qZEILBERGER, A Maple package, that implements the new-improved (and simplified) q-Zeilberger algorithm for single-sum definite hypergeometric summation. It does what qzeil does in qEKHAD, and what is done in Axel Riese’s Mathematica package qZeil. The article ”Sharp upper bounds for the orders of the recurrences output by the Zeilberger and q-Zeilberger algorithms” is accompanied by Maple packages ZEILBERGER and qZEILBERGER that implement the simplified Zeilberger and q-Zeilberger Algorithms, described in the article.