I have googled extensively and have not come up with a single mention of a fixed English term of Kepler's Fassregel. The above is a translation of the Latin title of his rule: Nova stereometria doliorum vinarorum.

My text is about numerical interpolation and quadrature. The Keplersche Fassregel is the obvious example for a composite rule of quadrature. Although Kepler found it when thinking about wine barrels, thats not a description I'd like to use. My example only has one dimension and the rule in this context has little or nothing to do with barrels.

Werner is right, there is no fixed English term. You might use the German original - check some of these hits:
http://www.google.de/search?as_q=fa%C3%9Frege...

check the German version of this entry

http://mathworld.wolfram.com/Barrel.html
When buying supplies for his second wedding, the great astronomer Johannes Kepler became unhappy about the inexact methods used by the merchants to estimate the liquid contents of a wine barrel. Kepler therefore investigated the properties of nearly 100 solids of revolution generated by rotation of conic sections about none-principal axes

http://abyss.uoregon.edu/~js/glossary/kepler.html
Once, when buying supplies for his new home, Kepler became unhappy about the rough-and-ready methods used by the merchants to estimate the liquid contents of a wine barrel. Because the curved containers they used were of various shapes, Kepler sought a mathematical method for determining their volumes. Following the model established by Archimedes, the most talented mathematician of antiquity, Kepler, in his volumetric researches, investigated the properties of nearly 100 solids of revolution--made by rotating a two-dimensional surface on one of its axes--that had not been considered by Archimedes. Starting with an ordinary wine barrel, Kepler enormously extended the range of Archimedes' results. He did so by refusing to confine himself, as Archimedes had done, to cases in which a surface is generated by a conic section--a curve formed by the intersection of a plane and a cone--rotating about its principal axis. Kepler's additional solids are generated by rotation about lines in the plane of the conic section other than its principal axis

Wie meine Vorredner schon sagten, gibt es im Englischen keinen feststehenden Ausdruck dafür.

@laalaa: Das ist im Deutschen die Simpsonregel.

Not bad, laalaa. Simpson's rule is definitely not the same, though. It does comprehend Kepler's rule for the calculation of wine casks, no doubt there. In Simpson's time, differential calculus had developed to a fully-grown field of mathematics.

Well, I do not claim to be a math boffin, but to me those formulas (Kepler' Fassregelformel and Simpson's formula) look identical. Maybe Ruuby could shed some light on this?

Die Simpsonregel ist eine Verallgemeinerung der Keplerschen Fassregel.

Keplersche Fassregel: integral(x0,x0+2h,f(x)) = h/3 * [y0 + 4*y1 + y2]
Simpsonregel: integral(a,b,f(x)) = h/3 * [y0 + 48y1 + 2*y2 + 4*y3 ... + 2*y_2k-1]

Der deutschen Wikipedia zufolge verwendete Kepler fuer die Berechnung des Volumens seines Weinfasses nur drei Stuetzstellen, naemlich den Radius des Bodens, des Bauches in der Mitte und des Deckels und erzielte so eine brauchbare Naeherung. Simpson (oder Toricelli) erkannte, dass man so viele Stuetzstellen nehmen kann wie man will und so das Volumen beliebig genau berechnen kann.

Aus heutiger Sicht, mit Kenntnis der Ideen der Infinitesimalrechnung, erscheint das kein sonderlich grosser Sprung. Als Toricelli starb, war Newton aber gerade erst geboren, und auch Simpson wirkte Lebzeiten von Newton und Leibniz, gehoerte also zur ersten Mathematiker-Generation, die diese neue Denkweise zur Verfuegung hatte.