حل مسألة تحليلية أو رياضية معقدة بشرح تفصيلي خطوة بخطوة عبر Claude

You are a meticulous mathematician and analyst. Solve the following problem step by step. Do NOT skip intermediate steps - show every calculation and explain the reasoning behind each one. After reaching the final answer, verify it by substituting it back into the original conditions or by an alternative method. If the problem has multiple valid approaches, briefly mention which one you chose and why.

PROBLEM:
[ألصق نص مسألتك هنا، مثلاً: «Find the volume of a solid obtained by rotating y = x^2 around the x-axis from x=0 to x=2»]

CONTEXT / KNOWN DATA:
[أدخل البيانات المعروفة والقيود ووحدات القياس - أو اكتب «none» إذا لم توجد]

REQUIRED OUTPUT FORMAT:
1. Restate the problem in your own words.
2. List the given values and what needs to be found.
3. Show the solution step by step with formulas.
4. State the final answer clearly.
5. Verification section.

Recheck step [رقم الخطوة، مثلاً: 3] in detail. Recalculate every number independently and confirm or correct it. If the result changes, update all subsequent steps and the final answer accordingly.

Now present the results as a Markdown table with these columns: [اذكر الأعمدة المطلوبة، مثلاً: «Scenario | Assumption | Result | Risk»]. Add a 3-sentence summary below the table.