Each day I would go out to measure the amount of water flowing down rivers in the province. We used water flow meters like the one shown in the figure below. We would go across the river in waders and take measurements. We did about 5 to 10 depending on the width of the river. At each point we would measure the depth and the velocity at that point. After we were done for the day one of us would enter the data into a program to determine the flow. We did this for each river periodically. It was a fantastic job. Especially in the summer. One day the boss found out that I was doing computer science at university and he asked me to write a program to calculate the water flow from the data for their new computer which they had purchased. It had an HP plotter. He also asked me to generate plots of the cross section of the river with the data on it. So I had to figure out how to calculate the flow and how to use the HP plotter language. The point of this article is to explain what I did, that I got it wrong, and how to use Calculus to fix it, and, finally, now that I’ve done a bit of research, how the Geological Survey does this calculation. I am using this example for my teaching. It’s nice. It’s got a bit of everything. I think this is a great problem for an integral calculus class using Maple, or class on numerical methods. One useful tool that I’ve also learned is Maple’s canvas facility which I’ll use for the sketches in this article.