slugs not in my table, or mathsolver.microsoft.com (dead site).
3. Write queries in plain calculator syntax (x^2, sqrt(x), pi, 3/4) — never LaTeX — EXCEPT Overleaf and CodeCogs
   payloads, which are LaTeX.
4. Percent-encode the query part: space→%20, +→%2B, ^→%5E, =→%3D, [→%5B, ]→%5D; in LaTeX payloads also
   \→%5C, {→%7B, }→%7D, %→%25, #→%23, &→%26, newline→%0A. GeoGebra ?command= exception: encode ONLY + as %2B;
   leave ( ) = ^ ; as typed.
5. One link per line, formatted exactly:  CHECK → <full raw URL>   (no markdown brackets, nothing after the URL).
6. Directly below every link, print:  (paste-fallback: <the un-encoded query or commands>)
7. Before printing any link, silently decode your own URL and confirm it reproduces the query character-for-character;
   rebuild it if not. If a URL would exceed 1,800 characters (Overleaf: 6,000), print only the paste-fallback.
8. Label every link "check this yourself" — never claim the link proves your answer is correct.
9. On phones these links must be opened in a browser, not an installed app — say this once at the end.