The Bernoulli numbers are among the most interesting and important number sequences in mathematics. They first appeared in the posthumous work "Ars Conjectandi" (1713) by Jacob Bernoulli (1654-1705) in connection with sums of powers of consecutive integers (Bernoulli, 1713; or Smith, 1959). Bernoulli numbers are particularly important in number theory, especially in connection with Fermat's last theorem (Ribenboin, 1979). They also appear in the calculus of finite differences (Norlund, 1924), in combinatorics (Comtet, 1970), and in other fields. Bernoulli polynomials and Bernoulli numbers possess many interesting properties and arise in many areas of mathematics and physics. This paper shows how to derive the sum of the nth powers of positive q-integers up to k-1, and displays the shapes of q-Bernoulli polynomials. (Contains 8 figures and 3 tables.)