Please help!

I need to use RSA encryption to encrypt (decryption not needed) strings as part of a security model for communication with a remote service.

I was given a public key:

<RSAKeyValue>
<Modulus>27rvs6kZEi7GxFT9/tYHtiZApVl8LUGy5q9MMHpJf1tcVtjzRovdnpz4ZPgSfDSZPJ7bISBrHfA3IG+4bCbfaE2CJBq7woG3JFEmWr3X+91XXlJnaFL27sa3vggu8R/RgUiE+JFZaXXImsTA+Yxp9s1X2a1WUz+NJcb+Ih07Jlc=</Modulus>
<Exponent>AQAB</Exponent>
</RSAKeyValue>

that i must use for encryption. How do i do this? i've looked at openSSL but no clear solution comes to mind.

i was also given the following example:

The following is a sample unencrypted MAC Code:

20169876FD41AE4AE74A56D5F7EC607C959FB64D

This is the same MAC Code that has been encrypted and outputted as a Base-64 String

BJBJDeSiYNtzuQzy8Tgj3CtuSJRpwfEgChoqrIYESyV7Tsz+F55MCZPfUM/LLyj6dvIEdUpFphnifePBX/niTmonMXJaBi8uZfcYTZmqAiiarjYwVg3T1LKHg3yt43YwuSiOeTILxr/DmczFUXEaM5cUkipg/+mneatKI3iZQc0=

I would greatly appreciate any help!