'The aim of an automatic integration scheme is to relieve the person who has to compute an integral-[the user] of any need to think.' This is the opening sentence of Chapter 6, 'Automatic Integration' of the standard textbook Numerical Integration, by P. Davis and P. Rabinowitz (1967). Informal discussion indicates that views about this aim vary from extreme to extreme. Some say the user should be made to think; others, that it is impossible to relieve him of all need to think and 'consequently' no attempt should be made to relieve him of any need to think. Another view is that this should be the aim of all numerical analysis or at least the aim of any published algorithm. Occasionally the same individual subscribes to all of these views. However, the present author accepts the opening sentence as a laudable aim, and discusses below the presently available implementations of this aim. The textbook goes on to describe an automatic integration scheme in general terms (as it appears to the user). The user is to provide the upper and lower limits B and A, a tolerance EP, a subroutine FUN(A') and N, an upper limit on the number of function evaluations to be used. After using N function evaluations the routine gives up and provides the best result available and some indication or message to this effect. Although in the text it is suggested that N be provided by the user, in the examples in the same book, N is usually provided by the program. In the Romberg Integration Code N = 2 + 1 = 32,769, and in the Adaptive Simpson Code N = 2-3 + 1 ~ 4 X 10. Presumably experience has shown that it is difficult enough to get the average user to think out what value EP he requires. (This is the author's experience.) When asked in addition for a value of TV, mental exhaustion leads him to make some wild guess. Thus in the present state of the art, the aim (which is to relieve the user of any need to think) has been attained to the following extent. He does not have to think (at least not at this stage) about A, B, or FUN(JT). He is forced to give some thought to EP. He has refused to think about N and the programmer has usually done it for him. An automatic quadrature routine may be considered as containing two essential ingredients. One is the standard rule evaluation part, which is capable of obtaining numerical approximations in terms of function values. The other is the 'strategy component' using which the routine considers the results it has already obtained and decides what further calculation is necessary to obtain a result of the desired accuracy. An example is the automatic routine ROMBERG {A, B, EP, FUN). The rule evaluation part is capable of calculating successive approximations R{f R2f, •.., R\5f to the required integral. Here Rjf is the standard Romberg approximation requiring 2+ 1 function values (Bauer, Rutishauser, and Stiefel, 1963). The strategy section is particularly simple. After each evaluation Rjf, 2 > j > 14, the number