The bottom line is CPUs** are capable of arithmetic,. A CPU by itself cannot do calculus. They require a great deal of extra programming and hardware support for calculus.
At it's most basic level CPUs are capable of arithmetic, boolean logic and a few other tasks. For more information google logic circuits or truth tables. Start with the simple ones which will be "and", "or" and "xor". Their arithmetic capabilities include multiplication. So CPU's can calculate area. as in 5 * 7 = 35
However, CPUs are not yet capable of word problems such as this one.
A rectangle has a length of 7 inches and a width of 5 inches. Find its area.
This, requires two steps,
Step I. A = L * W
Step II. A = 5 * 7.
Although extremely sophisticated computer software systems may be able figure out the word problem, basic CPU's have no idea how to do step I, Transform the two sentences question into a formula A = L * W.
Nor can a CPU recognize length is 5, and width is 7 to start step 2.
The only part the CPU can do unassisted is 5 * 7 = 35.
Computer algebra systems like the TI calculator series are capable of manipulating variables. They require a good deal of programming and support from other pieces telling the CPU how to do an integral like
Integrate x2 into
A. identify this is a single term polynomial.
B. Figure out that the power rule for integration
C. identify the exponent as 2.
D. Divide by 3 = 2+1
E. write x with a new exponent, x3
F. add +C
Field programmable gate arrays(FPGAs) are an exception which fascinates me. FPGAs are hardware chips which can literally reconfigure themselves for specific tasks. For example, one day they can do play chess problems, then do calculus problems the next day, then the next day assist in calculating graphics for your video game. It can even be custom configured for a task which has not even been invented yet.
I am sure somewhere in this world, a chip manufacturer has a custom designed hardware chip which can do calculus directly, very fast.
**By CPU, it sounds like you mean central processing unit, like those sold by Intel and AMD. They are often thought of as the brains inside a computer. Some people use the term CPU to refer to an entire computer. That meaning does not apply to my answer.
