This expression can be simplified as follows:

cos^B + sin^2B * cos^2B + sin^2B

Since sin^2B + cos^2B = 1, we can substitute in this value:

cos^B + 1 * cos^2B + sin^2B

Now, we can factor out a cos^B:

cos^B(1 + cos^2B) + sin^2B

Finally, we can simplify further using the Pythagorean identity sin^2B = 1 - cos^2B:

cos^B(1 + cos^2B) + 1 - cos^2B

Expanding the terms inside the brackets, we get:

cos^B + cos^3B + 1 - cos^2B

Combining like terms, the final simplified expression is:

cos^3B + 1