The math::calculus::newtonraphson module takes an algebraic expression, parses it and then uses the newton raphson method to solve it. the newton raphson method relies on the fact that the expression you pass in evaluates to zero where there is a solution. that is, to solve:-

x^2 = 5

you would need to pass in:-

x^2 - 5

it understands expressions containing any of the operators +, -, *, / and ^ (raise to power), bracketed expressions to enable correct precedence and the functions ln, exp, sin, cos, tan, sec, cosec, cot, sinh, cosh, tanh, sech, cosech, coth, asin, acos, atan, asinh, acosh and atanh.