1.) It is often useful to be able to count the number of times 
a given procedure has been called during the course of a computation.  
Write a procedure (count-calls f) that takes a procedure of one argument 
and returns a third procedure.  This new function, when applied to the 
symbol 'how-many-calls?, returns the number of times the wrapped function 
f has been called.  When applied to the symbol 'reset-count!, sets the 
internal counter to zero.  Applied to any other argument, the returned 
function returns the result of calling f with that argument and updates 
the internal counter.

For example,
> (define s (count-calls sqrt)
> (s 'how-many-calls?)
0
> (s 100)
10
> (s 'how-many-calls?)
1

2.) Besides measuring run-time using the "time" function in Scheme, the 
number of times some function gets called can be a useful measure of the 
cost of an algorithm (this measure reflects less on the programmer and 
more on the algorithm).  Use your result in 1.) to measure the number of 
comparisons that are used in the various sorting algorithms we have used 
in class (qsort, sort, another-sort) plus the built-in quicksort.

3.) In numerical integration, we often consider _adaptive_ procedures 
which keep using more subintervals until convergence happens.  We saw such 
a global iteration in class.  You need to implement a locally adaptive 
process that uses the following criteria.  First, integrate the function 
over the whole interval using one interval and repeat the process with two 
intervals.  We refine an interval if the difference between these two 
integrations is greater than some criteria.  However, if we do two 
intervals and check the error on each of those intervals, we may find, 
say, that the left interval has most of the error.  We only want to refine 
that side.  Implement such an adaptive procedure, and measure the number 
of times you call the integrated function f compared with using a small 
number of intervals everywhere.  (Note: the error threshhold on an 
interval should decrease with respect to it's size.  If tolerance is the 
overall tolerance, we should allow h * tolerance error on an interval of 
size h.)