Changed behaviour of even kwd for integrate.simpson

PR #18209 improves the accuracy of integrate.simpson when there is an even
number of points (odd number of intervals). I'm sending a message to the ML
as it will result in changed behaviour for `integrate.simpson`.

Historical behaviour has been to use trapezoidal integration for the
last/first intervals and adding it on to the _basic_simpson sum of the
other intervals. This is what the even kwd was used for. When even='avg'
the mean of last and first approaches was returned.

It was pointed out in #18151 that there is a more accurate way of dealing
with this situation, as outlined on wikipedia. This uses a parabolic
segment over the last three points to calculate the sum of the last
interval, thereby using simpson behaviour for the last interval as well.

PR #18209:

- adds the machinery for performing the improved calculation for the last
interval when there is an even number of samples.
- this machinery is accessed by adding a 'simpson' option to the even kwd.
- Since even='simpson' should offer improved behaviour in most cases (i.e.
it continues the quadratic nature of the rest of the summation) this now
becomes the default for the even kwd.
- Because even='simpson' offers this improved behaviour it shouldn't be
necessary to access the {'first', 'last', 'avg'} options anymore. It's
therefore suggested that the even kwd be deprecated and removed in a future
version of scipy. After that point the 'simpson' behaviour will be used all
the time.
- To achieve this deprecation the even kwdis removed from the function
signature and replaced by**kwds. Existing code that uses even` will
continue to work, but will receive a warning.
- If the integration axis only has two points (i.e. impossible to form a
parabolic segment with the last three points) then the integration is done
trapezoidally.
- Tests are added to check simpson integration over multiple axes, for odd
and even number of points in the integration axis. These tests were missing
and strengthen the test suite.

If there is downstream code using simpson they will:

- start getting the DeprecationWarning. This may come as a surprise as the
even keyword for simpson has been present for a long time.
- get different results if they integrate with an even number of points.
The new behaviour is more accurate, but people may complain that their code
isn't giving the same numbers any more.


--
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Dr. Andrew Nelson


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