Initial data commit

Task/Numerical-integration/BASIC/numerical-integration.basic

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+FUNCTION leftRect(a, b, n)
+     h = (b - a) / n
+     sum = 0
+     FOR x = a TO b - h STEP h
+        sum = sum + h * (f(x))
+     NEXT x
+     leftRect = sum
+END FUNCTION
+
+FUNCTION rightRect(a, b, n)
+     h = (b - a) / n
+     sum = 0
+     FOR x = a + h TO b STEP h
+        sum = sum + h * (f(x))
+     NEXT x
+     rightRect = sum
+END FUNCTION
+
+FUNCTION midRect(a, b, n)
+     h = (b - a) / n
+     sum = 0
+     FOR x = a + h / 2 TO b - h / 2 STEP h
+        sum = sum + h * (f(x))
+     NEXT x
+     midRect = sum
+END FUNCTION
+
+FUNCTION trap(a, b, n)
+     h = (b - a) / n
+     sum = f(a) + f(b)
+     FOR i = 1 TO n-1
+        sum = sum + 2 * f((a + i * h))
+     NEXT i
+     trap = h / 2 * sum
+END FUNCTION
+
+FUNCTION simpson(a, b, n)
+     h = (b - a) / n
+     sum1 = 0
+     sum2 = 0
+
+     FOR i = 0 TO n-1
+        sum1 = sum1 + f(a + h * i + h / 2)
+     NEXT i
+
+     FOR i = 1 TO n - 1
+        sum2 = sum2 + f(a + h * i)
+     NEXT i
+
+     simpson = h / 6 * (f(a) + f(b) + 4 * sum1 + 2 * sum2)
+END FUNCTION