Stack

public int evaluate(String expression) {
    return eval(expression, new HashMap<>());
}
private int eval(String exp, Map<String, Integer> parent) {
    if (exp.charAt(0) != '(') {
        // just a number or a symbol
        if (Character.isDigit(exp.charAt(0)) || exp.charAt(0) == '-')
            return Integer.parseInt(exp);
        return parent.get(exp);
    }
    // create a new scope, add add all the previous values to it
    Map<String, Integer> map = new HashMap<>();
    map.putAll(parent);
    List<String> tokens = parse(exp.substring(exp.charAt(1) == 'm' ? 6 : 5, exp.length() - 1));
    if (exp.startsWith("(a")) { // add
        return eval(tokens.get(0), map) + eval(tokens.get(1), map);
    } else if (exp.startsWith("(m")) { // mult
        return eval(tokens.get(0), map) * eval(tokens.get(1), map);
    } else { // let
        for (int i = 0; i < tokens.size() - 2; i += 2)
            map.put(tokens.get(i), eval(tokens.get(i + 1), map));
        return eval(tokens.get(tokens.size() - 1), map);
    }
}
private List<String> parse(String str) {
    // seperate the values between two parentheses
    List<String> res = new ArrayList<>();
    int par = 0;
    StringBuilder sb = new StringBuilder();
    for (char c: str.toCharArray()) {
        if (c == '(') par++;
        if (c == ')') par--;
        if (par == 0 && c == ' ') {
            res.add(new String(sb));
            sb = new StringBuilder();
        } else {
            sb.append(c);
        }
    }
    if (sb.length() > 0) res.add(new String(sb));
    return res;
}