Question Blank Page and Errors on Checkout

traced code through to:
administrator/components/com_virtuemart/html/basket.php
Where:
$tax_total = $ps_checkout->calc_order_tax($order_taxable, $vars);
was the offending line.
grepped for function calc_order_tax declaration, and located the function in:
administrator/components/com_virtuemart/classes/ps_checkout.php
Line 1652 contains:
@$order_tax_details[$taxrate] += $rate - ($rate / ($taxrate+1));
This appears to be the offending line, the "@" silences errors/warnings and is the lazy man's way of keeping an application from throwing warnings.
Removing the "@" created the error (again) of:
Fatal error: Unsupported operand types in /home/machort/public_html/administrator/components/com_virtuemart/classes/ps_checkout.php on line 1652
$rate is an array, it should be a int or other numeric value, since the code is trying to perform math on it.
the value comes from:
line 1650
$this->_SHIPPING->get_rate( $d );
This function *appears* to come from:
/home/machort/public_html/administrator/components/com_virtuemart/classes/shipping/ship_product.php
Line 44

return array ($total,$i);

return $total;