Abstract: Koksma's inequality for the unit interval gives, for a finite list of N points, an estimate on the difference between the average of a sufficient nice function on those N points versus its integral on the unit interval. The bound is given in terms of the discrepancy of the sequence and the total variation of the function. In this talk, we will explore a new non-archimedean analogue of Koksma's inequality for the complex p-adic unit disc, and compare this to previously known non-archimedean analogues for finite extensions of the p-adic numbers. (Joint work with G. Hubbard.)