1. **State the problem:** Calculate the value of the expression $-37 + 30 + 13$. 2. **Use the formula:** Addition and subtraction of integers follow the rule of combining positive and negative numbers. 3. **Calculate step-by-step:** $$-37 + 30 = -7$$ 4. **Add the remaining number:** $$-7 + 13 = 6$$ 5. **Final answer:** The value of the expression $-37 + 30 + 13$ is $6$.