Interpret Repetition!
JavaScript (ES6), 110 bytes

s=&gt;eval((" "+s)[R='replace'](/[^\)](?!\()/g,x=&gt;x+i++%10,i=1)[R](/c| (\ds)+|s\d/g,"")[R](/\d+\/\d+/g,"($&amp;|0)"))


Very simple, but integer division adds 25 bytes. For some reason a regex in JS can't match both the beginning of a string and the first character, so that adds a few bytes as well.

How it works


Prepend a space to the input.
Append the next digit to each character (except )) that isn't immediately before a (.
Remove each c, a digit + s at the beginning (1s2 -> 2), and each s + a digit (3s4 -> 3).
Turn each division operation into int-division (1/2 -> (1/2|0)).
Evaluate and return.