/*  Calculate a natural logarithm using Simpson's Rule  */
/*  ∫ab​ f(x) dx ≈ (b-a)/(3n)[FIRST+4(sum of ODDs) +2(sum of EVENs)+LAST]  */

aTobStrip : 1000$

a : 1$
b : 2$  /*  log(b)  */

funDom : makelist(n, n, a*aTobStrip, b*aTobStrip)$
listSize : length(funDom)$

evenIndex : sublist(makelist(n, n, 1, listSize), evenp)$
oddIndex : sublist(makelist(n, n, 2, listSize - 1), oddp)$

f(x) := 1/x$

funRan : makelist(f(n/aTobStrip),n, funDom)$

firstItem : funRan[1]$
lastItem : funRan[listSize]$

evenItems : makelist(funRan[n]*4, n, evenIndex)$
oddItems : makelist(funRan[n]*2, n, oddIndex)$

rangeSum : firstItem + lsum(n, n, append(evenItems, oddItems)) + lastItem$

answer : (b-a)/3/aTobStrip*rangeSum$

ev(answer, numer);