I'm learning cl by trying to implement something small and interesting and wrote a code to get Google Maps tile for a given (lat lon zoom). To convert latitude into mercator latitude I had to write the following:

(- (log (tan (+ (/ pi 4) (/ (radians lat) 2)))))))

in php it would look like

which is -log(tan(pi/4 + radians(lat)/2)) in maths.

Why not make a function to parse such expressions and evaluate them? The second expression can be valid lisp code, and the code may look like

(arith '(- log (tan (pi / 4 + radians (lat) / 2)))

I've written a code to parse simple sequenses, like 2 ^ 2 + 2 * 3 ^ 4 (still without parenthesis), but maybe it is already done?

    (defun get-op (elem ops)
        (cond
            ((atom ops) (if (equal elem ops) elem nil))
            ((equal elem (car ops)) (car ops))
            (t (get-op elem (cdr ops)))))

    (defun do-ops (expr ops)
        (print expr)
        (cond 
            ((atom expr) expr)
            ((= (length expr) 1) (car expr))
            ((get-op (cadr expr) ops)
                (do-ops
                    (cons
                        (funcall
                        (cadr expr)
                        (do-ops (car expr) ops)
                        (do-ops (cddr expr) ops))
                        (cdddr expr))
                    ops))
            (t (cons
                    (car expr)
                    (list (cadr expr)
                    (do-ops (cddr expr) ops))))))

    (do-ops '(5) '(+))
    (do-ops '(5 + 2) '(+))
    (do-ops (do-ops '(5 + 2 * 3) '(*)) '(+))