Tinkering with trap and exit commands

TYPICAL COMMANDLINE SESSION
[bash]
$echo $?
0
$echo $?
0
$exit 10 | tee solve.txt
$cat solve.txt
$rm solve.txt
$exit 10 | echo $?
0
$exit -1 | echo $?
0
$exit -1 | echo $?
0
$false | true
$echo $?
0
$false
$echo $?
1
$true
$echo $?
0
$exit 5 | tee var=$?
$file var\=0
var=0: empty
$type var
bash: type: var: not found
$file var\=0
var=0: empty
$
[/bash]

[bash]
$trap $? > solve.txt exit 10
$cat solve.txt
Display all 296 possibilities? (y or n)
$cat solve.txt
$trap echo $? > solve.txt exit 10
$cat solve.txt
$trap `echo $? > solve.txt` exit 10
$cat solve.txt
0
$
[/bash]

[bash]
$bash -c ‘exit 7’; echo $?
7
$bash -c `exit 7`; echo $?
bash: -c: option requires an argument
2
$bash -c ‘exit 7’; echo $?
7
$trap ‘echo $? > solve.txt’ exit 10
$cat solve.txt
0
$cat solve.txt
0
$bash -c ‘exit 11’; echo $?
11
$
[/bash]