Write a Prolog relation eval$($E$,$V$)$ that evaluates integer arithmetic expressions consisting of integer constants and operators $+,-,*,/,^$ to a constant value. The first argument E is an arbitrary arithmetic expression, and the second argument V is the single integer value resulting from evaluating the entire expression E$.$ Some tests to get started:

$?-$ eval$(5-6*18/3+2,$ Y$).$

Y $=-29$

$?-$ eval$(10*20-9/3+20,$ Y$).$

Y $=217$

$?-$ eval$(10^3*9-1,$ Y$).$

Y $=8999$

Write a Prolog relation simplify$($E$,$S$)$ that simplifies polynomial arithmetic expressions involving constants, variables $($which are Prolog atoms that start with a lowercase letter$),$ and operators $+,-,*,/,^.$ The first argument E is a polynomial arithmetic expression, and the second argument is the simplified expression, which must be expressed in canonical form $($for example, $2*$x$^2+4$x$-3).$ Handle multiplying, dividing by $0$ or $1,$ adding or subtracting $0,$ x$/$x$=1,$ x$-$x$=0,$ x$^0,$ x$^1.$

Some tests to get started: