Before calculus, land under an irregular shore was measured by laying down strips of known width and adding up their areas. Each brass strip here is one rectangle of a Riemann sum — the estimate is just Σ height × width.
The rule sets where in each strip you read the height. On a rising shore the left rule reads the low near-edge and falls short; the right rule reads high and over-counts; the midpoint rule reads the middle and its over- and under-shoots largely cancel.
Crank more strips and the gap to the truth shrinks — left and right like 1/n, midpoint like 1/n². The dashed-gold line in the ledger is the exact area ∫f, found by Simpson's rule. It is the destination the crank is walking toward — that limit is the definite integral.
Flip the surprise: drag the shore into a downhill and the "always-under" left rule starts to over-count. The sign of the error is not the rule's — it is the shore's.
Something in the simulation stopped unexpectedly — the lesson continues without it. Nothing you did was wrong; you can move on.