Mark Dickinson <dicki...@gmail.com> added the comment:

According to GP/Pari, the correctly value for the first result, to the first 
few dozen places, is:

0.995275743920768157605659214368609706759611629000344854339231928536087783251913252354...

I'm assuming you meant 5.374 rather than 5.372 in the first Nspire result.

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