: (shuntingYard "3 + 4 * 2 / (1 - 5) \^ 2 \^ 3")
Token  Output                        Stack
3      3
+      3                             +
4      3 4                           +
*      3 4                           *+
2      3 4 2                         *+
/      3 4 2 *                       /+
(      3 4 2 *                       (/+
1      3 4 2 * 1                     (/+
-      3 4 2 * 1                     -(/+
5      3 4 2 * 1 5                   -(/+
)      3 4 2 * 1 5 -                 /+
^      3 4 2 * 1 5 -                 ^/+
2      3 4 2 * 1 5 - 2               ^/+
^      3 4 2 * 1 5 - 2               ^^/+
3      3 4 2 * 1 5 - 2 3             ^^/+
       3 4 2 * 1 5 - 2 3 ^           ^/+
       3 4 2 * 1 5 - 2 3 ^ ^         /+
       3 4 2 * 1 5 - 2 3 ^ ^ /       +
       3 4 2 * 1 5 - 2 3 ^ ^ / +
-> (3 4 2 "*" 1 5 "-" 2 3 "\^" "\^" "/" "+")