Even backup and restore can be done through Invoke-Sqlcmd. It is just a matter of passing the actual BACKUP and RESTORE command to Invoke-Sqlcmd. The following is an example:

Import-Module SQLPS -DisableNameChecking

#current server name
$servername = "ROGUE"    # or localhost
$database = "Chinook"

$query = @"
BACKUP DATABASE Chinook
TO DISK='Z:\Backups\Chinook.bak'
WITH
    FORMAT, 
    COMPRESSION
"@

#code below in one line
Invoke-Sqlcmd -ServerInstance $servername -Database $database -Query $query

Although this is possible, it would be more elegant to use the Backup-SqlDatabase and Restore-SqlDatabase cmdlets (which were discussed in Chapter 4, Basic SQL Server Administration) since these are already provided with the SQLPS module.