Error de sintaxis de Perl: se encontró una palabra desnuda donde el operador esperaba

When a string has double quotes within it, you need to escape them with \.

$cmd .= "-U $user_name -P $password -S $host -d master -Q \"BACKUP DATABASE [$database_name] TO DISK = N'$path'\" ";

Also, Perl lets you use other characters for quote delimiters. qq followed by almost any character is the same as double quotes. So you could do things like this to avoid the need of backslashes:

$cmd .= qq(-U $user_name -P $password -S $host -d master -Q "BACKUP DATABASE [$database_name] TO DISK = N'$path'" );

$cmd .= qq|-U $user_name -P $password -S $host -d master -Q "BACKUP DATABASE [$database_name] TO DISK = N'$path'" |;

Y así sucesivamente ...

Actualizar: How to execute a system command in Perl. There are three basic ways:

system($cmd);  #Goes through the shell if shell metacharacters are detected.
system(@command_and_args);  #first element is the command, the rest are arguments

system executes a command and waits for it to return. The return value is the exit status of the program.

my @results = `$cmd`;  #Always goes through shell.

tildes execute a command and return its output. You should only use this if you actually need the output; otherwise, it is better to go with system.

exec $cmd;
exec @command_and_args;

exec is exactly like system, except that it never returns. It effectively ends your program by calling another program.

Use the one that is most appropriate to your situation. Or in this case, since you are executing SQL, consider using the Dbi module. It's definitely a better approach for anything more than a couple of simple commands.

Parece que tienes tu " characters in the wrong place. I'm not sure where they should be.

In your second line, the string literal:

"-U $user_name -P $password -S $host -d master -Q "

is immediately followed by the bareword

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