There are probably very few people, other than math teachers, who routinely solve calculus problems on a daily basis. (Most of the applied fields would use computers, especially since most models would not be amenable to easy hand calculations.)
However, most of us use or rely on the fruits of calculations made possible by the calculus. Finding maximums or minimums (maximize profit, traffic flow, output, or minimize cost, personnel, or material) is useful every day in a large number of fields including economics, social sciences, the hard sciences, business management, and game theory applications.
The foundations of statistics are based on applications of calculus to the area under a probability curve.
We also frequently want to find the rate of change or rate of rate of change of various processes, which use calculus. (How fast does the medicine/ drug leave your system, how is the demand for a product/ service changing over time, etc.)