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Errors in Mathematica

NDSolve[{P'[x] ==   Q[x], Q'[x]  == 10^(-10) ,
P[10^(-6)]==0,  Q[10^(-6)] == 0,
n[x] == Exp[-A[x]]  ,
A'[x] == -A[x]/236,
A[10^(-6)]== -.0001},
{P,Q,A,n}, {x, 10^(-6),1000},
MaxSteps rightarrow Infinity]
Plot[Evaluate[P[x]/. %], {x,10^(-6), 10}]

Here 2 equations link the functions P and Q.
Two other equations link the functions n and A.
There is no coupling between the two sets, and yet:

Note the denominator 236 that  appears in the second set.
As this number is changed the solution for P[x], and in particular the
value P[6] changes.
Of course this should not happen.
There is a discontinuity between 236 and 237 and another between 274
and 275.
After that, further increase has no effect on P[6].

The problem goes away if the small numbers are increased.
It also goes away if the exponential function is replaced by  unity or
some elementary function.

If the small numbers are made much smaller it causes Mathematica to
shut down.

Can anyone tell me how to handle this?

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