Update llm_utils.py

llm_utils.py

@@ -39,14 +39,33 @@ def explain_with_llm(solution_text, equation_type, llm_url):
         context = generate_context(theorems, equation_type)
 
         prompt = (
-            f"{context}\n\n"
-            f"---\n\n"
-            f"### User-Solved Steps for a {equation_type} equation:\n\n"
-            f"{solution_text}\n\n"
-            f"### Task:\n"
-            f"Write a detailed but understandable explanation of how the above solution works, "
-            f"referencing the relevant theorems from the context if applicable. Avoid overly technical jargon."
-        )
+    f"You are a mathematical reasoning assistant trained to give clear and insightful explanations.\n"
+    f"You are provided below with a curated database of mathematical theorems.\n"
+    f"Each theorem includes:\n"
+    f"- A name\n"
+    f"- A formal statement\n"
+    f"- Tags (keywords indicating the topics it's related to)\n"
+    f"- A brief note on 'When to Use'\n"
+    f"- A short explanation that sometimes refers to previous theorems\n\n"
+    f"---\n\n"
+    f"### 📘 Theorem Database:\n\n"
+    f"{context}\n\n"
+    f"---\n\n"
+    f"### 🧮 Problem Solving Steps for a {equation_type} Equation:\n\n"
+    f"{solution_text}\n\n"
+    f"---\n\n"
+    f"### 🎯 Task:\n"
+    f"Provide a detailed and understandable explanation of how the above solution works.\n"
+    f"Make sure to:\n"
+    f"- Explain **why** each step is valid.\n"
+    f"- **Cite the relevant theorems** by name and number when appropriate.\n"
+    f"- Maintain a **teaching tone** aimed at a high school or undergraduate student.\n"
+    f"- If multiple theorems apply, mention them and clarify how they connect.\n"
+    f"- Avoid simply repeating the theorems — integrate them meaningfully.\n"
+    f"- Include both **symbolic reasoning** and **conceptual insights**.\n\n"
+    f"End the explanation once the reasoning and result are fully justified."
+)
+
 
         response = requests.post(
             f"{llm_url}/explain",