Majority of the integers from 1 to 100 can be evaluated using three 4's, +, -, *, /, ^, sqrt, decimal point, dot above a number, and !,!!,...? (both as factorials, multifactorials and subfactorials).
Clearly, both concatenation and brackets are allowed.
Let's try to minimize the set of "not achievable" numbers.
Team work to include all possible answers is encouraged.
(In reply to computer solutions (spoilers)
53=44+?4 or you have a better one
Now in a hurry, will add my comments later to-day.