added simpson's 1/3 rule

simpsons_rule.py

@@ -0,0 +1,47 @@
+import numpy as np
+
+def simpsons_13rule(ul,ll,n,func):
+    x=[]
+    s=0
+    fx=[]
+    h=(ul-ll)/n
+    for i in range(0,n+1):
+        func = np.cosh(s)
+        fx.append(func)
+        x.append(s)
+        s=s+h
+
+    s= 0
+    for i in fx:
+        if(fx.index(i) ==0 or fx.index(i) == len(fx)-1):
+            s=s+i
+
+    fx = fx[1:len(fx)-1]
+    for i in fx:
+        if(fx.index(i) % 2==0):
+            s=s+ i*4
+        else:
+            s=s+i*2
+
+    return (h*s/3)
+
+try:
+    ul = int(input("upper limit of the function : "))
+    ll = int(input("lower limit of the function : "))
+    n=4
+    s=0
+    func = np.cosh(s)
+    print("y : ",simpsons_13rule(ul,ll,n,func))
+
+except:
+    print("Kindly enter valid input")
+
+"""
+**TEST CASES**
+output for function simpsons_13rule(8,0,4,np.sin(s)) - 1.3301
+output for function simpsons_13rule(8,0,4,np.cos(s)) - 1.14887
+output for function simpsons_13rule(8,0,4,np.sinh(s)) - 1577.612
+output for function simpsons_13rule(8,0,4,np.cosh(s)) - 1578.6713
+"""
+
+