Update app.py

app.py

@@ -7,16 +7,68 @@ from tools.final_answer import FinalAnswerTool
 
 from Gradio_UI import GradioUI
 
+import math
+import random
+from typing import Literal
+
 # Below is an example of a tool that does nothing. Amaze us with your creativity !
+import math
+import random
+from typing import Literal
+from your_agent_framework import tool  # adjust import to your AI agent framework
+
+
 @tool
-def my_custom_tool(arg1:str, arg2:int)-> str: #it's import to specify the return type
-    #Keep this format for the description / args / args description but feel free to modify the tool
-    """A tool that does nothing yet 
+def get_approximate_integral(
+    expr: str,
+    a: float,
+    b: float,
+    method: Literal["auto", "simpson", "montecarlo"] = "auto",
+    samples: int = 1000
+) -> str:
+    """Approximate the definite integral of a function over [a, b].
+    
     Args:
-        arg1: the first argument
-        arg2: the second argument
+        expr: A Python expression in variable `x`, e.g. "math.sin(x) + x**2".
+        a: Lower limit of integration.
+        b: Upper limit of integration.
+        method: Which algorithm to use:  
+            - "simpson": composite Simpson’s rule  
+            - "montecarlo": randomized Monte Carlo  
+            - "auto" (default): picks Simpson for smoothness, Monte Carlo otherwise.
+        samples: Number of panels (for Simpson) or random points (for Monte Carlo).
     """
-    return "What magic will you build ?"
+    # Safely compile the expression
+    code = compile(expr, "<string>", "eval")
+    def f(x):
+        return eval(code, {"__builtins__": {}}, {"x": x, "math": math})
+
+    # Auto‑choose method by sampling curvature
+    if method == "auto":
+        mid = (a + b) / 2
+        # estimate curvature via second finite difference
+        f0, f1, f2 = f(a), f(mid), f(b)
+        curvature = abs((f0 - 2*f1 + f2) / ((b - a)/2)**2)
+        method = "montecarlo" if curvature > 1e3 else "simpson"
+
+    if method == "simpson":
+        n = samples if samples % 2 == 0 else samples + 1
+        h = (b - a) / n
+        total = f(a) + f(b)
+        for i in range(1, n):
+            weight = 4 if i % 2 else 2
+            total += weight * f(a + i * h)
+        result = total * h / 3
+        return f'{{"value": {result}, "method": "simpson", "panels": {n}}}'
+
+    # Monte Carlo fallback
+    inside = 0.0
+    for _ in range(samples):
+        x = random.uniform(a, b)
+        inside += f(x)
+    result = (b - a) * inside / samples
+    return f'{{"value": {result}, "method": "montecarlo", "samples": {samples}}}'
+
 
 @tool
 def get_current_time_in_timezone(timezone: str) -> str: