Pip, 46 bytes
FlRsX,4.:"/\"J'|WR'.X,3PE'^AE'_X7{(l2,5)X:aPl}
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Explanation
First, we generate this list
[" ^"
" /|\"
" /.|.\"
"/..|..\"
"_______"]
as follows:
RsX,4.:"/\"J'|WR'.X,3PE'^AE'_X7
,3 ; Range(3): [0;1;2]
'.X ; Repeat . that many times: ["";".";".."]
'|WR ; Wrap | in each of those strings: ["|";".|.";"..|.."]
"/\"J ; Insert each of those strings between / and \:
; ["/|\";"/.|.\";"/..|..\"]
PE'^ ; Prepend "^" to the front of that list
AE'_X7 ; and append "_______" to the end:
; ["^";"/|\";"/.|.\";"/..|..\";"_______"]
,4 ; Range(4): [0;1;2;3]
sX ; Repeat space that many times: ["";" ";" ";" "]
R ; Reverse: [" ";" ";" ";""]
.: ; Concatenate those two lists itemwise:
; [" ^";" /|\";" /.|.\";"/..|..\";"_______"]
Then we loop over each line, repeat the center section, and print the result:
Fl...{(l2,5)X:aPl}
Fl { } ; For each line l
... ; in the above list:
(l ) ; The section of l
2,5 ; at indices range(2,5) i.e. [2;3;4] (modular 0-based indexing)
X: ; string-repeat in place
a ; (program argument) times
Pl ; Print (the modified version of) l with a trailing newline