Hacham Moshe Rahamim Shayo, in his Mehkerei Eretz (v. 8 Orah Haim 41), discusses the following question: Is a person who prays a different prayer with the congregation considered to be praying with the community (tefilla b'tzibur)? The Shulhan Arukh (Orah Hayim 90:9) writes that "A person should do his best to pray in the Beit Kenesset with the community." What if the person is saying a different Amida than the community? For example, what if on Rosh Hodesh, the community is praying Musaf and he is praying Shaharit (or the opposite)? Similarly, often during the summer, a person comes late to synagogue, and wishes to pray Minha while the community is praying Arbit. Is that considered to be communal prayer? Hacham Shayo cites the rest of the passage from the Shulhan Arukh, cited above, which teaches that if a person is unable to come to synagogue, he should pray at the time at which the community prays. If the community says the Amida each morning at 9:00am, then one who prays at home should also try to say his Amida at 9:00 am. However, the Magen Avraham (17) comments that if one prays Musaf while the congregation is praying Shaharit, that is not considered to be similar to one who prays at the same time that the congregation prays. Although one might infer from this Magen Avraham that one who prays a different Amida than the community is not considered to be praying with the community, the Mishna Berura explains that if one is actually praying Musaf in the synagogue with those who are praying Shaharit, that is indeed similar to one who prays at the same time as the community. Hacham Shayo initially suggested, based upon this Mishna Berura that one who prays a different prayer than the community is considered to be part of the communal prayer (tefilla b'tzibur). The questioner, however, challenges Hacham Shayo and insists that while he may be considered like one who prays at the same time as the community, which is itself a higher level of prayer, his prayer is not considered to be communal prayer. Hacham Shayo accepts this argument and concludes that while not actually considered to be tefilla b'tzibur, there is a value of praying, even a different prayer, while the community is praying. Afterwards, he cites the Slah (R. Yehezkel Landau, known as the Noda BiYehuda), in his commentary to Berachot 6a, who explains that if an individual prays in a synagogue while the tzibur is still there, even if they have concluded their prayers but they are still saying praises to God, such as Ashrei and Uva LeSion, "the prayers of the individual who prays there are heard." He writes, based upon the verse "lishmo'a el harina ve'el hatefilla" (to hear the praise and the prayer), that once God hears the praises of the community, He also hears the prayers of the individual. He concludes by adding that "this is certainly true regarding one who prays Shaharit in a synagogue why the congregation is saying Musaf." In conclusion, we see that even one who wakes up late, or is late for prayers, should still come to synagogue and pray while the congregation is saying other prayers, as this is considered a higher level of prayer (even if it is not actually considered to be tefilla b'tzibur).